title: French Resistance

text: As various cities, towns and villages were liberated in France, the Resistance was usually the most organized force that took over. Many "résistants" were disgusted by the mass influx of new members in the dying days of the struggle, contemptuously calling them the FFS ("Forces Françaises de Septembre"-French Forces of September) or the "Septemberists" for short, as all these people had conveniently only discovered their French patriotism in September 1944. In the middle of 1944, Chaban-Delmas had reported to de Gaulle that the FFI numbered 15,000 in Paris, but the time of the liberation of Paris on 25 August 1944, between 50,000 and 60,000 people were wearing FFI armbands. The liberation of France began with D-Day on 6 June 1944, but different areas of France were liberated at different times. Strasbourg was not liberated until November 1944, and some coastal towns on the English Channel and the Atlantic like Dunkirk were still in German hands when the war ended on 8 May 1945. Ousby observed: "There was no national day for Liberation. Each town and village still celebrates a different day, the gaps between them marking advances that often looked bogged down, pockets of German defense that often turned out to be unexpectedly tough. It proved the bitterest of ends to a bitter war." As France was liberated, many "résistants" enlisted in the French Army, with 75,000 "résistants" fighting as regular soldiers by November 1944, and by the end of the war, 135,000 "résistants" were serving with the French forces advancing into Germany. For many resistance leaders who gave themselves the title of captain or colonel, it was quite a comedown to be reduced to a private.


title: French Resistance

text: Besides attempting to establish a government, the Resistance took its revenge on collaborators who were often beaten or killed in extrajudicial executions. "Miliciens" were usually shot without the bother of a trial, and at least 10,000 "miliciens" were shot in 1944. The young women who had engaged in "collaboration horizontale" by sleeping with the Germans were singled out and had their heads publicly shaven as a mark of their disgrace, which meant that a good percentage of the young women in France were shaven bald in 1944. The attacks on the young women who had German lovers had the "atmosphere of a savage carnival" as the women were rounded by mobs to be insulted, beaten and shaven. One "résistant" in the Gard region explained the violence to a reporter in September 1944: "I'll simply say that the majority of the FFI have been outlaws. They are lads from the mining areas...they have been hunted; they have been imprisoned; they have been tortured by "miliciens" whom they now recognize. It is understandable that they should now want to beat them up". At the time, many feared that France was on the verge of civil war as it was felt that the FTP might attempt to seize power, but owing to the shortage of arms and loyalty to Moscow which recognized General de Gaulle as France's leader, the Communists chose to pursue power via ballots rather than bullets.


title: French Resistance

text: In the aftermath of the Liberation, the SOE agents were all ordered out of France as the Anglophobic de Gaulle wished to maintain a version of history where the SOE never existed and the Resistance was entirely a French affair. De Gaulle also promoted a version of history where France for the entire occupation from 1940 to 1944 had been a "nation in arms" with the Resistance representing almost the entirety of the French people had been waging a guerrilla struggle from the beginning of the occupation right to its end. His concern was then to rebuild France not only on the material and international level, but also morally, pushing him to put forward the actions of the Resistance to re-establish national unity and pride, which the war had damaged. On 17 September 1944, in Bordeaux, the SOE agent Roger Landes, who become the leader of the Resistance in Bordeaux after André Grandclément, the previous leader had been exposed as a Gestapo informer, was taking part in the celebrations of the liberation of Bordeaux when General de Gaulle motioned to him to come aside for a chat. De Gaulle told Landes, who was wearing the uniform of a British Army officer that he was not welcome in France and had two hours to leave the city and two days to leave France. The Francophile Landes who had been born in Britain, but grew up in France was profoundly hurt by this request, and sadly left the nation he loved so much. De Gaulle had wanted a resistance to give proof of "France éternelle" that held out against the occupation; however, he was angered by the fact that the "résistants" often seemed to consider themselves as the new legitimate authorities of the towns and cities they had liberated. Therefore, in the wake of the liberation of the national territory, he openly considered them as troublemakers hindering the return to normalcy and rule of law which he pursued. Everywhere, the "résistants" were pushed out of power to be replaced by the same civil servants who had served first the Third Republic to be followed by Vichy or the "naphtalinés", Army officers who had gone into retirement in 1940, and resumed their service with the liberation.


title: French Resistance

text: The French Resistance involved men and women representing a broad range of ages, social classes, occupations, religions and political affiliations. In 1942, one resistance leader claimed that the movement received support from four groups: the "lower middle" and "middle middle" classes, university professors and students, the entire working class and a large majority of the peasants.


title: French Resistance

text: Resistance leader Emmanuel d'Astier de La Vigerie observed, in retrospect, that the Resistance had been composed of social outcasts or those on the fringes of society, saying "one could be a resister only if one was maladjusted". Although many, including d'Astier himself, did fit this description, most members of the Resistance came from traditional backgrounds and were "individuals of exceptional strong-mindedness, ready to break with family and friends" to serve a higher purpose.


title: French Resistance

text: The question of how many were active in the Resistance has been raised. While stressing that the issue was sensitive and approximate, François Marcot, a professor of history at the Sorbonne, ventured an estimate of 200,000 activists and a further 300,000 with substantial involvement in Resistance operations. Historian Robert Paxton estimated the number of active resisters at "about 2% of the adult French population (or about 400,000)", and went on to observe that "there were, no doubt, wider complicities, but even if one adds those willing to read underground newspapers, only some two million persons, or around 10% of the adult population", had been willing to risk any involvement at all. The post-war government of France officially recognised 220,000 men and women.


title: French Resistance

text: The doctrine of Gaullism was born during the Second World War as a French movement of patriotic resistance to the German invasion of 1940. Men of all political stripes who wanted to continue the fight against Adolf Hitler and who rejected the armistice concluded by Maréchal Philippe Pétain rallied to General Charles de Gaulle's position. As a consequence, on 2 August 1940, de Gaulle was condemned to death "in absentia" by the Vichy régime.


title: French Resistance

text: Between July and October 1940, de Gaulle rejected the unconstitutional, repressive and racist laws instituted by Pétain, and established his own "bona fides" (good faith) as the principal defender of republican values. He asked, in his "Appeal of 18 June 1940", that every patriot who could reach British territory should do so and join the Free French Army to fight in company with the Allies. The Free French forces also rallied the various French overseas colonies to fight back against the Vichy régime. His approval of this link between the Resistance and the colonials legitimised it.


title: French Resistance

text: De Gaulle's influence grew, despite few in France knowing what he looked like or anything about him. The first open defiance of Nazi rule in Paris was in November 1940, when 3,000 students at the Arc de Triomphe shouted "" and "", some carrying two fishing rods (). Vichy police called arrested subversives "Gaullists"; although Pétain never mentioned his rival's name in public, everyone knew what "dissidents" meant in speeches. In 1942 Richard de Rochemont quoted a resistance leader describing de Gaulle as "the only possible leader for the France that fights". Most Gaullists could not join him in Britain and remained in the territories ruled by Vichy. The Allies helped build networks of propagandists, spies and saboteurs to harass and discomfit the occupiers. Eventually, leaders of all of these separate and fragmented Resistance organizations were gathered and coordinated by Jean Moulin under the auspices of the National Council of Resistance (CNR), de Gaulle's formal link to the irregulars throughout occupied France.


title: French Resistance

text: During the Italian campaign of 1943, 130,000 Free French soldiers fought on the Allied side and, by the time of the Normandy invasion, Free French forces numbered approximately half a million regulars and more than 100,000 French Forces of the Interior (FFI). The Free French 2nd Armored Division, under General Philippe Leclerc, landed in Normandy, and, in the waning days of summer 1944, led the drive toward Paris. The FFI in Normandy and the Île-de-France region surrounding Paris began to harass German forces intensively, cutting roads and railways, setting ambushes and fighting conventional battles alongside their allies.


title: French Resistance

text: The Free French 2nd Armored Division rolled ashore in Normandy on 1 August 1944, and served under General Patton's Third Army. The division played a critical role in Operation Cobra, the Allies' "breakout" from its Normandy beachhead, where it served as a link between American and Canadian armies and made rapid progress against German forces. The 2nd Armored all but destroyed the 9th Panzer Division and mauled several other German units as well. During the battle for Normandy this German division lost 133 killed, 648 wounded and 85 missing. The division's matériel losses included 76 armored vehicles, seven cannons, 27 halftracks and 133 other vehicles.


title: French Resistance

text: The most celebrated moment in the unit's history involved the liberation of Paris. Allied strategy emphasized destroying German forces retreating towards the Rhine, but when the French Resistance under Henri Rol-Tanguy staged an uprising in the city, De Gaulle, upon receiving intelligence that the French Resistance had openly risen up against the German occupiers, and unwilling to allow his countrymen to be slaughtered against the entrenched and better-armed Germans, as had happened to the Polish Resistance in the Warsaw Uprising, petitioned Eisenhower for an immediate frontal assault. He threatened to detach the French 2nd Armored Division (2e DB) and order them to single-handedly attack Paris, bypassing the SHAEF chain of command, if he delayed approval unduly. Eisenhower relented, and Leclerc's forces headed toward Paris. After hard fighting that cost the 2nd Division 35 tanks, 6 self-propelled guns and 111 vehicles, Dietrich von Choltitz, the military governor of Paris, surrendered the city in a ceremony at the Hotel Meurice. Jubilant crowds greeted the French forces, and de Gaulle led a renowned victory parade through the city.


title: French Resistance

text: De Gaulle not only kept the patriotic resistance alive; he also did everything possible to re-establish the French claim to independence and sovereignty. As a leader, the American and British governments preferred the less popular, but less abrasively vindictive, General Giraud to de Gaulle, but for the French population de Gaulle was almost universally recognised as the true leader in their victory. These events forced Roosevelt to recognise, finally and fully, the provisional government installed in France by de Gaulle.


title: French Resistance

text: After the signing of the Molotov–Ribbentrop Pact and the outbreak of World War II in 1939, the French Communist Party (PCF) was declared a proscribed organisation by Édouard Daladier's government. Many of its leaders were arrested and imprisoned or forced to go underground. The PCF adopted an antiwar position on orders of the Comintern in Moscow, which remained in place for the first year of the German occupation, reflecting the September 1939 nonaggression pact between Germany and the USSR. Conflicts erupted within the party, as many of its members opposed collaboration with the Germans while others toed the party line of neutrality as directed by Stalin in Moscow. On Armistice Day, November 11, 1940, communists were among the university students demonstrating against German repression by marching along the Champs-Élysées. It was only when Germany invaded the Soviet Union in 1941 that French communists actively began to organize a resistance effort. They benefited from their experience in clandestine operations during the Spanish Civil War.


title: French Resistance

text: On 21 August 1941, Colonel Pierre-Georges Fabien committed the first overt violent act of communist resistance by assassinating a German officer at the Barbès-Rochechouart station of the Paris Métro. The attack, and others perpetrated in the following weeks, provoked fierce reprisals, culminating in the execution of 98 hostages after the Feldkommandant of Nantes was shot on 20 October.


title: French Resistance

text: The military strength of the communists was still relatively feeble at the end of 1941, but the rapid growth of the Francs-Tireurs et Partisans (FTP), a radical armed movement, ensured that French communists regained their reputation as an effective anti-fascist force. The FTP was open to non-communists but operated under communist control, with its members predominantly engaged in acts of sabotage and guerrilla warfare. By 1944, the FTP had an estimated strength of 100,000 men.


title: French Resistance

text: Towards the end of the occupation the PCF reached the height of its influence, controlling large areas of France through the Resistance units under its command. Some in the PCF wanted to launch a revolution as the Germans withdrew from the country, but the leadership, acting on Stalin's instructions, opposed this and adopted a policy of cooperating with the Allied powers and advocating a new Popular Front government.


title: French Resistance

text: During the Nazi occupation of France, the French Trotskyist group Parti Ouvrier Internationaliste printed the clandestine magazine "Arbeiter und Soldat" ("Worker and Soldier") for German troops. The publication opposed both fascism and western imperialism, and 12 issues were distributed from July 1943 through July 1944.


title: French Resistance

text: Many well-known intellectual and artistic figures were attracted to the Communist party during the war, including the artist Pablo Picasso and the writer and philosopher Jean-Paul Sartre. Philosophers Georges Politzer and Valentin Feldman and writer Jacques Decour were among others. After the German invasion of the USSR, many Russian white émigrés, inspired by Russian patriotic sentiment, would support the Soviet war effort. A number of them formed the Union of Russian Patriots, which adopted pro-Soviet positions and collaborated closely with the French Communist Party.


title: French Resistance

text: At the end of the summer of 1940, Daniel Mayer was asked by Leon Blum to reconstitute the SFIO (in ruins because of Paul Faure's defection to the Vichy régime). In March 1941 Daniel Mayer created, with other socialists like Suzanne Buisson and Félix Gouin, the Comité d'action socialiste (CAS) in Nîmes. The same thing was created by Jean-Baptiste Lebas in the Nord-Pas-de-Calais (administratively joined with Belgium) in January 1941, along the lines of a prior network created in September 1940.


title: French Resistance

text: In 1942, "Le Populaire", newspaper of the SFIO from 1921 to 1940, was publishing again, clandestinely. The same year, André Philip became "commissaire national à l'Intérieur" of the Free French (France libre), and Félix Gouin joined Charles de Gaulle in London to represent the socialists. In Algeria, left-wing networks of resistance were already formed. As the Riom trial began in 1942, the fervour and the number of socialists in the Resistance grew. The CAS-Sud became the secret SFIO in March 1943.


title: French Resistance

text: There was a majority from the SFIO in Libération-Nord, one of the eight great networks to make up the National Council of the Resistance, and in the Brutus network. Socialists were also important in the organisation civile et militaire (OCM) and in Libération-Sud.


title: French Resistance

text: Other socialist leaders in the Resistance included Pierre Brossolette, Gaston Defferre, Jean Biondi, Jules Moch, Jean Pierre-Bloch, Tanguy-Prigent, Guy Mollet and Christian Pineau. François Camel and Marx Dormoy were assassinated, while Jean-Baptiste Lebas, Isidore Thivrier, Amédée Dunois, Claude Jordery and Augustin Malroux died during their deportation.


title: French Resistance

text: Before the war, there were several ultrarightist organisations in France including the monarchist, antisemitic and xenophobic "Action Française". Another among the most influential factions of the right was Croix-de-Feu (Cross of Fire), which gradually moderated its positions during the early years of the war and grew increasingly popular among the aging veterans of the First World War.


title: French Resistance

text: Despite some differences in their positions on certain issues, these organizations were united in their opposition to parliamentarism, a stance that had led them to participate in demonstrations, most notably the "political disturbance" riots of 6 February 1934. At about the same time, La Cagoule, a fascist paramilitary organisation, launched various actions aimed at destabilising the Third Republic. These efforts continued until La Cagoule could be infiltrated and dismantled in 1937. Thousands not only welcomed the Vichy régime, but collaborated with it to one degree or another. But the powerful appeal of French nationalism drove others to engage in resistance against occupying German forces.


title: French Resistance

text: In 1942, after an ambiguous period of collaboration, the former leader of Croix de Feu, François de La Rocque, founded the "Klan Network", which provided information to the British intelligence services. Georges Loustaunau-Lacau and Marie-Madeleine Fourcade—who had both supported La Cagoule—founded the Alliance network, and Colonel of the Vichy secret services founded the Gilbert network. Some members of Action Française engaged in the Resistance with similar nationalistic motives. Some prominent examples are Daniel Cordier, who became Jean Moulin's secretary, and Colonel Rémy, who founded the Confrérie Notre-Dame. These groups also included Pierre de Bénouville, who, together with Henri Frenay, led the "Combat" group, and Jacques Renouvin, who founded the group of resisters known as "Liberté".


title: French Resistance

text: Sometimes contact with others in the Resistance led some operatives to adopt new political philosophies. Many gradually moved away from their antisemitic prejudices and their hatred of "démocrassouille", 'dirty democracy' (which many equated with "mob rule"), or simply away from their traditional grass-roots conservatism. Bénouville and Marie-Madeleine Fourcade became députés in the French parliament after the war; François Mitterrand moved towards the left, joined the Resistance and eventually became the first socialist president of the Fifth Republic, Henri Frenay evolved towards European socialism, and Daniel Cordier, whose family had supported Charles Maurras for three generations, abandoned his views in favor of the ideology of the republican Jean Moulin.


title: French Resistance

text: The historian Jean-Pierre Azéma coined the term "vichysto-résistant" to describe those who at first supported the Vichy régime (mostly based on the patriotic image of Pétain rather than the Révolution Nationale) but later joined the Resistance. The founder of Ceux de la Libération ("Those of the Liberation"), Maurice Ripoche, initially defended Vichy but soon placed the liberation of France above all other goals and in 1941 opened his movement to leftists. In contrast, many extreme right-wing members of the Resistance, such as Gabriel Jeantet and Jacques Le Roy Ladurie, never renounced their tolerant attitudes towards Vichy.


title: French Resistance

text: The "Affiche Rouge" (red placard) was a famous propaganda poster distributed by the Vichy French and German authorities in the spring of 1944 in occupied Paris. It was intended to discredit a group of 23 Franc-Tireurs known as the "Manouchian group". After its members were arrested, tortured and publicly tried, they were executed by firing squad in Fort Mont-Valérien on 21 February 1944. The poster emphasised the composition of the group's membership, many of whom were Jews and communists, to discredit the Resistance as not "French" enough in its fundamental allegiance and motivations.


title: French Resistance

text: The Vichy régime had legal authority in both the north of France, which was occupied by the German Wehrmacht; and the southern "free zone", where the régime's administrative centre, Vichy, was located. Vichy voluntarily and willfully collaborated with Nazi Germany and adopted a policy of persecution towards Jews, demonstrated by the passage of antisemitic legislation as early as October 1940. The law on the status of Jews, which legally redefined French Jews as a non-French underclass, deprived them of citizenship. According to Philippe Pétain's chief of staff, "Germany was not at the origin of the anti-Jewish legislation of Vichy. That legislation was spontaneous and autonomous." The laws led to confiscations of property, arrests, and deportations to concentration camps. As a result of the fate promised them by Vichy and the Germans, Jews were over-represented at all levels of the French Resistance. Studies show that although Jews in France constituted only one percent of the French population, they comprised ≈15–20 percent of the Resistance. Among these were many Jewish émigrés, such as Hungarian artists and writers.


title: French Resistance

text: The Jewish youth movement "Eclaireuses et Eclaireurs israélites de France" (EEIF), equivalent to Boy Scouts and Girl Scouts in other countries, had, during the early years of the occupation, shown support for the traditional values of the Vichy régime, until it was banned in 1943, after which its older members soon formed armed resistance units.


title: French Resistance

text: A militant Jewish Zionist resistance organisation, the Jewish Army (Armée Juive), was founded in 1942. It was established and led by Abraham Polonski, Eugénie Polonski, Lucien Lublin, David Knout and Ariadna Scriabina (daughter of the Russian composer Alexander Scriabin). They continued armed resistance under a Zionist flag until liberation finally arrived. The "Armée juive" organised escape routes across the Pyrenées to Spain, and smuggled about 300 Jews out of the country during 1943–1944. They distributed millions of dollars from the American Joint Distribution Committee to relief organisations and fighting units within France. In 1944, the EIF and the Jewish Army combined to form the "Organisation Juive de Combat" (OJC). The OJC had four hundred members by the summer of 1944, and participated in the liberations of Paris, Lyon, Toulouse, Grenoble and Nice.


title: French Resistance

text: In the southern occupation zone, the Œuvre de Secours aux Enfants (roughly, "Children's Relief Effort"), a French-Jewish humanitarian organisation commonly called OSE, saved the lives of between 7,000 and 9,000 Jewish children by forging papers, smuggling them into neutral countries and sheltering them in orphanages, schools, and convents.


title: French Resistance

text: The Armenian community of France played an active role in the Resistance. Armenian poet and communist Missak Manouchian became one of the leaders of the French Resistance and commander of the Manouchian Group (the family of Charles Aznavour had supported Missak and his wife Meliné when they were in hiding). Arpen Tavitian, another executed member of the Manouchian group, industrialist Napoléon Bullukian (1905–1984), poets Kégham Atmadjian (1910–1940) and Rouben Melik were other famous participants in the French Resistance. The Anti-Fascist Underground Patriotic Organization was also commanded by Armenian officiers. Armenian-French writer Louise Aslanian (1906–1945), another French Resistance activist, was arrested among with her husband Arpiar Aslanian on July 24, 1944, taken to the Nazi concentration camps by Nazis and killed in 1945. Many of Louise's manuscripts and diaries were confiscated and destroyed by Nazis. Resisters Alexander Kazarian and Bardukh Petrosian were awarded by the highest military orders of France by General Charles de Gaulle. Henri Karayan (1921–2011), a member of the Manouchian Group, participated in illegal distribution of "L'Humanité" in Paris and was engaged in armed struggle until the Libération. In 2012, 95-year-old Arsene Tchakarian, the last survivor of the Manouchian resistance group who fought against occupying Nazi German forces during the Second World War, was decorated as Officer of the Legion of Honour by the president of France.


title: French Resistance

text: Georgians living in France and the French colonies and people of Georgian ethnicity played an active and symbolic role in the French resistance. One of the most renowned figures of the Free French Forces was Prince Dimitri Amilakhvari, who participated in every important operation that involved French forces until 1942 and led the Légion étrangère into battle in the Norwegian and later African campaigns against Erwin Rommel's Africa Corps. Under General Koenig, he and his heavily outnumbered troops committed daring raids, dealing decisive losses to the Germans at the Battle of Bir Hakeim. During the battle he is said to have written: "We, foreigners, have only one way to prove to France our gratitude: to be killed ..." General de Gaulle personally awarded Amilakhvari the Order of Liberation and posthumously named him and his men the honour of France. He was also known by the French populace as "Bazorka". The lieutenant colonel was one of the 66 French recipients of the Norwegian War Cross and was also posthumously awarded the Legion of Honour. He led his troops by example and died in combat during the Second Battle of El Alamein in October 1942. Another known resistance fighter was Beglar Samkharadze, a captured Soviet soldier who was transferred to France where he escaped and joined the Resistance. Upon return to his homeland, he was imprisoned by Soviet authorities on charges of high treason but two commanders of the French Resistance testified to his commitment in the fight against Nazi Germany.


title: French Resistance

text: Although inequalities persisted under the Third Republic, the cultural changes that followed the First World War allowed differences in the treatment of men and women in France to narrow gradually, with some women assuming political responsibilities as early as the 1930s. The defeat of France in 1940 and the appointment of the Vichy régime's conservative leader, Philippe Pétain, undermined feminism, and France began a restructuring of society based on the "femme au foyer" or "women at home" imperative. On at least one occasion, Pétain spoke out to French mothers about their patriotic duty:


title: French Resistance

text: Despite opposing the collaborationist régime, the French Resistance generally sympathised with its antifeminism and did not encourage the participation of women in war and politics, following, in the words of historian Henri Noguères, "a notion of inequality between the sexes as old as our civilisation and as firmly implanted in the Resistance as it was elsewhere in France". Consequently, women in the Resistance were less numerous than men and averaged only 11% of the members in the formal networks and movements. Not all of the women involved in the Resistance limited themselves to subordinate roles. Intellectuals like Germaine Tillion and Suzanne Hiltermann-Souloumiac, highly aware of the signification of Nazism and collaboration, were among the few early resistants. Suzanne Hiltermann-Souloumiac played an important role in the Dutch-Paris movement, specialised in rescuing Allied pilots. Lucie Aubrac, the iconic resister and co-founder of Libération-Sud, was never assigned a specific role in the hierarchy of the movement. Hélène Viannay, one of the founders of Défense de la France and married to a man who shared her political views, was never permitted to express her opinions in the underground newspaper, and her husband took two years to arrive at political conclusions she had held for many years.


title: French Resistance

text: Marie-Madeleine Fourcade, the only major female leader in the Resistance, headed the Alliance network. The Organisation Civile et Militaire had a female wing headed by Marie-Hélène Lefaucheux, who took part in setting up the Œuvre de Sainte-Foy to assist prisoners in French jails and German concentration camps. But no women were chosen to lead any of the eight major Resistance movements. After the liberation of France, the provisional government appointed no women ministers or "commissaires de la République". However, as head of the Provisional Government of the French Republic, general de Gaulle, as a recognition of and a reward for their role in the Resistance, granted women the right to vote in 1945.


title: French Resistance

text: Charles de Gaulle spoke of "French resistance" in his broadcast on 18 June 1940. English-language use of the phrase "the Resistance" in reference to French anti-Axis activity dates back to at least 1944. Boris Kovalyov states that the Resistance movement in France and its name originated among White Movement Russian émigrés. The Russian Boris Vildé co-founded one of the first anti-occupation groups, and in December 1940 started co-publishing the underground newspaper "Résistance".


title: French Resistance

text: In this context, it is customary to distinguish the various organisations of the French Resistance as "movements" or "networks". A Resistance "network" was an organisation created for a specific military purpose, usually intelligence-gathering, sabotage or aiding Allied air crews who had been shot down behind enemy lines. A Resistance "movement", on the other hand, was focused on educating and organising the population, i.e., "to raise awareness and organise the people as broadly as possible."


title: French Resistance

text: In July 1940, after the defeat of the French armies and the consequent armistice with Germany, British prime minister Winston Churchill asked the Free French government-in-exile (headed by General Charles de Gaulle) to set up a secret service agency in occupied France to counter the threat of a German operation code-named Operation Sea Lion, the expected cross-channel invasion of Britain. Colonel André Dewavrin (also known as Colonel Passy), who had previously worked for France's military intelligence service, the "Deuxième Bureau", took on the responsibility for creating such a network. Its principal goal was to inform London of German military operations on the Atlantic coast and in the English Channel. The spy network was called the "Bureau Central de Renseignements et d'Action" (BCRA), and its actions were carried out by volunteers who were parachuted into France to create and nourish local Resistance cells.


title: French Resistance

text: Of the nearly 2,000 volunteers who were active by the end of the war, one of the most effective and well-known was the agent Gilbert Renault, who was awarded the Ordre de la Libération and later the Legion of Honour for his deeds. Known mainly by the pseudonym Colonel Rémy, he returned to France in August 1940 not long after the surrender of France, where the following November he organised one of the most active and important Resistance networks of the BCRA, the "Confrérie de Notre Dame" (Brotherhood of Our Lady), which provided the Allies with photographs, maps and important information on German defences in general and the Atlantic Wall in particular. From 1941 on, networks such as these allowed the BCRA to send armed paratroopers, weapons and radio equipment into France to carry out missions.


title: French Resistance

text: Another important BCRA operative, Henri Honoré d'Estienne d'Orves, a naval officer, developed a 26-person network in France. He was betrayed, arrested in May 1941, and shot on 29 August 1941.


title: French Resistance

text: Christian Pineau, one of the founders of the Libération Nord movement, also had BCRA roots. During his trip to London in April 1942, the BCRA entrusted him with the creation of two new intelligence systems, and . Both networks proved vital later in the war.


title: French Resistance

text: "Mouvements Unis de la Résistance" (Unified Movements of the Resistance, MUR) was a French Resistance organisation resulting from the regrouping of three major Resistance movements ("Combat", "Franc-Tireur" and "Libération-Sud") in January 1943. Later that year, the BCRA and the United Movements of Resistance merged their intelligence networks.


title: French Resistance

text: Another BCRA appendage was called , a fact-gathering network specialising in military intelligence and police activities. Its importance increased throughout the second half of 1943 and into the spring of 1944. It eventually became the largest BCRA network in the Vichy zone, employing about 2,500 sources, contacts, couriers and analysts. Gallia's work did not stop after the 1944 landings in Normandy and Provence; it provided information to the Allies that allowed for the bombing of the retreating German armies' military targets.


title: French Resistance

text: Dutch-Paris built an important network in France to help resistants, Jews and allied pilots to cross the Pyrenees and flee to Britain. 800 Jews and 142 pilots were saved. Near the end of the war, because of a denunciation, nearly all members of the network were caught and deported to concentration camps, where many died.


title: French Resistance

text: Armenians living in France took the arms and fought the resistance against the Axis forces. The most significant Armenian resistants were 23 strong men led by Missak Manouchian, who were hanged on February 21, 1944.


title: French Resistance

text: Following their defeat in the Spanish Civil War in early 1939, about half a million Spanish Republicans fled to France to escape imprisonment or execution. On the north side of the Pyrenees, such refugees were confined in internment camps such as Camp Gurs and Camp Vernet. Although over half of these had been repatriated to Spain (or elsewhere) by the time Pétain proclaimed the Vichy régime in 1940, the 120,000 to 150,000 who remained became political prisoners, and the foreign equivalent to the "Service du Travail Obligatoire", the "Compagnies de Travailleurs Étrangers" (Companies of Foreign Workers) or CTE, began to pursue them for slave labour. The CTE permitted prisoners to leave the internment camps if they agreed to work in German factories, but as many as 60,000 Republicans recruited for the labour service managed to escape and join the French Resistance. Thousands of suspected anti-fascist Republicans were deported to German concentration camps instead, however. Most were sent to Mauthausen where, of the 10,000 Spaniards registered, only 2,000 survived the war.


title: French Resistance

text: Many Spanish escapees joined French Resistance groups; others formed their own autonomous groups which became known as the Spanish maquis. In April 1942, Spanish communists formed an organisation called the XIV Corps, an armed guerrilla movement of about 3,400 combatants by June 1944. Although the group first worked closely with the Francs-Tireurs et Partisans (FTP), it re-formed as the "Agrupación de Guerrilleros Españoles" (Spanish Guerrilla Group, AGE) in May 1944. The name change was intended to convey the group's composition: Spanish soldiers ultimately advocating the fall of General Francisco Franco. After the German Army had been driven from France, the Spanish maquis refocused on Spain.


title: French Resistance

text: Among Czechs and Slovaks who joined the French Resistance were Otakar Hromádko, Věra Waldes and Artur London.


title: French Resistance

text: From spring 1943, German and Austrian anti-fascists who had fought in the International Brigades during the Spanish Civil War fought in Lozère and the Cévennes alongside the French Resistance in the Francs-Tireurs et Partisans. During the first years of the occupation they had been employed in the CTE, but following the German invasion of the southern zone in 1942 the threat increased and many joined the maquis. They were led by militant German communist Otto Kühne, a former member of the Reichstag in the Weimar Republic who had over 2,000 Germans in the FTP under his command by July 1944. He fought the Nazis directly, as in an April 1944 battle in Saint-Étienne-Vallée-Française in which his soldiers destroyed a Feldgendarmerie unit, or in an ambush of the Waffen-SS on June 5, 1944.


title: French Resistance

text: 400 men from Luxembourg (which was annexed into Germany), many of whom had refused to serve in, or who had deserted from, the German Wehrmacht, left their tiny country to fight in the French maquis, where they were particularly active in the regions of Lyon, Grenoble and the Ardennes although many of them were killed in the war. Others, like Antoine Diederich, rose to high rank in the Resistance. Diederich, known only as "Capitaine Baptiste", had 77 maquis soldiers under his command and is best known for attacking Riom prison, where he and his fighters freed every one of 114 inmates who had been sentenced to death.


title: French Resistance

text: Many Hungarian émigrés, some of them Jewish, were artists and writers working in Paris at the time of the occupation. They had gone to Paris in the 1920s and 1930s to escape repression in their homeland. Many joined the Resistance, where they were particularly active in the regions of Lyon, Grenoble, Marseille and Toulouse. Jewish resisters included Imre Epstein in the Hungarian group at Toulouse; György Vadnai (future Lausanne rabbi) at Lyon; the writer Emil Szittya at Limoges. Also participating were the painter Sándor Józsa, the sculptor István Hajdú (Étienne Hajdu), the journalists László Kőrös and Imre Gyomrai; the photographers Andor (André) Steiner, Lucien Hervé and Ervin Martón. Thomas Elek (1924–1944), Imre Glasz (1902–1944) and József Boczor (1905–1944) were among 23 resisters executed for their work with the legendary Manouchian Group. The Germans executed nearly 1,100 Jewish resisters of different nationalities during the occupation, while others were killed in action.


title: French Resistance

text: On 3 March 1943, representatives of the Italian Communist Party and Italian Socialist Party who had taken refuge in France, signed the "Pact of Lyon" which marked the beginning of their participation in the Resistance. Italians were particularly numerous in the Hitler-annexed Moselle industrial area, where they played a determining role in the creation of the Département's main resistance organisation, "Groupe Mario". Vittorio Culpo is an example of Italians in the French Resistance.


title: French Resistance

text: The majority of the Polish soldiers, and some Polish civilians, who stayed in France after the German victory in 1940, as well as one Polish pilot shot down over France (one of many Polish pilots flying for the RAF), joined the French Resistance, notably including Tony Halik and Aleksander Kawałkowski.


title: French Resistance

text: While not part of the French Resistance, French-speaking Cajun soldiers in the United States military posed as local civilians in France to channel American assistance to the Resistance.


title: French Resistance

text: From 1940 to 1942, the first years of the German occupation of France, there was no systematically organised Resistance capable of coordinated fighting throughout France. Active opposition to the German and Vichy authorities was sporadic, and carried out only by a tiny and fragmented set of operatives. Most French men and women put their faith in the Vichy government and its figurehead, Marshal Pétain, who continued to be widely regarded as the "savior" of France, opinions which persisted until their unpopular policies, and their collaboration with the foreign occupiers, became broadly apparent.


title: French Resistance

text: The earliest Resistance organisations had no contact with the western Allies, and received no material aid from London or anywhere else. Consequently, most focused on generating nationalist propaganda through the distribution of underground newspapers. Many of the major movements, such as Défense de la France, were primarily engaged in publishing and distributing their newspapers. Even after they became more intensively activist, propaganda and the cultivation of positive morale remained, until the very end of the war, their most important concerns.


title: French Resistance

text: Early acts of violent resistance were often motivated more by instinct and fighting spirit than by any formal ideology, but later several distinct political alignments and visions of post-liberation France developed among the Resistance organisations. These differences sometimes resulted in conflicts, but the differences among Resistance factions were usually papered over by their shared opposition to Vichy and the Germans; and over time, the various elements of the Resistance began to unite.


title: French Resistance

text: Many of the networks recruited and controlled by the British and Americans were not perceived by the French as particularly interested in establishing a united or integrated Resistance operation, and the guerrilla groups controlled by the communists were only slightly more attracted by the idea of joining of a Resistance "umbrella" organisation. Nonetheless, a contact between de Gaulle's envoys and the communists was established at the end of 1942. The liberation of Corsica in September 1943, a clear demonstration of the strength of communist insurgency, was accomplished by the FTP, an effective force not yet integrated into the Secret Army and not involved with General Henri Giraud, the Free French or the political unification of the Resistance.


title: French Resistance

text: The French Resistance began to unify in 1941. This was evidenced by the formation of movements in the Vichy zone centred on such figures as Henri Frenay ("Combat"), Emmanuel d'Astier de La Vigerie ("Libération-Sud") and François de Menthon, ("Liberté"), each of whom was, independently, an agent of the Free French. Formal consolidation was accomplished through the intervention of Jean Moulin.


title: French Resistance

text: Prefect of Eure-et-Loir in 1939, Moulin was subsequently a part of the Air Ministry of Pierre Cot. In this context, he had forged a strong network of relationships in anti-fascist circles. Some time after November 1940, the idea of teaming up with his former colleague, , to identify and contact a number of potential Resistance "centres of influence" occurred to him; but only during the summer of 1941 was he able to make the most critical contacts, including contact with Henri Frenay, leader of the movement not yet called "Combat" but still known as the . He also established contact with de Menthon and Emmanuel d'Astier. In the report he wrote for de Gaulle, he spoke of these three movements and entertained the possibility of bringing them together under the acronym "LLL".


title: French Resistance

text: The Maquis () were rural guerrilla bands of French Resistance fighters, called "maquisards", during the Occupation of France in World War II. Initially, they were composed of men who had escaped into the mountains to avoid conscription into Vichy France's Service du travail obligatoire (STO) to provide forced labor for Nazi Germany. To avert capture and deportation to Germany, they became increasingly organized into non-active resistance groups.


title: French Resistance

text: The majority of resistance movements in France were unified after Moulin's formation of the "Conseil National de la Résistance" (CNR) in May 1943. CNR was coordinated with the Free French forces under the authority of French Generals Henri Giraud and Charles de Gaulle and their body, the "Comité Français de Libération Nationale" (CFLN).


title: French Resistance

text: By June 1941, 81% of the miners employed by the national coal mining company, Charbonnages de France, were on strike, slowing deliveries of coal to German industrial plants supporting the war effort.


title: French Resistance

text: The first action of many Resistance movements was the publication and distribution of clandestine press material. This was not the case with all movements, since some refused civil action and preferred armed resistance by groups such as CDLR and CDLL. Most clandestine newspapers were not consistent in their editorial stance and often consisted of only a single sheet, because the sale of all raw materials—paper, ink, stencils—was prohibited.


title: French Resistance

text: By 1942, however, about 300,000 copies of underground publications reached around two million readers. Resistance workers used friendly print-shop facilities at night. Staff risked the Germans noticing that a resistance newspaper used the same type face as officially sanctioned documents. Profession-specific newspapers also existed. "Le Médecin Français" advised doctors to immediately approve known collaborators for "Service du travail obligatoire" while medically disqualifying everyone else. "La Terre" advised farmers on how to send food to resistance members. "Bulletin des Chemins de Fer" encouraged railroad workers to sabotage German transportation. "Unter Uns" ("Among Us"), published in German for the occupiers, printed stories of German defeats on the Eastern Front.


title: French Resistance

text: In September 1940, Agnès Humbert and Jean Cassou, then employed at the "Musée national des Arts et Traditions Populaires" in Paris and finding they were to be replaced by German-approved staff, used a roneo machine belonging to the Museum to publish an open letter by Paul Rivet to Marshal Pétain. This was followed by their first tract, "Vichy fait la guerre" ("Vichy Wages War"), written by Cassou. At the end of 1940, a group of 10, including Humbert, Cassou, Marcel Abraham and Claude Aveline founded a clandestine newsletter called "Résistance", respecting and supporting De Gaulle but circumspect in references to "that ridiculous old fool Pétain". It ran to five issues before the arrest of the editors in March 1940.


title: French Resistance

text: In the northern zone, "Pantagruel", the newspaper of Franc-Tireur, had a circulation of 10,000 by June 1941 but was quickly replaced by "Libération-Nord" which attained a circulation of 50,000, and by January 1944 "Défense de la France" was distributing 450,000 copies. In the southern zone, François de Menthon's newspaper "Liberté" merged with Henri Frenay's "Vérité" to form Combat in December 1941, which grew to a circulation of 200,000 by 1944. During the same period "Pantagruel" brought out 37 issues, "Libération-Sud" 54 and "Témoignage chrétien" 15.


title: French Resistance

text: The underground press brought out books as well as newspapers through publishing houses, such as Les Éditions de Minuit (the Midnight Press), which had been set up to circumvent Vichy and German censorship. The 1942 novel "Le Silence de la Mer" ("The Silence of the Sea"), by Jean Bruller, quickly became a symbol of mental resistance through its story of how an old man and his niece refused to speak to the German officer occupying their house.


title: French Resistance

text: The intelligence networks were by far the most numerous and substantial of Resistance activities. They collected information of military value, such as coastal fortifications of the Atlantic Wall or Wehrmacht deployments. The BCRA and the different British intelligence services often competed with one another to gather the most valuable information from their Resistance networks in France.


title: French Resistance

text: The first agents of the Free French to arrive from Britain landed on the coast of Brittany as early as July 1940. They were Lieutenants Mansion, Saint-Jacques and Corvisart and Colonel Rémy, and didn't hesitate to get in touch with the anti-Germans within the Vichy military such as Georges Loustaunau-Lacau and Georges Groussard.


title: French Resistance

text: The various Resistance movements in France had to understand the value of intelligence networks in order to be recognized or receive subsidies from the BCRA or the British. The intelligence service of the Francs-Tireurs et Partisans was known by the code letters FANA and headed by Georges Beyer, the brother-in-law of Charles Tillon. Information from such services was often used as a bargaining chip to qualify for airdrops of weapons.


title: French Resistance

text: The transmission of information was first done by radio transmitter. Later, when air links by the Westland Lysander became more frequent, some information was also channeled through these couriers. By 1944, the BCRA was receiving 1,000 telegrams by radio every day and 2,000 plans every week. Many radio operators, called "pianistes", were located by German goniometers. Their dangerous work gave them an average life expectancy of around six months. Even children partook in radio work (see Eddy Palacci). According to the historian Jean-François Muracciole, "Throughout the war, how to communicate remained the principal difficulty of intelligence networks. Not only were the operators few and inept, but their information was dangerous."


title: French Resistance

text: Sabotage was a form of resistance adopted by groups who wanted to go beyond just distributing clandestine press publications. Many laboratories were set up to manufacture explosives. In August 1941, the Parisian chemist France Bloch-Sérazin assembled a small laboratory in her apartment to provide explosives to communist Resistance fighters. The lab also produced cyanide capsules to allow the fighters to evade torture if arrested. Indeed, she herself was arrested in February 1942, tortured, and deported to Hamburg where she was beheaded by guillotine in February 1943. In the southern occupation zone, Jacques Renouvin engaged in the same activities on behalf of groups of francs-tireurs.


title: French Resistance

text: Stealing dynamite from the Germans eventually took preference over handcrafting explosives. The British Special Operations Executive also parachuted tons of explosives to its agents in France for essential sabotage missions. The railways were a favorite target of saboteurs, who soon understood that removing bolts from the tracks was far more efficient than planting explosives.


title: French Resistance

text: Train-derailment strategies varied considerably in their effectiveness. The Germans managed to repair the tracks quickly in agricultural areas with level ground, since the salvage of some matériel was a relatively easy proposition in such terrain. But unbolting a connector plate on an outside rail in a mountainous area (given the higher speed of trains going downhill) could result in the derailment of an entire train with considerable amounts of front-ready matériel strewn far down the mountainside. Among the SNCF employees who joined the resistance, a subset were in Resistance-Fer which focused on reporting the movement of German troops to the Allied forces and sabotaging the railways' rolling stock as well as their infrastructure. Following the invasions of Normandy and Provence in 1944, the sabotage of rail transport became much more frequent and effectively prevented some German troop deployments to the front and hindered the subsequent retreat of German occupying forces.


title: French Resistance

text: Generally, the sabotage of equipment leaving armaments factories and derailment in areas where equipment could not readily be salvaged was a more discreet form of resistance, and probably at least as effective as bombing. Sabotage by resistants freed up vulnerable and expensive aircraft for other uses rather than risk heavy losses by attacking heavily defended targets. It was also preferred since it caused less collateral damage and fewer civilian casualties than Allied bombing.


title: French Resistance

text: After the invasion of the Soviet Union in June 1941, communists engaged in guerrilla warfare, attacking German forces in French cities. In July 1942, the Allies' failure to open a second front resulted in a wave of communist guerrilla attacks aimed at maximizing the number of Germans deployed in the West to give the USSR military relief.


title: French Resistance

text: The assassinations that took place during summer and autumn 1941, starting with Colonel Pierre-Georges Fabien's shooting of a German officer in the Paris Métro, caused fierce reprisals and executions of hundreds of French hostages. As a result, the clandestine press was very discreet about the events and the communists soon decided to discontinue the assassinations.


title: French Resistance

text: From July to October 1943, groups in Paris engaging in attacks against occupying soldiers were better organized. Joseph Epstein was assigned responsibility for training Resistance fighters across the city, and his new commandos of fifteen men perpetrated a number of attacks that could not have been carried out before. The commandos were drawn from the foreign branch of the Francs-Tireurs et Partisans, and the most famous of them was the Manouchian Group.


title: French Resistance

text: Defining the precise role of the French Resistance during the German occupation, or assessing its military importance alongside the Allied Forces during the liberation of France, is difficult. The two forms of resistance, active and passive, and the north–south occupational divide, allow for many different interpretations, but what can broadly be agreed on is a synopsis of the events which took place.


title: French Resistance

text: Following the surrender of Fascist Italy in September 1943, a significant example of Resistance strength was displayed when the Corsican Resistance joined forces with the Free French to liberate the island from General Albert Kesselring's remaining German forces.


title: French Resistance

text: On mainland France itself, in the wake of the D-Day landings in Normandy in June 1944, the FFI and the communist fighting groups FTP, theoretically unified under the command of General Pierre Kœnig, fought alongside the Allies to free the rest of France. Several color-coded plans were co-ordinated for sabotage, most importantly "Plan Vert" (Green) for railways, "Plan Bleu" (Blue) for power installations and "Plan Violet" (Purple) for telecommunications. To complement these missions, smaller plans were drafted: "Plan Rouge" (Red) for German ammunition depots, "Plan Jaune" (Yellow) for German command posts, "Plan Noir" (Black) for German fuel depots and "Plan Tortue" (Tortoise) for road traffic. Their paralysis of German infrastructure is widely thought to have been very effective. British Prime Minister Winston Churchill later wrote in his memoirs praising the role the Resistance played in the liberation of Brittany, "The French Resistance Movement, which here numbered 30,000 men, played a notable part, and the peninsula was quickly overrun."


title: French Resistance

text: The Liberation of Paris on August 25, 1944, with the support of Leclerc's French 2nd Armored Division, was one of the most famous and glorious moments of the French Resistance. Although it is again difficult to gauge their effectiveness precisely, popular anti-German demonstrations, such as general strikes by the Paris Métro, the gendarmerie and the police, took place, and fighting ensued.


title: French Resistance

text: The liberation of most of southwestern, central and southeastern France was finally fulfilled with the arrival of the 1st French Army of General de Lattre de Tassigny, which landed in Provence in August 1944 and was backed by over 25,000 maquis.


title: French Resistance

text: One source often referred to is General Dwight D. Eisenhower's comment in his military memoir, "Crusade in Europe":


title: French Resistance

text: General Eisenhower also estimated the value of the Resistance to have been equal to ten to fifteen divisions at the time of the landings. (One infantry division comprised about ten thousand soldiers.) Eisenhower's statements are all the more credible since he based them on his GHQ's formal analyses and published them only after the war, when propaganda was no longer a motive. Historians still debate how effective the French Resistance was militarily, but the neutralization of the Maquis du Vercors alone involved the commitment of over 10,000 German troops within the theater, with several more thousand held in reserve, as the Allied invasion was advancing from Normandy and French Operation Jedburgh commandos were being dropped nearby to the south to prepare for the Allied landing in Provence. One American officer, Ralph Ingersoll who served in SHEAF wrote in his book "Top Secret":


title: French Resistance

text: It is estimated that FFI killed some 2,000 Germans, a low estimate based on the figures from June 1944 only. Estimates of the casualties among the Resistance are made harder by the dispersion of movements at least until D-Day, but credible estimates start from 8,000 dead in action, 25,000 shot and several tens of thousands deported. For perspective, the best estimate is that 86,000 were deported from France without racial motive, overwhelmingly comprising resistance fighters and more than the number of Gypsies and Jews deported from France.


title: French Resistance

text: Immediately following the liberation, France was swept by a wave of executions, public humiliations, assaults and detentions of suspected collaborators, known as the "épuration sauvage" (wild purge). This period succeeded the German occupational administration but preceded the authority of the French Provisional Government, and consequently lacked any form of institutional justice. Approximately 9,000 were executed, mostly without trial as summary executions, notably including members and leaders of the pro-Nazi milices. In one case, as many as 77 milices members were summarily executed at once. An inquest into the issue of summary executions launched by Jules Moch, the Minister of the Interior, came to the conclusion that there were 9,673 summary executions. A second inquest in 1952 separated out 8,867 executions of suspected collaborators and 1,955 summary executions for which the motive of killing was not known, giving a total of 10,822 executions. Head-shaving as a form of humiliation and shaming was a common feature of the purges, and between 10,000 and 30,000 women accused of having collaborated with the Germans or having had relationships with German soldiers or officers were subjected to the practice, becoming known as "les tondues" (the shorn).


title: French Resistance

text: The official "épuration légale" ("legal purge") began following a June 1944 decree that established a three-tier system of judicial courts: a High Court of Justice which dealt with Vichy ministers and officials; Courts of Justice for other serious cases of alleged collaboration; and regular Civic Courts for lesser cases of alleged collaboration. Over 700 collaborators were executed following proper legal trials. This initial phase of the purge trials ended with a series of amnesty laws passed between 1951 and 1953 which reduced the number of imprisoned collaborators from 40,000 to 62, and was followed by a period of official "repression" that lasted between 1954 and 1971.


title: French Resistance

text: During this period, and particularly after de Gaulle's return to power in 1958, the collective memory of ""Résistancialisme"" tended toward a highly-resistant France opposed to the collaboration of the Vichy régime. This period ended when the aftermath of the events of May 1968, which had divided French society between the conservative "war generation" and the younger, more liberal students and workers, led many to question the Resistance ideals promulgated by the official history.


title: French Resistance

text: In coming to terms with the events of the occupation, several different attitudes have emerged in France, in an evolution the historian Henry Rousso has called the "Vichy Syndrome". The questioning of France's past had become a national obsession by the 1980s, fuelled by the highly publicized trials of war criminals such as Klaus Barbie and Maurice Papon. Although the occupation is often still a sensitive subject in the early 21st century, contrary to some interpretations the French as a whole have acknowledged their past and no longer deny their conduct during the war.


title: French Resistance

text: After the war, the influential French Communist Party (PCF) projected itself as ""Le Parti des Fusillés"" (The Party of Those Shot), in recognition of the thousands of communists executed for their Resistance activities. The number of communists killed was in reality considerably less than the Party's figure of 75,000. It is now estimated that close to 30,000 Frenchmen of all political movements combined were shot, of whom only a few thousand were communists. Others were deported, though, many of which died in concentration camps.


title: French Resistance

text: The Vichy régime's prejudicial policies had discredited traditional conservatism in France by the end of the war, but following the liberation many former "Pétainistes" became critical of the official "résistancialisme", using expressions such as ""le mythe de la Résistance"" (the myth of the Resistance), one of them even concluding, "The 'Gaullist' régime is therefore built on a fundamental lie."


title: French Resistance

text: The French Resistance has had a great influence on literature, particularly in France. A famous example is the poem "Strophes pour se souvenir", which was written by the communist academic Louis Aragon in 1955 to commemorate the heroism of the Manouchian Group, whose 23 members were shot by the Nazis. The Resistance is also portrayed in Jean Renoir's wartime "This Land is Mine" (1943), which was produced in the US. In the immediate postwar years, French cinema produced a number of films that portrayed a France broadly present in the Resistance. "La Bataille du rail" (1946) depicted the courageous efforts of French railway workers to sabotage German reinforcement trains, and in the same year "Le Père tranquille" told the story of a quiet insurance agent secretly involved in the bombing of a factory. Collaborators were unflatteringly portrayed as a rare unpopular minority, as played by Pierre Brewer in "Jéricho" (also 1946) or Serge Reggiani in "Les Portes de la nuit" (1946 as well), and movements such as the Milice were rarely evoked.


title: French Resistance

text: In the 1950s, a less heroic interpretation of the Resistance to the occupation gradually began to emerge. In Claude Autant-Lara's "La Traversée de Paris" (1956), the portrayal of the city's black market and the prevailing general mediocrity disclosed the reality of war-profiteering during the occupation. In the same year, Robert Bresson presented "A Man Escaped", in which an imprisoned Resistance activist works with a reformed collaborator inmate to help him escape. A cautious reappearance of the image of Vichy emerged in "Le Passage du Rhin" (The Crossing of the Rhine)(1960), in which a crowd successively acclaims both Pétain and de Gaulle.


title: French Resistance

text: After General de Gaulle's return to power in 1958, the portrayal of the Resistance returned to its earlier "résistancialisme". In this manner, in "Is Paris Burning?" (1966), "the role of the resistant was revalued according to [de Gaulle's] political trajectory". The comic form of films such as "La Grande Vadrouille" (also 1966) broadened the image of Resistance heroes in the minds of average Frenchmen. The most famous and critically acclaimed of all the "résistancialisme" movies is "L'armée des ombres" (Army of Shadows) by French filmmaker Jean-Pierre Melville in 1969, a film inspired by Joseph Kessel's 1943 book as well as Melville's own experience as a Resistance fighter who participated in Operation Dragoon. A 1995 television screening of "L'armée des ombres" described it as "the best film made about the fighters of the shadows, those anti-heroes." The shattering of France's "résistancialisme" following the civil unrest of May 1968 was made particularly clear in French cinema. The candid approach of the 1971 documentary "The Sorrow and the Pity" shone a spotlight on antisemitism in France and disputed the official Resistance ideals. "Time" magazine's positive review of the film wrote that director Marcel Ophüls "tries to puncture the bourgeois myth—or protectively skew memory—that allows France generally to act as if hardly any Frenchmen collaborated with the Germans."


title: French Resistance

text: Franck Cassenti, with "L'Affiche Rouge" (1976); Gilson, with "La Brigade" (1975); and Mosco with the documentary "Des terroristes à la retraite" addressed foreign resisters of the EGO, who were then relatively unknown. In 1974, Louis Malle's "Lacombe, Lucien" caused scandal and polemic for his lack of moral judgment regarding the behavior of a collaborator. Malle later portrayed the resistance of Catholic priests who protected Jewish children in his 1987 film "Au revoir, les enfants". François Truffaut's 1980 film "Le Dernier Métro" was set during the German occupation of Paris and won ten Césars for its story of a theatrical production staged while its Jewish director is concealed by his wife in the theater's basement. The 1980s began to portray the resistance of working women, as in "Blanche et Marie" (1984). Later, Jacques Audiard's "Un héros très discret" (1996) told the story of a young man's traveling to Paris and manufacturing a Resistance past for himself, suggesting that many heroes of the Resistance were impostors. In 1997 Claude Berri produced the biopic "Lucie Aubrac" based on the life of the Resistance heroine of the same name, which was criticized for its Gaullist portrayal of the Resistance and its overemphasizing the relationship between Aubrac and her husband.


title: French Resistance

text: In 2003, Kimberly Brubaker Bradley first published a book entitled "For Freedom: The Story of a French Spy". Though classified as a work of fiction, the book is based on the real-life memories of Suzanne David Hall. Training to become an opera singer, Suzanne was traveling for rehearsals, costume fittings, and lessons when she was recruited by an organizer of the French Resistance and became a secret courier.


title: French Resistance

text: After the war, museums and memorials commemorating the events and the people involved in the resistance were established throughout France.


title: French Resistance

text: The well-known personalities of France—intellectuals, artists, and entertainers—faced a serious dilemma in choosing to emigrate or to remain in France during the country's occupation. They understood that their post-war reputations would depend, in large part, on their conduct during the war years. Most who remained in France aimed to defend and further French culture and thereby weaken the German hold on occupied France. Some were later ostracized following accusations that they had collaborated. Among those who actively fought in the Resistance, a number died for it—for instance the writer Jean Prévost, the philosopher and mathematician Jean Cavaillès, the historian Marc Bloch, and the philosopher Jean Gosset; among those who survived and went on to reflect on their experience, a particularly visible one was André Malraux.


title: French Resistance

text: Among prominent foreign figures who participated in the French Resistance was the political scientist and later Iranian Prime Minister Shapour Bakhtiar. After serving as the prime minister and strong man of the authoritarian Shah régime in Iran, he was forced back into Paris in the aftermath of the Islamic Revolution. He was assassinated on order of the Iranian Islamic Republic in 1991.


title: French Resistance

text: The Resistance features in the Kevin Doherty novels "Villa Normandie" (Endeavour Press, 2015), particularly notable for its depiction of a female Resistance cell leader as the novel's main character, and "Charlie's War" (Endeavour Press, 2016), and also in the 1964 film "The Train", based on fact about the Resistance's efforts to prevent a train carrying looted French art from getting to Germany.


title: French Resistance

text: In television; the series' "Un village français" (English: "A French Village") tells the extended story of a community of resistance members and the harsh realities that such a group faced during the entirety of the French occupation, and "Resistance", created by TF1 in France (as "Résistance"), is a drama set in German-occupied Paris in 1940 depicting the lives of students and teachers within the Resistance, loosely based on the activities of the Groupe du musée de l'Homme. "'Allo 'Allo!", a British sitcom featuring Resistance activities, was conceived as a parody of the earlier BBC drama series "Secret Army", and a number of characters in the "Star Trek" television franchise are members of the maquis.


title: French Resistance

text: Emmanuel d'Astier de La Vigerie, credited as "Bernard", wrote the original French lyrics of Anna Marly's 1943 song "La Complainte du partisan", which later gained worldwide popularity as "The Partisan" with English lyrics adapted by Hy Zaret. The song describes the trials of a Resistance member from their perspective. Many artists have released versions of the song, in many languages, with the most well known release being by Leonard Cohen in 1969.


title: Chinese respelling of the English alphabet

text: In China, letters of the English alphabet are pronounced somewhat differently because they have been adapted to the phonetics (i.e. the syllable structure) of the Chinese language. The knowledge of this spelling may be useful when spelling Western names, especially over the phone, as one may not be understood if the letters are pronounced as they are in English. (The letters that are pronounced differently – not counting tone differences – according to different sources are given in bold.)


text: The respelling of Z mimics the British English "zed" rather than the American English "zee" or the Hong Kong English variant "izzard" .


title: Euclidean space

text: Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's "Elements", it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension, including the three-dimensional space and the "Euclidean plane" (dimension two). The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics.


title: Euclidean space

text: Ancient Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the ancient Greek mathematician Euclid in his "Elements", with the great innovation of "proving" all properties of the space as theorems, by starting from a few fundamental properties, called "postulates", which either were considered as evident (for example, there is exactly one straight line passing through two points), or seemed impossible to prove (parallel postulate).


title: Euclidean space

text: After the introduction at the end of 19th century of non-Euclidean geometries, the old postulates were re-formalized to define Euclidean spaces through axiomatic theory. Another definition of Euclidean spaces by means of vector spaces and linear algebra has been shown to be equivalent to the axiomatic definition. It is this definition that is more commonly used in modern mathematics, and detailed in this article. In all definitions, Euclidean spaces consist of points, which are defined only by the properties that they must have for forming a Euclidean space.


title: Euclidean space

text: There is essentially only one Euclidean space of each dimension; that is, all Euclidean spaces of a given dimension are isomorphic. Therefore, in many cases, it is possible to work with a specific Euclidean space, which is generally the real -space formula_1 equipped with the dot product. An isomorphism from a Euclidean space to formula_2 associates with each point an -tuple of real numbers which locate that point in the Euclidean space and are called the "Cartesian coordinates" of that point.


title: Euclidean space

text: Euclidean space was introduced by ancient Greeks as an abstraction of our physical space. Their great innovation, appearing in Euclid's "Elements" was to build and "prove" all geometry by starting from a few very basic properties, which are abstracted from the physical world, and cannot be mathematically proved because of the lack of more basic tools. These properties are called postulates, or axioms in modern language. This way of defining Euclidean space is still in use under the name of synthetic geometry.


title: Euclidean space

text: In 1637, René Descartes introduced Cartesian coordinates and showed that this allows reducing geometric problems to algebraic computations with numbers. This reduction of geometry to algebra was a major change in point of view, as, until then, the real numbers were defined in terms of lengths and distances.


title: Euclidean space

text: Euclidean geometry was not applied in spaces of dimension more than three until the 19th century. Ludwig Schläfli generalized Euclidean geometry to spaces of dimension , using both synthetic and algebraic methods, and discovered all of the regular polytopes (higher-dimensional analogues of the Platonic solids) that exist in Euclidean spaces of any dimension.


title: Euclidean space

text: Despite the wide use of Descartes' approach, which was called analytic geometry, the definition of Euclidean space remained unchanged until the end of 19th century. The introduction of abstract vector spaces allowed their use in defining Euclidean spaces with a purely algebraic definition. This new definition has been shown to be equivalent to the classical definition in terms of geometric axioms. It is this algebraic definition that is now most often used for introducing Euclidean spaces.


title: Euclidean space

text: One way to think of the Euclidean plane is as a set of points satisfying certain relationships, expressible in terms of distance and angles. For example, there are two fundamental operations (referred to as motions) on the plane. One is translation, which means a shifting of the plane so that every point is shifted in the same direction and by the same distance. The other is rotation around a fixed point in the plane, in which all points in the plane turn around that fixed point through the same angle. One of the basic tenets of Euclidean geometry is that two figures (usually considered as subsets) of the plane should be considered equivalent (congruent) if one can be transformed into the other by some sequence of translations, rotations and reflections (see below).


title: Euclidean space

text: In order to make all of this mathematically precise, the theory must clearly define what is a Euclidean space, and the related notions of distance, angle, translation, and rotation. Even when used in physical theories, Euclidean space is an abstraction detached from actual physical locations, specific reference frames, measurement instruments, and so on. A purely mathematical definition of Euclidean space also ignores questions of units of length and other physical dimensions: the distance in a "mathematical" space is a number, not something expressed in inches or metres.


title: Euclidean space

text: The standard way to mathematically define a Euclidean space, as carried out in the remainder of this article, is as a set of points on which a real vector space acts, the "space of translations" which is equipped with an inner product. The action of translations makes the space an affine space, and this allows defining lines, planes, subspaces, dimension, and parallelism. The inner product allows defining distance and angles.


title: Euclidean space

text: The set formula_2 of -tuples of real numbers equipped with the dot product is a Euclidean space of dimension . Conversely, the choice of a point called the "origin" and an orthonormal basis of the space of translations is equivalent with defining an isomorphism between a Euclidean space of dimension and formula_2 viewed as a Euclidean space.


title: Euclidean space

text: It follows that everything that can be said about a Euclidean space can also be said about formula_5 Therefore, many authors, especially at elementary level, call formula_2 the "standard Euclidean space" of dimension , or simply "the" Euclidean space of dimension .


title: Euclidean space

text: A reason for introducing such an abstract definition of Euclidean spaces, and for working with it instead of formula_2 is that it is often preferable to work in a "coordinate-free" and "origin-free" manner (that is, without choosing a preferred basis and a preferred origin). Another reason is that there is no origin nor any basis in the physical world.


title: Euclidean space

text: A Euclidean space is an affine space over the reals such that the associated vector space is a Euclidean vector space. Euclidean spaces are sometimes called "Euclidean affine spaces" for distinguishing them from Euclidean vector spaces.


title: Euclidean space

text: If is a Euclidean space, its associated vector space (Euclidean vector space) is often denoted formula_8 The "dimension" of a Euclidean space is the dimension of its associated vector space.


title: Euclidean space

text: The elements of are called "points" and are commonly denoted by capital letters. The elements of formula_9 are called "Euclidean vectors" or "free vectors". They are also called "translations", although, properly speaking, a translation is the geometric transformation resulting of the action of a Euclidean vector on the Euclidean space.


title: Euclidean space

text: Note: The second in the left-hand side is a vector addition; all other denote an action of a vector on a point. This notation is not ambiguous, as, for distinguishing between the two meanings of , it suffices to look on the nature of its left argument.


title: Euclidean space

text: The fact that the action is free and transitive means that for every pair of points there is exactly one displacement vector such that . This vector is denoted or formula_11


title: Euclidean space

text: As previously explained, some of the basic properties of Euclidean spaces result of the structure of affine space. They are described in and its subsections. The properties resulting from the inner product are explained in and its subsections.


title: Euclidean space

text: For any vector space, the addition acts freely and transitively on the vector space itself. Thus a Euclidean vector space can be viewed as a Euclidean space that has itself as the associated vector space.


title: Euclidean space

text: A typical case of Euclidean vector space is formula_2 viewed as a vector space equipped with the dot product as an inner product. The importance of this particular example of Euclidean space lies in the fact that every Euclidean space is isomorphic to it. More precisely, given a Euclidean space of dimension , the choice of a point, called an "origin" and an orthonormal basis of formula_9 defines an isomorphism of Euclidean spaces from to formula_5


title: Euclidean space

text: As every Euclidean space of dimension is isomorphic to it, the Euclidean space formula_2 is sometimes called the "standard Euclidean space" of dimension .


title: Euclidean space

text: Some basic properties of Euclidean spaces depend only of the fact that a Euclidean space is an affine space. They are called affine properties and include the concepts of lines, subspaces, and parallelism, which are detailed in next subsections.


title: Euclidean space

text: as the associated vector space of is a linear subspace (vector subspace) of formula_8 A Euclidean subspace is a Euclidean space with formula_19 as the associated vector space. This linear subspace formula_19 is also called the "direction" of .


title: Euclidean space

text: is a Euclidean subspace of direction formula_22. (The associated vector space of this subspace is formula_22.)


title: Euclidean space

text: A Euclidean vector space formula_9 (that is, a Euclidean space that is equal to formula_9) has two sorts of subspaces: its Euclidean subspaces and its linear subspaces. Linear subspaces are Euclidean subspaces and a Euclidean subspace is a linear subspace if and only if it contains the zero vector.


title: Euclidean space

text: In a Euclidean space, a "line" is a Euclidean subspace of dimension one. Since a vector space of dimension one is spanned by any nonzero vector, a line is a set of the form


title: Euclidean space

text: It follows that "there is exactly one line that passes through (contains) two distinct points." This implies that two distinct lines intersect in at most one point.


title: Euclidean space

text: In a Euclidean vector space, the zero vector is usually chosen for ; this allows simplifying the preceding formula into


title: Euclidean space

text: The "line segment", or simply "segment", joining the points and is the subset of points such that in the preceding formulas. It is denoted or ; that is


title: Euclidean space

text: Two subspaces and of the same dimension in a Euclidean space are "parallel" if they have the same direction (i.e., the same associated vector space). Equivalently, they are parallel, if there is a translation vector that maps one to the other:


title: Euclidean space

text: Given a point and a subspace , there exists exactly one subspace that contains and is parallel to , which is formula_34 In the case where is a line (subspace of dimension one), this property is Playfair's axiom.


title: Euclidean space

text: The concept of parallel subspaces has been extended to subspaces of different dimensions: two subspaces are parallel if the direction of one of them is contained in the direction to the other.


title: Euclidean space

text: The vector space formula_9 associated to a Euclidean space is an inner product space. This implies a symmetric bilinear form


title: Euclidean space

text: The inner product of a Euclidean space is often called "dot product" and denoted . This is specially the case when a Cartesian coordinate system has been chosen, as, in this case, the inner product of two vectors is the dot product of their coordinate vectors. For this reason, and for historical reasons, the dot notation is more commonly used than the bracket notation for the inner product of Euclidean spaces. This article will follow this usage; that is formula_38 will be denoted in the remainder of this article.


title: Euclidean space

text: The inner product and the norm allows expressing and proving metric and topological properties of Euclidean geometry. The next subsection describe the most fundamental ones. "In these subsections," "denotes an arbitrary Euclidean space, and formula_9 denotes its vector space of translations."


title: Euclidean space

text: The "distance" (more precisely the "Euclidean distance") between two points of a Euclidean space is the norm of the translation vector that maps one point to the other; that is


title: Euclidean space

text: The "length" of a segment is the distance between its endpoints "P" and "Q". It is often denoted formula_42.


title: Euclidean space

text: The distance is a metric, as it is positive definite, symmetric, and satisfies the triangle inequality


title: Euclidean space

text: Moreover, the equality is true if and only if a point belongs to the segment . This inequality means that the length of any edge of a triangle is smaller than the sum of the lengths of the other edges. This is the origin of the term "triangle inequality".


title: Euclidean space

text: Two nonzero vectors and of formula_9 (the associated vector space of a Euclidean space ) are "perpendicular" or "orthogonal" if their inner product is zero:


title: Euclidean space

text: Two linear subspaces of formula_9 are orthogonal if every nonzero vector of the first one is perpendicular to every nonzero vector of the second one. This implies that the intersection of the linear subspaces is reduced to the zero vector.


title: Euclidean space

text: Two lines, and more generally two Euclidean subspaces (A line can be considered as an one Euclidean subspace.) are orthogonal if their directions (the associated vector spaces of the Euclidean subspaces) are orthogonal. Two orthogonal lines that intersect are said "perpendicular".


title: Euclidean space

text: Two segments and that share a common endpoint are "perpendicular" or "form a right angle" if the vectors formula_47 and formula_48 are orthogonal.


title: Euclidean space

text: This is the Pythagorean theorem. Its proof is easy in this context, as, expressing this in terms of the inner product, one has, using bilinearity and symmetry of the inner product:


title: Euclidean space

text: where is the principal value of the arccosine function. By Cauchy–Schwarz inequality, the argument of the arccosine is in the interval . Therefore is real, and (or if angles are measured in degrees).


title: Euclidean space

text: In an oriented Euclidean plane, one can define the "oriented angle" of two vectors. The oriented angle of two vectors and is then the opposite of the oriented angle of and . In this case, the angle of two vectors can have any value modulo an integer multiple of . In particular, a reflex angle equals the negative angle .


title: Euclidean space

text: The angle of two vectors does not change if they are multiplied by positive numbers. More precisely, if and are two vectors, and and are real numbers, then


title: Euclidean space

text: If , , and are three points in a Euclidean space, the angle of the segments and is the angle of the vectors formula_47 and formula_56 As the multiplication of vectors by positive numbers do not change the angle, the angle of two half-lines with initial point can be defined: it is the angle of the segments and , where and are arbitrary points, one on each half-line. Although this is less used, one can define similarly the angle of segments or half-lines that do not share an initial point.


title: Euclidean space

text: The angle of two lines is defined as follows. If is the angle of two segments, one on each line, the angle of any two other segments, one on each line, is either or . One of these angles is in the interval , and the other being in . The "non-oriented angle" of the two lines is the one in the interval . In an oriented Euclidean plane, the "oriented angle" of two lines belongs to the interval .


title: Euclidean space

text: Every Euclidean vector space has an orthonormal basis (in fact, infinitely many in dimension higher than one, and two in dimension one), that is a basis formula_57 of unit vectors (formula_58) that are pairwise orthogonal (formula_59 for ). More precisely, given any basis formula_60 the Gram–Schmidt process computes an orthonormal basis such that, for every , the linear spans of formula_61 and formula_62 are equal.


title: Euclidean space

text: Given a Euclidean space , a "Cartesian frame" is a set of data consisting of an orthonormal basis of formula_23 and a point of , called the "origin" and often denoted . A Cartesian frame formula_64 allows defining Cartesian coordinates for both and formula_9 in the following way.


title: Euclidean space

text: The Cartesian coordinates of a vector of formula_9 are the coefficients of on the orthonormal basis formula_67 For example, the Cartesian coordinates of a vector formula_68 on an orthonormal basis formula_69 (that may be named as formula_70 as a convention) in a 3-dimensional Euclidean space is formula_71 if formula_72. As the basis is orthonormal, the -th coefficient formula_73 is equal to the dot product formula_74


title: Euclidean space

text: As a Euclidean space is an affine space, one can consider an affine frame on it, which is the same as a Euclidean frame, except that the basis is not required to be orthonormal. This define affine coordinates, sometimes called "skew coordinates" for emphasizing that the basis vectors are not pairwise orthogonal.


title: Euclidean space

text: An affine basis of a Euclidean space of dimension is a set of points that are not contained in a hyperplane. An affine basis define barycentric coordinates for every point.


title: Euclidean space

text: Many other coordinates systems can be defined on a Euclidean space of dimension , in the following way. Let be a homeomorphism (or, more often, a diffeomorphism) from a dense open subset of to an open subset of formula_5 The "coordinates" of a point of are the components of . The polar coordinate system (dimension 2) and the spherical and cylindrical coordinate systems (dimension 3) are defined this way.


title: Euclidean space

text: For points that are outside the domain of , coordinates may sometimes be defined as the limit of coordinates of neighbour points, but these coordinates may be not uniquely defined, and may be not continuous in the neighborhood of the point. For example, for the spherical coordinate system, the longitude is not defined at the pole, and on the antimeridian, the longitude passes discontinuously from –180° to +180°.


title: Euclidean space

text: This way of defining coordinates extends easily to other mathematical structures, and in particular to manifolds.


title: Euclidean space

text: In the case of a Euclidean vector space, an isometry that maps the origin to the origin preserves the norm


title: Euclidean space

text: An isometry formula_81 of Euclidean spaces defines an isometry formula_82 of the associated Euclidean vector spaces. This implies that two isometric Euclidean spaces have the same dimension. Conversely, if and are Euclidean spaces, , , and formula_83 is an isometry, then the map formula_81 defined by


title: Euclidean space

text: It follows from the preceding results that an isometry of Euclidean spaces maps lines to lines, and, more generally Euclidean subspaces to Euclidean subspaces of the same dimension, and that the restriction of the isometry on these subspaces are isometries of these subspaces.


title: Euclidean space

text: If is a Euclidean space, its associated vector space formula_9 can be considered as a Euclidean space. Every point defines an isometry of Euclidean spaces


title: Euclidean space

text: which maps to the zero vector and has the identity as associated linear map. The inverse isometry is the map


title: Euclidean space

text: An isometry from a Euclidean space onto itself is called "Euclidean isometry", "Euclidean transformation" or "rigid transformation". The rigid transformations of a Euclidean space form a group (under composition), called the "Euclidean group" and often denoted of .


title: Euclidean space

text: They are in bijective correspondence with vectors. This is a reason for calling "space of translations" the vector space associated to a Euclidean space. The translations form a normal subgroup of the Euclidean group.


title: Euclidean space

text: A Euclidean isometry of a Euclidean space defines a linear isometry formula_93 of the associated vector space (by "linear isometry", it is meant an isometry that is also a linear map) in the following way: denoting by the vector formula_94, if is an arbitrary point of , one has


title: Euclidean space

text: The map formula_96 is a group homomorphism from the Euclidean group onto the group of linear isometries, called the orthogonal group. The kernel of this homomorphism is the translation group, showing that it is a normal subgroup of the Euclidean group.


title: Euclidean space

text: The isometries that fix a given point form the stabilizer subgroup of the Euclidean group with respect to . The restriction to this stabilizer of above group homomorphism is an isomorphism. So the isometries that fix a given point form a group isomorphic to the orthogonal group.


title: Euclidean space

text: Let be a point, an isometry, and the translation that maps to . The isometry formula_97 fixes . So formula_98 and "the Euclidean group is the semidirect product of the translation group and the orthogonal group."


title: Euclidean space

text: The special orthogonal group is the normal subgroup of the orthogonal group that preserves handedness. It is a subgroup of index two of the orthogonal group. Its inverse image by the group homomorphism formula_96 is a normal subgroup of index two of the Euclidean group, which is called the "special Euclidean group" or the "displacement group". Its elements are called "rigid motions" or "displacements".


title: Euclidean space

text: Rigid motions include the identity, translations, rotations (the rigid motions that fix at least a point), and also screw motions.


title: Euclidean space

text: Typical examples of rigid transformations that are not rigid motions are reflections, which are rigid transformations that fix a hyperplane and are not the identity. They are also the transformations consisting in changing the sign of one coordinate over some Euclidean frame.


title: Euclidean space

text: As the special Euclidean group is a subgroup of index two of the Euclidean group, given a reflection , every rigid transformation that is not a rigid motion is the product of and a rigid motion. A glide reflection is an example of a rigid transformation that is not a rigid motion or a reflection.


title: Euclidean space

text: The Euclidean distance makes a Euclidean space a metric space, and thus a topological space. This topology is called the Euclidean topology. In the case of formula_100 this topology is also the product topology.


title: Euclidean space

text: The open sets are the subsets that contains an open ball around each of their points. In other words, open balls form a base of the topology.


title: Euclidean space

text: The topological dimension of a Euclidean space equals its dimension. This implies that Euclidean spaces of different dimensions are not homeomorphic. Moreover, the theorem of invariance of domain asserts that a subset of a Euclidean space is open (for the subspace topology) if and only if it is homeomorphic to an open subset of a Euclidean space of the same dimension.


title: Euclidean space

text: Euclidean spaces are complete and locally compact. That is, a closed subset of a Euclidean space is compact if it is bounded (that is, contained in a ball). In particular, closed balls are compact.


title: Euclidean space

text: The definition of Euclidean spaces that has been described in this article differs fundamentally of Euclid's one. In reality, Euclid did not define formally the space, because it was thought as a description of the physical world that exists independently of human mind. The need of a formal definition appeared only at the end of 19th century, with the introduction of non-Euclidean geometries.


title: Euclidean space

text: Two different approaches have been used. Felix Klein suggested to define geometries through their symmetries. The presentation of Euclidean spaces given in this article, is essentially issued from his Erlangen program, with the emphasis given on the groups of translations and isometries.


title: Euclidean space

text: On the other hand, David Hilbert proposed a set of axioms, inspired by Euclid's postulates. They belong to synthetic geometry, as they do not involve any definition of real numbers. Later G. D. Birkhoff and Alfred Tarski proposed simpler sets of axioms, which use real numbers (see Birkhoff's axioms and Tarski's axioms).


title: Euclidean space

text: In "Geometric Algebra", Emil Artin has proved that all these definitions of a Euclidean space are equivalent. It is rather easy to prove that all definitions of Euclidean spaces satisfy Hilbert's axioms, and that those involving real numbers (including the above given definition) are equivalent. The difficult part of Artin's proof is the following. In Hilbert's axioms, congruence is an equivalence relation on segments. One can thus define the "length" of a segment as its equivalence class. One must thus prove that this length satisfies properties that characterize nonnegative real numbers. Artin proved this with axioms equivalent to those of Hilbert.


title: Euclidean space

text: Since ancient Greeks, Euclidean space is used for modeling shapes in the physical world. It is thus used in many sciences such as physics, mechanics, and astronomy. It is also widely used in all technical areas that are concerned with shapes, figure, location and position, such as architecture, geodesy, topography, navigation, industrial design, or technical drawing.


title: Euclidean space

text: Space of dimensions higher than three occurs in several modern theories of physics; see Higher dimension. They occur also in configuration spaces of physical systems.


title: Euclidean space

text: Beside Euclidean geometry, Euclidean spaces are also widely used in other areas of mathematics. Tangent spaces of differentiable manifolds are Euclidean vector spaces. More generally, a manifold is a space that is locally approximated by Euclidean spaces. Most non-Euclidean geometries can be modeled by a manifold, and embedded in a Euclidean space of higher dimension. For example, an elliptic space can be modeled by an ellipsoid. It is common to represent in a Euclidean space mathematical objects that are "a priori" not of a geometrical nature. An example among many is the usual representation of graphs.