Blaise Pascal
Blaise Pascal (, , ;  Faransanci: [blɛz paskal]; 19 June 1623 – 19 August 1662) masanin lissafi ne dan kasar Faransa, masanin physics, mai kirkira, masanin Falsafa, kuma marubucin katolika.  

Pascal ya kasance yana bincike mai ma'ana tuna yana kasa da shekaru 10 wanda mahaifinsa ya koyar da shi, wani jami'in haraji dan kasar Rouen. Aikinsa na farko farko akan lissafi shine conic sections. Yayi rubutu masu tasiri sosai akan darasin  projective geometry a lokacin yana da shekaru 16. Daga nan yayi aiki tare da  Pierre de Fermat akan probability theory. Wanda yayi tasiri sosai a wajen bunkasa tattalin arziki na zamani da kuma Kimiyyar zamantakewa. Acikin shekarar 1642, ya fara aiki akan wasu na'urorin lissafi (wanda ake kira da  Pascal's calculators sannan daga baya Pascalines), hakan ya sanya shi ya zama daya daga cikin mutum biyu da suka fara kirkirar Nau'rar Lissafi.

Kamar dai René Descartes, shima Pascal na daga cikin wanda suka fara bunkasa kimiyyar natural and applied sciences. Pascal yayi rubutu sosai akan Salon Kimiyya (scientific method) kuma rubuta jayayya da dama akan hakan. Ya bada gudummawa sosai a wajen nazarin fluids (kaman ruwa, iska da dai sauransu), kuma yayi karin haske game da nazarin Pressure da kuma Vacuum ta hanyar tattara ayyukan  Evangelista Torricelli. Shima ya goyi bayan Torricelli da Galileo Galilei kuma ya musunta aikin Aristotle da Descartes wanda suka ce, cewa duniya bata dauke da vacuum a shekarar 1647.   

A cikin shekara ta 1646, an bayyana shi da kanwansa Jacqueline a matsayin mabiya tafarkin katolika wanda aka fi sani da  Jansenism. Bayan hikimar da ya samu ta hanyar addini a karshen shekarar 1654, ya fara rubuta ayyuka masu tasiri ta fuskar falsafa da fiqhu. Ayyukansa guda biyu da suka yi fice a wancan lokacin:  Lettres provinciales da kuma Pensées, na farkon ya ta'allaka ne akan rikici tsakanin Jansenists da Jesuits.   

Pascal yayi fama da laulayi na rashin lafiya, musamman tun daga bayan shekaru 18; ya mutu bayan watanni biyu kacal bayan bikin murnan zagayowar ranan haihuwarsa shekara 39.

Rayuwarsa

Kuruciya da ilimi 

An haifi Pascal a Clermont-Ferrand, wanda ke yankin Auvergne Faransa, aMassif ta Tsakiya. Mahaifiyarsa ta rasu a lokacin yana da shekaru uku. Mahaifinsa Étienne Pascal (1588–1651), wanda shima yana sha'awar kimiyya da lissafi, ya kasance alkalin kauye kuma memba na  "Noblesse de Robe". Pascal na da kannai mata guda biyu, karamar Jacqueline da kuma babbar Françoise Gilberte Périer. 

A cikin shekarar 1631, shekaru biyar bayan mutuwar matarsa, Étienne Pascal  ya koma Paris da 'ya'yansa. Da isarsu, sai suka dauki 'yar aiki  Louise Delfault wacce daga bisani ta zama muhimmiyar memba na iyalin. Étienne, wanda bai sake kara yin wani auren ba, ya bayar da sauran rayuwarsa wajen kula da 'ya'yansa wanda sun nuna bajinta sosai, musamman dansa namiji Blaise. Dan nasa ya nuna gwaninta sosai a fannin lissafi da kimiyya.

Barin Faransa 

A kasar Faransa, ana siya ana saida ayyuka da mukamai a lokacin. Étienne ya sayar da mukaminsa akan kudi 65,665 Livres. An biya kudin wajen samun alaka da gwamnati, wanda aka biya a wadace don ba wa iyalin na Pascal daman komawa da zama na jin dadi a birnin Paris. Amma a shekarar 1638, Richelieu, don bukatar kudin gudanar da Yakin Shekaru Talatin, ya saba wannan alkwarin na gwamnati, sannan arzikin Étienne Pascal ya fai warwas daga 66,000 livres zuwa 7,300.

Kamar dai mutane da dama, an tilasta wa Etiene shima barin kasar Faris, a dalilin sabbin ka'idojin haraji na gwamnatin Cardinal Richelieu, inda ya bar 'ya'yan shi a karkashin kulawar makwabciyarsa Madame Sainctot, wata kyakyawa kuma sananniyar mace, wanda take da shagon saloon na musamman a kasar gabaki daya kasar Faransa. Sai dai ta dalilin wani taka rawa da 'yarsa Jacqueline tayi a wajen wani taro da Richelieu ya halarta sannan aka yafe wa Étienne. Étienne ya dawo tare da kyakkyawar aminci daga gwamnatin Cardinal sannan a shekarar 1639 aka nada shi kwamishinan sarki na haraji a birnin Rouen—birnin da harkokin haraji ke cikin cakwakiya kafin nadin nashi.

Nau'rar Pascaline 

A shekarar 1642, don yunkurin ragewa mahaifinsa tarin ayyukan lissafi masu gajiyarwa, da sake lissafe-lissafe, na haraji dake shiga da wanda ke fita (a yayinda Pascal karami shima an dauke shi aiki), Pascal, dan kasa da shekaru 19, ya kirkiri na'urar lissafi wanda ke iya tarawa da ragewa, wanda ake kira da Pascal's calculator ko kuma Pascaline. Daga cikin na'urorin pascaline guda takwas da suka tsira, hudu na nan a ajiye a gidan tarihin  Musée des Arts et Métiers a Paris, sai guda daya a gidan tarihin Zwinger museum dake a Dresden, Gemany, sai kuma wasu guda biyu da ake nuni dasu.

Lissafi

Probability 
Bunkasa lissafin probability theory da Pascal yayi shine gudummawansa mafi tasiri ga lissafi. Ainihi ya fara samar da iya ne don karta, a yau tana da muhimmanci a fannin tattalin arziki, kimiyyar lissafi - "actuarial science"  da kuma ga mutane da kungiyoyi don kintatar abun da zai faru nan gaba. Duk da haka, Pascal da Fermat duk da cewa su suka fara muhimmin ayyuka da probability theory, amma basu bunkasa fannin yayi zurfi ba.  Christiaan Huygens bayan ya koya daga Pascal da Fermat ya rubuta littafi na farko akan darasin. Daga nan, magabata daban daban sun cigaba da bunkasa wannan ilimi, irinsu Abraham de Moivre da Pierre-Simon Laplace. 

A shekarar 1654, bayan abokinsa  Chevalier de Méré ya tuntube shi, ya hada kai da abokinsa  Pierre de Fermat akan matsalar karta, sannan daga wannan hadin kai ya jawo bunkasar dokokin lissafin probability. Asalin matsalar itace, wasu 'yan wasan karta su biyu suna so su gama wasan da wuri, a yanayin yadda wasan ya kama, suna so su raba wasan dai dai a tsakanisu, dangane da dama da kowanne daga cikinsu yake dashi wajen lashe wasan daga wannan kasafin. Daga wannan muhawara ne aka samar da mas'alar abubuwan da ake tsammani expected value. Daga bisani (a Pensées), Pascal yayi amfani da gardama ta probability ta Pascal's wager a wajen tabbatar da wanzuwar Ubangiji da kuma nagartacciyar rayuwa. Ayyukan da Fermat da Pascal sukayi akan lissafin calculus na probability, ya samar da muhimmiyar matashiya da aikin Leibniz wajen samar da lissafin calculus.

Rubuce-rubuncensa akan Alwatikan Lissafi Arithmetical Triangle

Littafin Pacal mai suna Traité du triangle arithmétique, an rubuta shi ne a shekarar 1654, amma sai bayan mutuwarsa aka wallafa a shekarar  1665, yana nuna tsarin  binomial coefficients a jere, wanda yake kira da alwatikan lissafi (arithmetical triangle).

Teburin shine kamar haka:

Ya kira lambobi acikin alwatikan da recursion. Ya kira lambobin kamar haka (m + 1)th row da kuma (n + 1)th column tmn. Sannan kuma tmn = tm–1,n + tm,n–1, for m = 0, 1, 2, ... da kuma n = 0, 1, 2, ... Ka'idojin iyakokinsu shine tm,−1 = 0, t−1,n = 0 for m = 1, 2, 3, ... da kuma n = 1, 2, 3, ... Mai jawo sila  

00 = 1. Pascal ya karkare da hujja,

Manazarta