Imagine a cup of tea. Wrap a piece of string around the circumference of the cup, and measure the length of the string. Then, lay your spoon on top of the cup, making sure it lies across the center of the cup, and measure the length from side to side – the diameter. Finally, divide the circumference by the diameter, and record the result. Next time you eat soup, repeat the process with the bowl.
You will discover that the ratios of the circumference to the diameter in both cases are remarkably close to each other. If you decide to experiment with other circular shapes, you will find that no matter how large or small the objects are, as long as they are round, the ratios will all be very close to 3.14. You just stumbled upon a universal law of circular objects.
The Greek letter pi (π) was introduced in 1706 to denote that constant ratio between the circumference of a circle to its diameter. But the fascination with the number pi goes back millennia.
While pi exists through the constancy of the result of dividing circumference by diameter for all circles, it’s important to note that this constancy is not quite as universal as the ancient Greeks thought. For circles drawn on curved surfaces, such as the spherical surface of Earth, the division is not constant at all, and pi ceases to exist.
Flat geometry, also known as Euclidean geometry, is the universe of mathematical objects where pi exists. The ancient Greeks only studied flat geometry and so for them, the constant pi was truly a universal wonder whose precise value they sought to pinpoint. Being just a simple ratio, how hard could it be?
Archimedes placed pi between 223/71 and 22/7, so between 3.140 and 3.142, while Ptolemy found the first approximation correct to three decimal places: 3.141. Improvements to seven decimal places were achieved by Chinese mathematicians in the 5th century AD, based on a new technique discovered in the 3rd century by mathematician and writer Liu Hui. A millennium would pass before further significant advances led the 14th-century Indian mathematician Madhava of Sangamagrama to reach 11 decimal places.
Progress accelerated with better analytical tools. With modern computers, as of August 2021, the record stands at 62.8 trillion digits.
As the knowledge of the digits of pi expanded, people tried to detect a pattern. A simple rule to describe all digits in one go, or to pinpoint pi, as the ancient Greeks had hoped to do. However, in the 1760s, the French-Swiss mathematician Johann Heinrich Lambert proved that the decimal expansion of pi does not follow any simple rule for its digits; pi is irrational, meaning that its decimal expansion does not repeat or terminate.
The number pi is simple to define and captures a fundamental geometric fact. At the same time, computing it was a challenge for some of the best mathematicians who ever lived. In a sense, it can never be fully captured by simple computations. These factors contribute to the allure of pi and are perhaps a source of its ongoing influence on our culture. Pies and poems
The impact of pi on society can be gleaned from the fact it has its very own day, and its presence in poetry, among other cultural manifestations.
Pi Day falls on March 14, or 3/14 according to the American dating system. It’s celebrated by the recitation of pi’s digits and the enjoyment of round pies.
As profound as eating pies is, pi has generated an entire literary style. Consider the following poem:
I wish I could determine pi
Eureka, cried the great inventor
Christmas pudding, Christmas pie
Is the problem’s very centre.
If you count the letters in each word, you’ll get 3.14159265358979323846, which is pi correct to 20 decimal places. This is an example of a “piem”. There are many more piems in English, as well as in various other languages. A piem can be both a mnemonic device (a linguistic tool to help us remember something) and an artistic endeavor.
This literary style, where the number of letters in consecutive words is dictated by the decimal expansion of pi, is called “Pilish”, and has been around since the early 1900s. Beyond short poems, Pilish has given rise to longer pieces of prose, and even an entire novel. Author Michael Keith indicates the first 10,000 digits of pi through a book, titled Not A Wake (as you can see, its title encodes 3.14).
If you’re feeling creative and want to test your Pilish, here is a Pilish checker you can use. Alternatively, eating pie isn’t a bad way to celebrate all things fascinating about pi.
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Hebu wazia kikombe cha chai. Weka kamba kwenye mviringo wa kikombe hicho, kisha upime urefu wa kamba hiyo. Kisha, weka kijiko chako juu ya kikombe, hakikisha kinapatikana katikati ya kikombe, na upime urefu kutoka upande mmoja hadi mwingine <unk> kipenyo. Mwishowe, gawanya mduara huo kwa kipenyo, na andika matokeo. Wakati mwingine unapokula supu, rudia utaratibu huo kwa bakuli. Utagundua kwamba uwiano wa mduara kwa kipenyo katika kesi zote mbili ni karibu sana na kila mmoja. Ikiwa unaamua kujaribu maumbo mengine ya mviringo, utapata kwamba haijalishi vitu ni vikubwa au vidogo, maadamu ni vya mviringo, uwiano wote utakuwa karibu sana na 3.14. Wewe tu stumbled juu ya sheria ya ulimwengu wa vitu mviringo. "Herufi ya Kigiriki ""pi"" ilianzishwa mwaka 1706 ili kuonyesha uwiano wa mduara na kipenyo chake." Lakini shauku kwa nambari pi inaanzia maelfu ya miaka iliyopita. Wakati pi ipo kupitia uthabiti wa matokeo ya kugawanya mduara kwa kipenyo kwa duru zote, ni muhimu kutambua kwamba uthabiti huu si kabisa kama ulimwengu kama Wagiriki wa kale walidhani. Kwa mviringo uliochorwa kwenye nyuso zilizopindika, kama vile uso wa dunia, mgawanyiko huo si wa kawaida kabisa, na pi huacha kuwepo. Jiometri tambarare, pia inajulikana kama jiometri ya Euclidean, ni ulimwengu wa vitu vya hisabati ambapo pi ipo. Wagiriki wa kale walijifunza tu jiometri ya gorofa na kwa hivyo kwa wao, pi ya mara kwa mara ilikuwa kweli ajabu ya ulimwengu ambao thamani sahihi walitafuta kugundua. Kuwa tu uwiano rahisi, jinsi vigumu inaweza kuwa? Archimedes aliweka pima kati ya 223-71 na 22-7 (kwa hiyo kati ya 3.140-3.142), wakati Ptolemy alipata approximation ya kwanza sahihi kwa nafasi tatu za decimal: 3.141. Katika karne ya 5 KK, hesabu za Kichina zilipata nafasi saba za decimal, kwa kuzingatia mbinu mpya iliyogunduliwa katika karne ya 3 KK na mwanahisabati na mwandishi Liu Hui. Katika karne ya 14 na zaidi, madaktari wa hesabu wa India, Madhava na Sangamagraha, walifanya maendeleo makubwa katika hesabu ya hesabu. Maendeleo yaliharakishwa kwa kutumia vifaa bora vya kuchanganua. Kwa kompyuta za kisasa, hadi Agosti 2021, rekodi inasimama kwa tarakimu 62.8 trilioni. Kadiri ujuzi wa tarakimu za pi ulivyozidi kuongezeka, watu walijaribu kugundua utaratibu. Kanuni rahisi ya kuelezea tarakimu zote kwa mara moja, au kuamua pi, kama vile Wagiriki wa kale walivyotarajia kufanya. Katika miaka ya 1760s, mwanahisabati wa Ufaransa na Uswisi Johann Heinrich Lambert alithibitisha kwamba upanuzi wa decimal wa pi haufuatani na sheria yoyote rahisi kwa tarakimu zake; pi ni isiyo na maana, ikimaanisha kwamba upanuzi wake wa decimal haurudi tena au kumalizika. Nambari pi ni rahisi kufafanua na huonyesha jambo la msingi la kijiometri. Wakati huohuo, kuhesabu ilikuwa changamoto kwa baadhi ya wanahisabati bora ambao wamewahi kuishi. Kwa njia fulani, haiwezi kamwe kueleweka kikamili kwa hesabu sahili. Mambo hayo huchangia kuvutia kwa pi na labda ndiyo chanzo cha uvutano wake wa kuendelea juu ya utamaduni wetu. "Kama vile ""pi"" na ""poem"" zinavyojulikana, pia kuna mambo mengine ya kihistoria ambayo yanaonekana katika mashairi na vitabu vya hadithi." Siku ya Pi huadhimishwa tarehe 14 Machi, kulingana na mfumo wa tarehe ya Marekani. Ni <unk> ni sherehe na recitation ya pi <unk>s tarakimu na kufurahia ya patties pande zote. Kama kina kama kula pies ni, pi imezalisha mtindo mzima wa fasihi. "Kama vile ilivyoandikwa katika shairi la ""I wish I could determine pi, Eureka,"" ilisema mtengenezaji wa Krismasi, ""Christmas pie is the very center of the problem.""" Ikiwa unahesabu herufi katika kila neno, utapata 3.14159265358979323846, ambayo ni pi sahihi kwa nafasi 20 za decimal. Hii ni mfano wa <unk>piem<unk>. Kuna nyimbo nyingi zaidi katika Kiingereza, na pia katika lugha nyingine mbalimbali. Piem inaweza kuwa kifaa cha kukumbuka (chombo cha lugha kutusaidia kukumbuka kitu) na jitihada ya kisanii. "Kama ilivyo kwa lugha ya Kiingereza, ""pili"" ni neno linalotumiwa kuelezea idadi ya herufi katika maneno ya mfululizo, na kwa hivyo ni jina la ""pili"" kwa sababu ya idadi ya herufi katika maneno ya mfululizo." Mbali na mashairi mafupi, Pilish ametoa vipande virefu vya mashairi, na hata riwaya nzima. "Mwandishi Michael Keith aliandika kitabu chake cha ""Not a Wake"" (Not a Wake) ambacho kinaonyesha namba 10,000 za kwanza za namba ya Pi." Kama wewe ni kuhisi ubunifu na wanataka mtihani Pilish yako, hapa ni Pilish checker unaweza kutumia. Vinginevyo, kula pie si njia mbaya ya kusherehekea mambo yote ya kuvutia kuhusu pi. Kupata jarida la TWT na habari muhimu zaidi za teknolojia katika sanduku lako la barua kila wiki