Blaise Pascal

Blaise Pascal (, , ;"Pascal". Random House Webster's Unabridged Dictionary.  Faransanci: [blɛz paskal]; 19 June 1623 – 19 August 1662) masanin lissafi ne ɗan ƙasar Faransa, masanin physics, mai ƙirƙira, masanin Falsafa, kuma marubucin katolika.  

Pascal ya kasance yana bincike mai ma'ana tuna yana ƙasa da shekaru 10 wanda mahaifinsa ya koyar da shi, wani jami'in haraji ɗan ƙasar 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 bunƙasa 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 ɗaya daga cikin mutum biyu da suka fara ƙirƙirar Nau'rar Lissafi.See Schickard versus Pascal: An Empty Debate?  and 

Kamar dai René Descartes, shima Pascal na daga cikin wanda suka fara bunƙasa 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 ƙarin 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 ɗauke da vacuum a shekarar 1647.   

A cikin shekara ta 1646, an bayyana shi da ƙanwansa Jacqueline a matsayin mabiya tafarkin katolika wanda aka fi sani da  Jansenism."Blaise Pascal". Catholic Encyclopedia. Retrieved 23 February 2009. Bayan hikimar da ya samu ta hanyar addini a ƙarshen shekarar 1654, ya fara rubuta ayyuka masu tasiri ta fuskar falsafa da fiqihu. 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.Hald, Anders A History of Probability and Statistics and Its Applications before 1750, (Wiley Publications, 1990) p. 44.

 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.Devlin, Keith (2008). The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. New York: Basic Books. ISBN 978-0-465-00910-7. p. 20 Mahaifinsa Étienne Pascal (1588–1651), wanda shima yana sha'awar kimiyya da lissafi, ya kasance alkalin ƙauye kuma memba na  "Noblesse de Robe". Pascal na da ƙannai mata guda biyu, ƙaramar Jacqueline da kuma babbar Françoise Gilberte Périer. 
A cikin shekarar 1631, shekaru biyar bayan mutuwar matarsa,O'Connor, J.J.; Robertson, E.F. (August 2006). "Étienne Pascal". University of St. Andrews, Scotland. Retrieved 5 February 2010. Étienne Pascal  ya koma Paris da 'ya'yansa. Da isarsu, sai suka ɗauki 'yar aiki  Louise Delfault wacce daga bisani ta zama muhimmiyar memba na iyalin. Étienne, wanda bai sake ƙara yin wani auren ba, ya bayar da sauran rayuwarsa wajen kula da ƴaƴansa wanda sun nuna bajinta sosai, musamman ɗansa namiji Blaise. Ɗan nasa ya nuna gwaninta sosai a fannin lissafi da kimiyya.

 Barin Faransa 

A ƙasar Faransa, ana siya ana saida ayyuka da muƙamai a lokacin. Étienne ya sayar da muƙaminsa akan kudi 65,665 Livres.Connor, James A., Pascal's wager: the man who played dice with God (HarperCollins, NY, 2006)  p. 42 An biya kuɗin wajen samun alaƙa 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 buƙatar kuɗin gudanar da Yakin Shekaru Talatin, ya saba wannan alkwarin na gwamnati, sannan arzikin Étienne Pascal ya fadi warwas daga 66,000 livres zuwa 7,300.

Kamar dai mutane da dama, an tilasta wa Etiene shima barin ƙasar Faris, a dalilin sabbin ƙa'idojin haraji na gwamnatin Cardinal Richelieu, inda ya bar 'ya'yan shi a ƙarƙashin kulawar maƙwabciyarsa Madame Sainctot, wata kyakyawa kuma sananniyar mace, wanda take da shagon saloon na musamman a ƙasar gabaki ɗaya ƙasar 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 naɗa shi kwamishinan sarki na haraji a birnin Rouen—birnin da harkokin haraji ke cikin cakwakiya kafin naɗin nashi.

 Nau'rar Pascaline 

A shekarar 1642, don yunƙurin ragewa mahaifinsa tarin ayyukan lissafi masu gajiyarwa, da sake lissafe-lissafe, na haraji dake shiga da wanda ke fita (a yayinda Pascal ƙarami shima an ɗauke shi aiki), Pascal, ɗan ƙasa da shekaru 19, ya ƙirƙiri 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, huɗu na nan a ajiye a gidan tarihin  Musée des Arts et Métiers a Paris, sai guda ɗaya a gidan tarihin Zwinger museum dake a Dresden, Gemany, sai kuma wasu guda biyu da ake nuni dasu.A complete list of known Pascalines and also a review of contemporary replicas can be found at Surviving Pascalines  and Replica Pascalines  at http://things-that-count.net

 Lissafi 
 Probability 
Bunƙasa 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 ƙungiyoyi 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 bunƙasa 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 bunƙasa wannan ilimi, irinsu Abraham de Moivre da Pierre-Simon Laplace. 
A shekarar 1654, bayan abokinsa  Chevalier de Méré ya tuntuɓe shi, ya haɗa kai da abokinsa  Pierre de Fermat akan matsalar karta, sannan daga wannan haɗin kai ya jawo bunƙasar dokokin lissafin probability.Devlin, Keith (2008). The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. New York: Basic Books. ISBN 978-0-465-00910-7. p. 24 Asalin matsalar itace, wasu ƴan 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:
01234560 1 1 1 11111 1 2  3  4  5  6 21 3  6  10  15   3 14  10  20     4 15  15       5 16         6 1           
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, ... ƙa'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 ƙarƙare da hujja,










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