Duba tsatso na Blaise Pascal

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[[File:Blaise pascal.jpg|thumb|200px|Blaise Pascal zanen]]
'''Blaise Pascal''' ({{IPAc-en|p|æ|ˈ|s|k|æ|l}}, {{IPAc-en|UK|-|ˈ|s|k|ɑː|l|,_|'|p|ae|s|k|@l|,_|-|s|k|æ|l}}, {{IPAc-en|US|p|ɑː|ˈ|s|k|ɑː|l}};<ref>{{cite book|last=Wells|first=John|author-link=John C. Wells|title=Longman Pronunciation Dictionary|publisher=Pearson Longman|edition=3rd|date=3 April 2008|isbn=978-1-4058-8118-0}}</ref><ref>[http://dictionary.reference.com/browse/pascal "Pascal"]. ''[[Random House Webster's Unabridged Dictionary]]''.</ref><ref>{{Cite encyclopedia|url=http://www.lexico.com/definition/Pascal,+Blaise|archive-url=https://web.archive.org/web/20211205064720/https://www.lexico.com/definition/pascal,_blaise|url-status=dead|archive-date=2021-12-05|title=Pascal, Blaise|dictionary=[[Lexico]] UK English Dictionary|publisher=[[Oxford University Press]]}}</ref><ref>{{cite web|url=https://www.collinsdictionary.com/dictionary/english/pascal|title=Pascal|work=[[Collins English Dictionary]]|publisher=[[HarperCollins]]|access-date=14 August 2019}}</ref><ref>{{Cite Merriam-Webster|Pascal|access-date=14 August 2019}}</ref>  Faransanci<small>:</small> [blɛz paskal]; 19 June 1623 – 19 August 1662) [[masanin lissafi]] ne ɗan ƙasar Faransa, ''masanin physics,'' mai ƙirƙira, masanin [[Falsafa]], kuma marubucin [[Cocin katolika|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|''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|Nau'rar Lissafi]]''.''<ref>See [http://metastudies.net/pmwiki/pmwiki.php?n=Site.SchicardvsPascal Schickard versus Pascal: An Empty Debate?] {{Webarchive|url=https://web.archive.org/web/20140408215848/http://metastudies.net/pmwiki/pmwiki.php?n=Site.SchicardvsPascal |date=2014-04-08 }} and {{cite book|last=Marguin|first=Jean|title=Histoire des instruments et machines à calculer, trois siècles de mécanique pensante 1642–1942|publisher=Hermann|year=1994|isbn=978-2-7056-6166-3|page=48|language=fr}}</ref><ref>{{cite book|last=d'Ocagne|first=Maurice|url=http://cnum.cnam.fr/CGI/fpage.cgi?8KU54-2.5/248/150/369/363/369|title=Le calcul simplifié|publisher=Gauthier-Villars et fils|year=1893|page=245|language=fr}}</ref>

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 [[Cocin katolika|katolika]] wanda aka fi sani da  [[Jansenizanci|''Jansenism'']].<ref>"Blaise Pascal". ''Catholic Encyclopedia''. Retrieved 23 February 2009.</ref> 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.   
[[Fayil:Portrait de Blaise Pascal par Bocourt.jpg|thumb|Blaise Pascal]]
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.<ref>Hald, Anders ''A History of Probability and Statistics and Its Applications before 1750'', (Wiley Publications, 1990) p. 44.</ref>

== Rayuwarsa ==

=== Kuruciya da ilimi ===

An haifi Pascal a [[Clermont-Ferrand]], wanda ke [[Auvergne|yankin Auvergne]] Faransa, a[[Massif ta Tsakiya]]. Mahaifiyarsa ta rasu a lokacin yana da shekaru uku.<ref>Devlin, Keith (2008). ''The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern''. New York: Basic Books. ISBN <bdi>978-0-465-00910-7</bdi>. p. 20</ref> 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 Pascal|Jacqueline]] da kuma babbar [[Françoise Gilberte Périer]]. 
[[Fayil:Blaise Pascal Versailles.JPG|thumb|Blaise Pascal]]
A cikin shekarar 1631, shekaru biyar bayan mutuwar matarsa,<ref>O'Connor, J.J.; Robertson, E.F. (August 2006). "Étienne Pascal". University of St. Andrews, Scotland. Retrieved 5 February 2010.</ref> 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 [[Livre tournois|Livres]].<ref>Connor, James A., ''Pascal's wager: the man who played dice with God'' (HarperCollins, NY, 2006) {{isbn|0-06-076691-3}} p. 42</ref> 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|Rouen—]]<nowiki/>birnin da harkokin haraji ke cikin cakwakiya kafin naɗin nashi.

=== Nau'rar Pascaline ===
[[File:Pascaline-CnAM 823-1-IMG 1506-black.jpg|thumb|na'urar [[Pascaline]] na farko a gidan tarihi na [[Musée des Arts et Métiers]], Paris|alt=]]

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.<ref>A complete list of known Pascalines and also a review of contemporary replicas can be found at [http://metastudies.net/pmwiki/pmwiki.php?n=Site.SurvivingPascalines Surviving Pascalines] {{Webarchive|url=https://web.archive.org/web/20211105180308/http://metastudies.net/pmwiki/pmwiki.php?n=Site.SurvivingPascalines |date=2021-11-05 }} and [http://metastudies.net/pmwiki/pmwiki.php?n=Site.ReplicaPascalines Replica Pascalines] {{Webarchive|url=https://web.archive.org/web/20211105181911/http://metastudies.net/pmwiki/pmwiki.php?n=Site.ReplicaPascalines |date=2021-11-05 }} at http://things-that-count.net</ref>
 
=== 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.<ref>{{cite journal|last1=Ross|first1=John F.|year=2004|title=Pascal's legacy|journal=EMBO Reports|volume=5|issue=Suppl 1|pages=S7–S10|doi=10.1038/sj.embor.7400229|pmc=1299210|pmid=15459727}}</ref> 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]]. 
[[Fayil:Blaise Pascal 1423.jpg|thumb|Blaise Pascal]]
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|''probability'']].<ref>Devlin, Keith (2008). ''The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern''. New York: Basic Books. ISBN <bdi>978-0-465-00910-7</bdi>. p. 24

</ref> 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 [[Gottfried Wilhelm Leibniz|Leibniz]] wajen samar da lissafin ''calculus''.<ref>{{cite web|title=The Mathematical Leibniz|url=http://www.math.rutgers.edu/courses/436/Honors02/leibniz.html|access-date=16 August 2009|publisher=Math.rutgers.edu}}</ref>
==== Rubuce-rubuncensa akan Alwatikan Lissafi ''Arithmetical Triangle''====
[[File:PascalTriangleAnimated2.gif|thumb|Alwatikan Pascal. Kowacce lamba tana zaman lambobi biyu dake saman ta. Wannan alwatika ya nuna al'amurran lissafi hadi da nuna ''binomial coefficients''.]]
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).''<ref name=":1">{{Cite book|last=Katz|first=Victor|title=A History of Mathematics: An Introduction|publisher=Addison-Wesley|year=2009|isbn=978-0-321-38700-4|pages=491|chapter=14.3: Elementary Probability}}</ref><ref>{{cite book|url=http://www.bookrags.com/research/pascals-triangle-wom/|title=Pascal's triangle {{!}} World of Mathematics Summary}}</ref>

Teburin shine kamar haka:
{| class="wikitable"
|-
! style="width:20px;" |
! style="width:20px;" |0
! style="width:20px;" |1
! style="width:20px;" |2
! style="width:20px;" |3
! style="width:20px;" |4
! style="width:20px;" |5
! style="width:20px;" |6
|-
|'''0'''|| 1|| 1|| 1|| 1||1||1||1
|-
|'''1'''|| 1 ||2 || 3 || 4 || 5 || 6 ||
|-
|'''2'''||1|| 3 || 6 || 10 || 15 ||  ||
|-
|'''3'''|| 1||4 || 10 || 20 ||  ||  ||
|-
|'''4'''|| 1||5 || 15 ||  ||  ||  ||
|-
|'''5'''|| 1||6 ||  ||  ||  ||  ||
|-
|'''6'''|| 1 ||  ||  ||  ||  ||  ||
|}
Ya kira lambobi acikin alwatikan da [[recursion]]. Ya kira lambobin kamar haka (''m'' + 1)th row da kuma (''n'' + 1)th column ''t<sub>mn</sub>''. Sannan kuma ''t<sub>mn</sub>'' = ''t<sub>m</sub>''<sub>–1,''n''</sub> + ''t<sub>m</sub>''<sub>,''n''–1</sub>, for ''m'' = 0, 1, 2, ... da kuma ''n'' = 0, 1, 2, ... ƙa'idojin iyakokinsu shine ''t<sub>m</sub>''<sub>,−1</sub> = 0, ''t''<sub>−1,''n''</sub> = 0 for ''m'' = 1, 2, 3, ... da kuma ''n'' = 1, 2, 3, ... Mai jawo sila  

<sub>00</sub> = 1. Pascal ya ƙarƙare da hujja,
:<math>t_{mn} = \frac{(m+n)(m+n-1)\cdots(m+1)}{n(n-1)\cdots 1}.</math>





 



  
 



 










 


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== Manazarta ==