Nas\u0131l bir pi say\u0131s\u0131? \u00d6rne\u011fin : m ve n birer tam say\u0131 olmak \u00fczere, pi nin de\u011feri m\/n \u015feklinde yaz\u0131labilir mi? yani p nin de\u011feri rasyonel bir say\u0131 m\u0131d\u0131r?
\n Ba\u015flang\u0131\u00e7ta, matematik\u00e7iler bu y\u00f6nde \u00fcmitliydiler. pi nin bu kadar \u00e7ok ondal\u0131k k\u0131sm\u0131n\u0131n hesaplanmas\u0131n\u0131n nedenlerinden biri de, buydu herhalde. Matematik\u00e7iler bekliyorlard\u0131 ki, bir yerden sonra, basamaklar \u00f6nceki de\u011ferlerini tekrar etsin, yani devirli bir ondal\u0131k say\u0131 halinde yaz\u0131labilsin. Ama bu olmad\u0131, Sonunda, 1761 y\u0131l\u0131nda, \u0130svi\u00e7re’li matematik\u00e7i Lambert, pi nin irrasyonel oldu\u011funu, yani dairenin \u00e7evresi ile \u00e7ap\u0131n\u0131n bir ortak \u00f6l\u00e7\u00fcs\u00fc olmad\u0131\u011f\u0131n\u0131 ispatlad\u0131.<\/p>\n
Pi Say\u0131s\u0131n\u0131n \u00dcstelli\u011fi:<\/p>\n
pi say\u0131s\u0131na ait de\u011ferin, gittik\u00e7e daha fazla basama\u011f\u0131n\u0131 hesaplama tutkusunun yan\u0131 s\u0131ra, matematik\u00e7ilerin r\u00fcyalar\u0131na giren ba\u015fka bir pi problemi de, daireyi kare yapma problemiydi. Bu u\u011fra\u015f\u0131ya, kendilerini kapt\u0131ranlar\u0131n \u00f6nderi Anaksagoras’t\u0131r (M.\u00d6. 500-428) Bir ara Atina’da, z\u0131nd\u0131kl\u0131kla su\u00e7lan\u0131p hapse at\u0131lan Anaksagoras, burada can s\u0131k\u0131nt\u0131s\u0131ndan, daireyi kare yapman\u0131n yollar\u0131n\u0131 aramaya ba\u015flar. Kendisinin \u00e7\u00f6zd\u00fc\u011f\u00fcn\u00fc sand\u0131\u011f\u0131, baz\u0131 yakla\u015f\u0131k sonu\u00e7lar elde eder. Daha sonra, Kilyos’lu Hippokrates (M.\u00d6. 5. y\u00fczy\u0131ll\u0131n ikinci yar\u0131s\u0131) , a\u015fa\u011f\u0131daki \u015fekilde taranm\u0131\u015f ACBA alan\u0131n\u0131n, AOB \u00fc\u00e7genin alan\u0131na e\u015fit oldu\u011funu g\u00f6sterir Buna benzer ba\u015fka \u00f6rnekler g\u00f6sterir ki, belli e\u011frilerle s\u0131n\u0131rlanm\u0131\u015f, baz\u0131 b\u00f6lgelerin alanlar\u0131na e\u015fit alanda kareler \u00e7izilebilir.
\n 18. y\u00fczy\u0131l\u0131n sonlar\u0131ndan ba\u015flayan dairenin kare yap\u0131lmas\u0131n\u0131n imkans\u0131z oldu\u011fu fikri, matematik\u00e7ilere hakim oldu. Bu ku\u015fku o kadar b\u00fcy\u00fck ki, 1775 te, Paris Bilimler Akademisi, devr-i daim makinesi projeleri, a\u00e7\u0131y\u0131 pergel ve cetvel kullanarak \u00fc\u00e7 e\u015fit par\u00e7aya b\u00f6lme y\u00f6ntemlerinin yan\u0131 s\u0131ra daireyi kare yapma y\u00f6ntemlerini de, art\u0131k inceleme karar\u0131 ald\u0131.
\n 1775 te Euler, 1794 te Legendra, pi nin belki de, cebirsel bir say\u0131 olmad\u0131\u011f\u0131na, \u00fcstel bir say\u0131 olmas\u0131 gerekti\u011fine ili\u015fkin inan\u00e7lar\u0131n\u0131 belirtirler. Fakat pi nin \u00fcstel oldu\u011funun kan\u0131tlanmas\u0131 i\u00e7in, 100 y\u0131l beklendi. Sonunda, 1882 y\u0131l\u0131nda, Alman matematik\u00e7i Lindermann, pi nin \u00fcstel oldu\u011funu ispatlad\u0131<\/p>\n","protected":false},"excerpt":{"rendered":"
Nas\u0131l bir pi say\u0131s\u0131? \u00d6rne\u011fin : m ve n birer tam say\u0131 olmak \u00fczere, pi nin de\u011feri m\/n \u015feklinde yaz\u0131labilir mi? yani p nin de\u011feri rasyonel bir say\u0131 m\u0131d\u0131r? Ba\u015flang\u0131\u00e7ta, matematik\u00e7iler bu y\u00f6nde \u00fcmitliydiler. pi nin bu kadar \u00e7ok ondal\u0131k k\u0131sm\u0131n\u0131n hesaplanmas\u0131n\u0131n nedenlerinden biri de, buydu herhalde. Matematik\u00e7iler bekliyorlard\u0131 ki, bir yerden sonra, basamaklar \u00f6nceki …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1404,1403],"tags":[3424,7209],"class_list":["post-3030","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-matematik","tag-pi-sayisinin-irrasyonelligi"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3030","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/comments?post=3030"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3030\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3030"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3030"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3030"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}