P\u0130 SAYISI HAKKINDA<\/p>\n
sembol\u00fc, Yunan alfabesinin 16. harfidir. Bu harf, ayn\u0131 zamanda, Yunanca \u00e7evre (\u00e7ember) anlam\u0131na gelen “perimetier” kelimesinin de ilk harfidir. \u0130svi\u00e7reli matematik\u00e7i Leonard Euler, 1737 y\u0131l\u0131nda yay\u0131nlad\u0131\u011f\u0131 eserinde, daire \u00e7evresinin \u00e7ap\u0131na oran\u0131 s\u00f6z konusu oldu\u011funda, bu sembol\u00fc kulland\u0131. Leonard Euler’den \u00f6nce gelen baz\u0131 matematik\u00e7iler taraf\u0131ndan da, bu sembol kullan\u0131lm\u0131\u015ft\u0131r. Ancak, Leonard Euler’den sonra gelen, t\u00fcm matematik\u00e7iler bu sembol\u00fc benimseyip kulland\u0131lar.
\n Ayr\u0131ca, do\u011fal logaritman\u0131n taban\u0131 olan 2, 71828… say\u0131s\u0131 i\u00e7in, L. Euler’in kulland\u0131\u011f\u0131 e harfi, sembol olarak b\u00fct\u00fcn matematik\u00e7iler taraf\u0131ndan kullan\u0131lmaya ba\u015flanm\u0131\u015f, benimsenmi\u015ftir. Gene, karek\u00f6k i\u00e7inde -1 imajineri i\u00e7in de, L. Euler ile birlikte i sembol\u00fc kullan\u0131lmaya ba\u015flanm\u0131\u015f ve genelle\u015fmi\u015ftir.<\/p>\n
\u0130nsano\u011flu; daire dedi\u011fimiz, kendine \u00f6zg\u00fc d\u00fczg\u00fcn yuvarlak \u015feklin fark\u0131na, tekerle\u011fin icad\u0131ndan \u00e7ok \u00f6nceki tarihlerde varm\u0131\u015ft\u0131r. Bu \u015fekli, di\u011fer insan ve hayvanlar\u0131n g\u00f6zbebekleri ile g\u00f6ky\u00fcz\u00fcndeki G\u00fcne\u015f ve Ayda g\u00f6r\u00fcyordu. Derken, elindeki sopa ile, kum gibi d\u00fczg\u00fcn y\u00fczeylere daire \u00e7izdi. Sonra d\u00fc\u015f\u00fcnd\u00fc; baz\u0131 daireler k\u00fc\u00e7\u00fck, baz\u0131lar\u0131 ise b\u00fcy\u00fck. G\u00f6r\u00fcyordu ki (sezinliyordu ki), dairenin bir ucundan \u00f6teki ucuna olan uzakl\u0131\u011f\u0131 (\u00e7ap\u0131), b\u00fcy\u00fcrse, \u00e7evresi de o kadar b\u00fcy\u00fcyordu. Sonra gene d\u00fc\u015f\u00fcnd\u00fc, cilal\u0131 ta\u015f devri insan\u0131, art\u0131k soyutlamas\u0131n\u0131 yapm\u0131\u015ft\u0131. Dairenin; \u00e7evresinin uzunlu\u011fu ile \u00e7ap\u0131n\u0131n uzunlu\u011fu orant\u0131l\u0131yd\u0131. \u00c7evrenin \u00e7apa oran\u0131, daireden daireye de\u011fi\u015fmiyor, sabit kal\u0131yordu. Demek ki; bug\u00fcnk\u00fc g\u00f6sterim \u015fekliyle, bu sabit orana dersek; \u00c7evre\/\u00c7ap = sabit. \u015eeklinde yaz\u0131labiliyordu.
\n Bu oran\u0131n sabitli\u011fi anla\u015f\u0131ld\u0131ktan sonra, sabit oran de\u011ferinin, say\u0131 olarak belirlenmesi gerekiyordu.<\/p>\n
Pi Say\u0131s\u0131n\u0131n Tarihsel Geli\u015fimi<\/p>\n
Kaynaklar, say\u0131s\u0131 i\u00e7in, ger\u00e7ek de\u011ferin ilk kez Archimides (M.\u00d6. 287-212) taraf\u0131ndan kullan\u0131ld\u0131\u011f\u0131n\u0131 belirtir. Ancak, Archimides’ten \u00f6nce, Eski M\u0131s\u0131rl\u0131lar’da ve Mezopotamya Babil devrinde, Archimiden’den sonra da, 15. y\u00fczy\u0131l T\u00fcrk-\u0130slam D\u00fcnyas\u0131n\u0131n \u00fcnl\u00fc matematik\u00e7isi G\u0131yas\u00fcddin Cem\u015fid (?-Semerkant 1429 ?) taraf\u0131ndan, say\u0131s\u0131 i\u00e7in yakla\u015f\u0131k baz\u0131 de\u011ferler kullan\u0131lm\u0131\u015ft\u0131r.<\/p>\n
Pi say\u0131s\u0131n\u0131n algoritmas\u0131<\/p>\n
EULER Y\u00d6NTEM\u0130 <\/p>\n
CLS<\/p>\n
INPUT “N=”; N
\n T = 0
\n FOR I = 1 TO N
\n T = T + (1 \/ I ^ 2)
\n PI = SQR(6 * T)
\n PRINT “YAKLASIK PI DEGERI=”; PI
\n NEXT I<\/p>\n
LEIBNITZ Y\u00d6NTEM\u0130<\/p>\n
CLS
\n INPUT “N=”; N
\n T = 0
\n C = 1
\n FOR I = 1 TO N
\n T = T + C \/ ((2 * I) – 1)
\n C = (-1) * C
\n PI = 4 * T
\n PRINT “YAKLASIK PI DEGERI=”; PI
\n NEXT I<\/p>\n
LORD BROUNCKER’\u0130N 1. Y\u00d6NTEM\u0130 <\/p>\n
CLS
\n INPUT “N=”; N
\n T = 0
\n C = 1
\n FOR I = 1 TO N
\n T = T + C \/ ((2 * I) – 1)
\n C = (-1) * C
\n PI = 4 * T
\n PRINT “YAKLASIK PI DEGERI=”; PI
\n NEXT I<\/p>\n
LORD BROUNCKER’\u0130N 2. Y\u00d6NTEM\u0130<\/p>\n
CLS
\n INPUT “N=”; N
\n T = 0<\/p>\n
FOR I = 1 TO N
\n T = T + (1 \/ ((2 * I) ^ 2))
\n PI = SQR(24 * T)
\n PRINT “YAKLASIK PI DEGERI=”; PI
\n NEXT I<\/p>\n
VIETA Y\u00d6NTEM\u0130<\/p>\n
CLS
\n INPUT “N=”; N
\n SAY = 1
\n T = 1
\n A = SQR(2)
\n HESAP:
\n T = T * (A \/ 2)
\n SAY = SAY + 1
\n PI = 2 \/ T
\n PRINT “SAY=”; SAY
\n PRINT “YAKLASIK PI DEGERI=”; PI
\n IF SAY > N THEN
\n END
\n END IF
\n A = SQR(A + 2)
\n GOTO HESAP<\/p>\n
WALLIS’\u0130N 1. Y\u00d6NTEM\u0130<\/p>\n
CLS
\n INPUT “N=”; N
\n T = 1<\/p>\n
FOR I = 1 TO N
\n T = T * (2 * I) ^ 2 \/ (((2 * I) + 1) * ((2 * I) – 1))
\n PI = 2 * T
\n PRINT “YAKLASIK PI DEGERI=”; PI
\n NEXT I<\/p>\n
WALLIS’\u0130N 2. Y\u00d6NTEM\u0130<\/p>\n
CLS
\n INPUT “N=”; N
\n T = 1<\/p>\n
FOR I = 1 TO N
\n T = T * (1 – (1 \/ ((2 * I) ^ 2)))
\n PI = 2 \/ T
\n PRINT “YAKLASIK PI DEGERI=”; PI
\n NEXT I…<\/p>\n","protected":false},"excerpt":{"rendered":"
P\u0130 SAYISI HAKKINDA sembol\u00fc, Yunan alfabesinin 16. harfidir. Bu harf, ayn\u0131 zamanda, Yunanca \u00e7evre (\u00e7ember) anlam\u0131na gelen “perimetier” kelimesinin de ilk harfidir. \u0130svi\u00e7reli matematik\u00e7i Leonard Euler, 1737 y\u0131l\u0131nda yay\u0131nlad\u0131\u011f\u0131 eserinde, daire \u00e7evresinin \u00e7ap\u0131na oran\u0131 s\u00f6z konusu oldu\u011funda, bu sembol\u00fc kulland\u0131. Leonard Euler’den \u00f6nce gelen baz\u0131 matematik\u00e7iler taraf\u0131ndan da, bu sembol kullan\u0131lm\u0131\u015ft\u0131r. Ancak, Leonard Euler’den sonra …<\/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":[7255,7232,7406,7404,7405],"class_list":["post-3177","post","type-post","status-publish","format-standard","hentry","category-matematik-odevleri","category-odevler","tag-giyasuddin-cemsid","tag-logaritma","tag-pi-sayisinin-algoritmasi","tag-pi-sayisinin-bulunmasi","tag-pi-sayisinin-tarihsel-gelisimi"],"_links":{"self":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3177","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=3177"}],"version-history":[{"count":0,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/posts\/3177\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/media?parent=3177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/categories?post=3177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.islamidavet.com\/kutuphane\/wp-json\/wp\/v2\/tags?post=3177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}