Bal\u0131kesir\u2019in Edremit il\u00e7esinde ya\u015fayan Ara\u015ft\u0131rmac\u0131-Yazar ve Emekli Fen Bilgisi \u00d6\u011fretmeni H\u00fcseyin Erg\u00fcl, her y\u0131l 14 Mart tarihinde kutlanan, g\u00fcn\u00fc bile olan \u201cPi Say\u0131s\u0131\u201d hesaplamalar\u0131yla silindir \u015feklindeki kaplar\u0131n hacimlerinin asl\u0131nda milyonlarca liral\u0131k haks\u0131z kazan\u00e7lar\u0131 beraberinde getirdi\u011fini savundu.<\/p>\n
Ge\u00e7ti\u011fimiz aylarda; \u201cCisimlerin 4. Boyutunu\u201d ke\u015ffetti\u011fini iddia ederek \u00fclke genelinde b\u00fcy\u00fck yank\u0131 uyand\u0131ran H\u00fcseyin Erg\u00fcl, bu kez de \u201cPi Say\u0131s\u0131\u201d ile ilgili \u00f6nemli a\u00e7\u0131klamalarda bulundu.<\/p>\n
Pi say\u0131s\u0131n\u0131n herhangi bir dairenin \u00e7evresini \u00e7ap\u0131na b\u00f6l\u00fcnd\u00fc\u011f\u00fcnde ortaya \u00e7\u0131kan A say\u0131s\u0131n\u0131n B\u2019ye b\u00f6l\u00fcm\u00fcyle ortaya \u00e7\u0131kan bir uzunluk oran\u0131 oldu\u011funu hat\u0131rlatan Erg\u00fcl, \u201cBunun da yakla\u015f\u0131k de\u011feri; 22 b\u00f6l\u00fc 7\u2019dir. 22\u2019yi , 7\u2019ye b\u00f6ld\u00fc\u011f\u00fcm\u00fcz zaman 3,14 ve bir bu\u00e7uk sayfa s\u00fcren bir rakamlar say\u0131s\u0131 ortaya \u00e7\u0131kar. Dolay\u0131s\u0131yla da Pi say\u0131s\u0131na gerek olmadan herhangi bir dairenin alan\u0131n\u0131 kendi geli\u015ftirdi\u011fim bir ba\u015fka form\u00fcl ile bulabilmemiz m\u00fcmk\u00fcnd\u00fcr\u201d dedi.<\/p>\n
H\u00fcseyin Erg\u00fcl, \u201cHerhangi bir daire \u00e7izdikten sonra, o daireye d\u0131\u015ftan te\u011fet bir d\u00f6rtgen \u00e7izerek s\u00f6z konusu d\u00f6rtgenin uzunlu\u011fu ile \u00e7ap\u0131n uzunlu\u011fu e\u015fit oldu\u011fu i\u00e7in bu bir karedir. Karenin alan\u0131, bir kenar uzunlu\u011funun kendisi ile \u00e7arp\u0131m\u0131na e\u015fittir. Yani burada \u00e7ap\u0131n kendisi ile \u00e7arp\u0131m\u0131na e\u015fittir. \u00c7ap\u0131 da bir bu karenin bir kenar uzunlu\u011funa e\u015fittir. Buradan hareketle; \u00e7izdi\u011fimiz d\u00f6rtgen \u00fczerindeki par\u00e7alara bak\u0131ld\u0131\u011f\u0131nda; b\u00fct\u00fcn par\u00e7alar\u0131na e\u015fittir. Yani b\u00fcy\u00fck karenin alan\u0131 4 adet X ve 4 adet Y ve 4 adet 0.5 r karenin toplam\u0131na e\u015fittir. Bundan en ufak bir \u015f\u00fcphe edilebilmesi m\u00fcmk\u00fcn de\u011fildir. Bu noktada; b\u00fcy\u00fck karenin alan\u0131ndan 4 adet Y\u2019yi \u00e7\u0131kard\u0131\u011f\u0131n\u0131zda, geriye dairenin alan\u0131 kal\u0131r. Bu birinci y\u00f6ntemdir. Bunun d\u0131\u015f\u0131nda ikinci y\u00f6ntem ise; yine \u2018B\u00fct\u00fcn par\u00e7alar\u0131na e\u015fittir\u2019 ilkesiyle yola \u00e7\u0131kt\u0131\u011f\u0131m\u0131zda, \u00e7izdi\u011fimiz dairenin alan\u0131 i\u00e7erideki karenin alan\u0131; 4 adet X\u2019in toplam\u0131yla ortaya \u00e7\u0131kmaktad\u0131r. Bu da dairenin alan\u0131na e\u015fittir. O halde iki alan\u0131n birbirine olan e\u015fitli\u011finden \u2018Da=2r kare+4x\u2019 form\u00fcl\u00fcn\u00fc elde etmi\u015f oluruz. T\u00fcm bunlar\u0131n d\u0131\u015f\u0131nda \u00e7izdi\u011fimiz \u015fekilde dairenin i\u00e7erisindeki karenin 4\u2019te 1\u2019i yar\u0131 \u00e7ap\u0131 uzunlu\u011funda yine k\u00fc\u00e7\u00fck bir karedir. Bu karenin alan\u0131 0.5r kare+X+Y\u2019dir. Burada X ve Y bilinmeyen say\u0131lard\u0131r. Bu bilinmeyenleri ara i\u015flemlerle bularak, 4 kat\u0131n\u0131 al\u0131r ilave ederiz. Bahsetti\u011fim form\u00fcllere uygun olarak, burada X\u2019in de\u011feri, k\u00fc\u00e7\u00fck karenin 1 b\u00f6l\u00fc 6\u2019s\u0131na e\u015fit olur. Bundan 4 adet oldu\u011fu i\u00e7in 4 ile \u00e7arp\u0131yorum ve sonu\u00e7ta dairenin alan\u0131 2r kare+2b\u00f6l\u00fc3 2r kare olarak kar\u015f\u0131m\u0131za \u00e7\u0131k\u0131yor. G\u00f6r\u00fcld\u00fc\u011f\u00fc \u00fczere Pi say\u0131s\u0131na ihtiya\u00e7 duymadan dairenin alan\u0131n\u0131 yar\u0131\u00e7ap\u0131 karesi \u00fczerinden bulabiliyoruz\u201d ifadelerini kulland\u0131.<\/p>\n
Pi say\u0131s\u0131n\u0131 kullanmadan buldu\u011fu form\u00fcl sayesinde daire bi\u00e7iminde g\u00f6r\u00fclen t\u00fcm \u015fekil ve cisimlerde alan hesaplar\u0131 yap\u0131l\u0131rken Pi Say\u0131s\u0131na gerek olmadan alanlar\u0131n bulunabilece\u011fini savunan Erg\u00fcl, \u201cBu sayede, yery\u00fcz\u00fcnde daire \u015feklinde ve buna ba\u011fl\u0131 olarak silindir \u015feklindeki t\u00fcm cisimlerin yada b\u00fcy\u00fck \u00e7apta f\u0131\u00e7\u0131lar\u0131n, tankerlerin, silolar\u0131n hacimlerinin hesap edilmesinde y\u00fczde 15\u2019lik bir hata pay\u0131 ortadan kalkacakt\u0131r. Yani ger\u00e7ek de\u011ferine ula\u015f\u0131lacakt\u0131r\u201d dedi.<\/p>\n
\u201cAradaki y\u00fczde 15\u2019lik fark, t\u00fcketiciye fazlal\u0131k olarak yans\u0131yor\u201d<\/p>\n
Taban\u0131 daire \u015feklinde olan herhangi bir silindirin hacmini hesaplayabilmek i\u00e7in y\u00fckseklikle \u00e7arp\u0131lmas\u0131 gerekti\u011fini kaydeden H\u00fcseyin Erg\u00fcl, \u201cBu hesaplamay\u0131 Pi Say\u0131s\u0131 ile yap\u0131yorsak ortaya farkl\u0131 bir say\u0131 \u00e7\u0131k\u0131yor, benim \u00f6nerdi\u011fim form\u00fcl ile bunu hesaplarsak ortaya farkl\u0131 bir say\u0131 \u00e7\u0131k\u0131yor. \u0130kisi aras\u0131nda y\u00fczde 15\u2019lik bir fark vard\u0131r. \u015eayet biz, silindir \u015feklindeki kaplarda farkl\u0131 iki \u015fekilde de yap\u0131yorsak aradaki y\u00fczde 15\u2019lik fark, t\u00fcketiciye fazlal\u0131k olarak yans\u0131yor. \u00d6rne\u011fin 5 litrelik bir su kab\u0131na zeytinya\u011f\u0131n\u0131 koydu\u011funuzda, kar\u015f\u0131m\u0131za tam olarak 5 litre zeytinya\u011f\u0131 \u00e7\u0131kmaz. 4 bu\u00e7uk litre civar\u0131nda bir zeytinya\u011f\u0131 olarak \u00e7\u0131kar. Kilogram baz\u0131nda buna bak\u0131ld\u0131\u011f\u0131nda, 1 kilogram\u0131n yerine daha k\u00fc\u00e7\u00fck oranda bir zeytinya\u011f\u0131 ile kar\u015f\u0131la\u015f\u0131r\u0131z. \u00c7\u00fcnk\u00fc zeytinya\u011f\u0131n\u0131n yo\u011funlu\u011fu farkl\u0131d\u0131r. 0.9\u2019dur. Ayn\u0131 kapa benzin koydu\u011funuzda bu oran daha d\u00fc\u015f\u00fckt\u00fcr. Eter koyuldu\u011funda bu yo\u011funluk daha da d\u00fc\u015f\u00fckt\u00fcr. Bunlar\u0131n k\u00fctleleri birbirinden farkl\u0131d\u0131r. Bu farkl\u0131l\u0131klar g\u00fcncel ekonomik hayata para olarak yans\u0131r. Mesela 100 liral\u0131k bir zeytinya\u011f\u0131 sat\u0131n al\u0131nd\u0131\u011f\u0131nda, vatanda\u015flardan 10 lira fazla para al\u0131nm\u0131\u015f oluyor. Bu durum sadece zeytinya\u011f\u0131nda de\u011fil; silindir \u015feklinde paketlenmi\u015f kolonya, alkol, benzin gibi t\u00fcm likit \u00fcr\u00fcnlerde ayn\u0131d\u0131r\u201d diye konu\u015ftu.<\/p>\n
Kendi geli\u015ftirdi\u011fi form\u00fcl\u00fcn g\u00fcncel hayatta kullan\u0131lmas\u0131 halinde bu olumsuzlu\u011fun tamamen ortadan kalkaca\u011f\u0131n\u0131 belirten H\u00fcseyin Erg\u00fcl, \u201c\u00c7\u00fcnk\u00fc Pi Say\u0131s\u0131 ile hesaplanan dairenin alan\u0131 y\u00fczde 15 fark etti\u011fi gibi, y\u00fckseklikle \u00e7arpt\u0131\u011f\u0131m\u0131zda hacmi de y\u00fczde 15 oran\u0131nda fark ediyor. Yani bu olumsuzluk ayn\u0131 zamanda hacime de yans\u0131yor. Dolay\u0131s\u0131yla i\u00e7indeki maddeye yans\u0131yor. T\u00fcm bunlar da halk\u0131n cebine yans\u0131yor. Yani bu t\u00fcr \u00fcr\u00fcnler vatanda\u015fa pahall\u0131ya patl\u0131yor. Milletin cebinden y\u00fczde 15 oran\u0131nda fazla para \u00e7\u0131km\u0131\u015f oluyor. Bunun da ad\u0131; \u2018haks\u0131z kazan\u00e7\u2019 oluyor\u201d dedi.<\/p>\n
\u201cBenim buldu\u011fum form\u00fcl\u00fc ortaya koyabilmek i\u00e7in klasik matemati\u011fin baz\u0131 kurallar\u0131n\u0131 \u00e7i\u011fnemek gerekiyor\u201d<\/p>\n
A\u00e7\u0131klamalar\u0131ndan Pi Say\u0131s\u0131\u2019n\u0131n b\u00fcy\u00fck bir hile oldu\u011funa ait bir anlam \u00e7\u0131kar\u0131lmamas\u0131 gerekti\u011finin alt\u0131n\u0131 \u00e7izen H\u00fcseyin Erg\u00fcl, \u201cBenim form\u00fcl\u00fcm bilinmedi\u011fi i\u00e7in, kullan\u0131lmad\u0131\u011f\u0131 i\u00e7in \u015fu anda bu alanda bilinen Pi Say\u0131s\u0131 kullan\u0131ld\u0131\u011f\u0131 i\u00e7in \u015fu anda mevcut durum budur. \u015eunu da \u00f6zellikle ifade etmek isterim ki; benim buldu\u011fum form\u00fcl\u00fc ortaya koyabilmek i\u00e7in klasik matemati\u011fin baz\u0131 kurallar\u0131n\u0131 \u00e7i\u011fnemek gerekiyor. Mesela klasik matematik de, bir i\u015flem yap\u0131l\u0131rken; \u2018parantez d\u0131\u015f\u0131nda eksi i\u015fareti varsa, i\u00e7indekiler ters olarak ortaya \u00e7\u0131kar\u2019 denilir. Oysa benim modelimde; parantezin d\u0131\u015f\u0131nda eksi yada art\u0131 i\u015fareti olsun fark etmez, hangi i\u015fareti ta\u015f\u0131yorsa o \u015fekilde sonu\u00e7 al\u0131n\u0131r. Ben klasik matematikteki o kural\u0131 y\u0131karak, \u00f6nerdi\u011fim kural\u0131 getiriyorum. Dolay\u0131s\u0131yla bu bir matematik modelidir. Bu modele ba\u011fl\u0131 olarak ortaya bunlar \u00e7\u0131k\u0131yor. Yoksa \u015fimdiye kadar \u00e7o\u011fu insan bunu s\u00f6yleyebilecekti. Ama bunlar\u0131 dile getirebilmek, bilinen klasik matematik kuramlar\u0131yla bunlar\u0131 dile getirebilmek imk\u00e2ns\u0131zd\u0131r. Benim buldu\u011fum ve \u0130msulatif Matematik\u2019 ad\u0131n\u0131 verdi\u011fim kuramda her kural, yarat\u0131l\u0131\u015fa uygundur. \u00c7\u00fcnk\u00fc \u015fu anda bilinenin aksine do\u011fal say\u0131 diye bir \u015fey yoktur. \u015eu anda bilinen say\u0131lar\u0131n hepsi sembolik say\u0131lard\u0131r\u201d ifadelerini kulland\u0131.<\/p>\n","protected":false},"excerpt":{"rendered":"
BALIKES\u0130R\u2019\u0130N EDREM\u0130T \u0130L\u00c7ES\u0130NDE YA\u015eAYAN ARA\u015eTIRMACI-YAZAR VE EMEKL\u0130 FEN B\u0130LG\u0130S\u0130 \u00d6\u011eRETMEN\u0130 H\u00dcSEY\u0130N ERG\u00dcL, HER YIL 14 MART TAR\u0130H\u0130NDE KUTLANAN, G\u00dcN\u00dc B\u0130LE OLAN \u201cP\u0130 SAYISI\u201d HESAPLAMALARIYLA S\u0130L\u0130ND\u0130R \u015eEKL\u0130NDEK\u0130 KAPLARIN HAC\u0130MLER\u0130N\u0130N ASLINDA M\u0130LYONLARCA L\u0130RALIK HAKSIZ KAZAN\u00c7LARI BERABER\u0130NDE GET\u0130RD\u0130\u011e\u0130N\u0130 SAVUNDU.<\/p>\n","protected":false},"author":1,"featured_media":239195,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[24],"tags":[59864,3155,611],"class_list":["post-239194","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-teknoloji","tag-matematikte","tag-gereksiz","tag-sayisi"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/www.tvturk.com\/wp-content\/uploads\/2019\/12\/matematikte-pi-sayisi-gereksiz_f679a2f.jpg?fit=1000%2C666","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/paKIfm-10dY","_links":{"self":[{"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/posts\/239194","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/comments?post=239194"}],"version-history":[{"count":0,"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/posts\/239194\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/media\/239195"}],"wp:attachment":[{"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/media?parent=239194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/categories?post=239194"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.tvturk.com\/index.php\/wp-json\/wp\/v2\/tags?post=239194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}