{"id":1206,"date":"2018-02-21T16:07:52","date_gmt":"2018-02-21T13:07:52","guid":{"rendered":"http:\/\/www.akademikidea.org\/a-kitap\/?p=1206"},"modified":"2026-07-07T02:05:33","modified_gmt":"2026-07-06T23:05:33","slug":"euler-ozdesligi","status":"publish","type":"post","link":"https:\/\/www.akademikidea.org\/a-kitap\/euler-ozdesligi\/","title":{"rendered":"Be\u015fi Bir Yerde"},"content":{"rendered":"\nMatemati\u011fin be\u015f temel sabiti,\n<ol><li>do\u011fal logaritman\u0131n taban\u0131 <i>e<\/i> a\u015fk\u0131n say\u0131s\u0131n\u0131,<\/li>\n<li>sanal birim \\(i=\\sqrt{-1}&#8217;\\)i,<\/li>\n<li> bir dairenin \u00e7evresinin \u00e7ap\u0131na oran\u0131 olan a\u015fk\u0131n say\u0131 \\(\\pi&#8217;\\)yi<\/li>\n<li>\u00e7arpma i\u015fleminde etkisiz eleman olan ilk do\u011fal say\u0131 \\(1&#8217;\\)i <\/li>\n<li>toplama i\u015fleminde etkisiz eleman olan ilk tam say\u0131 \\(0&#8217;\\)\u0131 <\/ol>\ntek bir denklemde birle\u015ftiren $$e^{\\pi i}+1=0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)  $$<p><i> Euler \u00f6zde\u015fli\u011fi<\/i>, estetik a\u00e7\u0131dan matemati\u011fin en g\u00fczel denklemlerinden biridir. <p><\/p>Euler \u00f6zde\u015fli\u011finin, \\( \\theta = \\pi \\) i\u00e7in, genel durumu olan $$e^{\\theta i}=\\cos \\theta + i \\sin \\theta. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)$$ <i>Euler form\u00fcl\u00fc<\/i> ile, matematik ve m\u00fchendislik alanlar\u0131nda kar\u015f\u0131la\u015f\u0131lan karma\u015f\u0131k fonksiyonlarla ilgili i\u015flemler basitle\u015fir: <ul><li>\\(\\cos (\\alpha + \\beta)= \\cos \\alpha \\cos \\beta &#8211; \\sin \\alpha \\sin \\beta \\)  ve  \\(\\sin (\\alpha + \\beta) = \\sin \\alpha \\cos \\beta + \\cos \\alpha \\sin \\beta \\)  \u00f6zde\u015flikleri \\(e^{i(\\alpha+\\beta)}=e^{i\\alpha}e^{i\\beta}\\) kullan\u0131larak kolayca ispatlan\u0131r, <\/li> <li> Ses, g\u00f6r\u00fcnt\u00fc, ve haberle\u015fme sistemlerinde sinyaller \\(Ae^{i\\omega t}\\) bi\u00e7iminde modellenir; Fourier serileri \u00f6zl\u00fc ve s\u0131k\u0131 olarak, \\(f(x)=\\sum_{n=-\\infty} ^{\\infty} c_n e^{inx}\\) bi\u00e7iminde yaz\u0131labilir,<\/li> <li> Kutupsal g\u00f6sterimle \\(z = re^{i\\theta}\\) karma\u015f\u0131k say\u0131s\u0131n\u0131n <i>n<\/i>&#8216;inci kuvveti \\(z^n=r^n e^{in\\theta}\\) \u00f6rne\u011finde oldu\u011fu gibi, karma\u015f\u0131k analizde, \u00fcs ve k\u00f6k alma i\u015flemleri kolayla\u015f\u0131r. <\/li><\/ul>\n&#8220;Beyin taramalar\u0131, matematiksel form\u00fcllerdeki karma\u015f\u0131k say\u0131 ve harf dizilerinin, sanat eserlerinin ve en b\u00fcy\u00fck bestecilerin m\u00fcziklerinin uyand\u0131rd\u0131\u011f\u0131 g\u00fczellik duygusunun ayn\u0131s\u0131n\u0131 uyand\u0131rabilece\u011fini g\u00f6steriyor.&#8221; [1] Diferansiyel denklem sistemleri de dahil olmak \u00fczere daha bir\u00e7ok uygulama alan\u0131 olan, ve teorik fizik\u00e7i\n<style>\n    .container {\n        display: flex;\n        align-items: center;\n        justify-content: space-between;\n    }\n<\/style>\n<div class=\"container\">\n    <img decoding=\"async\" src=\"https:\/\/www.akademikidea.org\/a-kitap\/wp-content\/uploads\/2026\/07\/Leonhard-Euler-6.png\" alt=\"Leonhard Euler\">  \n       Richard Feynman (1918-1988)&#8217;\u0131n &#8220;Matemati\u011fin en dikkate de\u011fer form\u00fcl\u00fc&#8221;, &#8220;M\u00fccevherimiz&#8221; dedi\u011fi Euler form\u00fcl\u00fcn\u00fcn ve \u00f6zde\u015fli\u011finin kan\u0131tlanmas\u0131 da, matematiksel bir senfoni gibidir. <br>\n<br>\u015eimdi, Leonhard Euler (1701-1788)&#8217;\u0131n 1748&#8217;de yay\u0131mlanan an\u0131tsal<br> <\/div> matematiksel analiz eseri <i>Introductio in analysin infinitorum<\/i>&#8216;da dile getirilen Euler form\u00fcl\u00fcn\u00fcn do\u011frudan bir sonucu olan Euler \u00f6zde\u015fli\u011finin, bile\u015fenleri ile ilgili temel bilgileri hat\u0131rlatarak bu senfoniyi icra etmeye ba\u015flayaca\u011f\u0131z.\n\n\n\n<p><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Ba\u015fvurular<\/h2>\n\n\n\n[1] <a href=\"https:\/\/www.bbc.com\/news\/science-environment-26151062\">Gallagher, James (2014) Mathematics: Why the brain sees maths as beauty<\/a>\n<a href=\"https:\/\/www.ryansmath.com\/Euler.pdf\">Hausner, Ryan (1925) Proof of Euler&#8217;s Identity and Formula<\/a>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Matemati\u011fin be\u015f temel sabiti, do\u011fal logaritman\u0131n taban\u0131 e a\u015fk\u0131n say\u0131s\u0131n\u0131, sanal birim \\(i=\\sqrt{-1}&#8217;\\)i, bir dairenin \u00e7evresinin \u00e7ap\u0131na oran\u0131 olan a\u015fk\u0131n say\u0131 \\(\\pi&#8217;\\)yi \u00e7arpma i\u015fleminde etkisiz eleman olan ilk do\u011fal say\u0131 \\(1&#8217;\\)i toplama i\u015fleminde etkisiz eleman olan ilk tam say\u0131 \\(0&#8217;\\)\u0131 tek bir denklemde birle\u015ftiren $$e^{\\pi i}+1=0 . . . . . . . . &#8230;.<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[26],"tags":[],"class_list":["post-1206","post","type-post","status-publish","format-standard","hentry","category-matematik"],"_links":{"self":[{"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/posts\/1206","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/comments?post=1206"}],"version-history":[{"count":191,"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/posts\/1206\/revisions"}],"predecessor-version":[{"id":2730,"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/posts\/1206\/revisions\/2730"}],"wp:attachment":[{"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/media?parent=1206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/categories?post=1206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.akademikidea.org\/a-kitap\/wp-json\/wp\/v2\/tags?post=1206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}