﻿{"id":6380,"date":"2016-04-17T14:02:17","date_gmt":"2016-04-17T11:02:17","guid":{"rendered":"http:\/\/www.karadenizli.biz\/yaren\/?p=6380"},"modified":"2016-06-27T12:28:11","modified_gmt":"2016-06-27T09:28:11","slug":"ramanujan-ve-1729un-hikayesi","status":"publish","type":"post","link":"https:\/\/www.karadenizli.biz\/yaren\/ramanujan-ve-1729un-hikayesi\/","title":{"rendered":"Ramanujan Ve 1729&#8217;un Hikayesi"},"content":{"rendered":"<p><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6381\" data-permalink=\"https:\/\/www.karadenizli.biz\/yaren\/ramanujan-ve-1729un-hikayesi\/ramanujan\/\" data-orig-file=\"https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2016\/04\/ramanujan.jpg?fit=300%2C395&amp;ssl=1\" data-orig-size=\"300,395\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"ramanujan\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2016\/04\/ramanujan.jpg?fit=300%2C395&amp;ssl=1\" class=\"alignleft size-full wp-image-6381\" src=\"https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2016\/04\/ramanujan.jpg?resize=300%2C395&#038;ssl=1\" alt=\"ramanujan\" width=\"300\" height=\"395\" srcset=\"https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2016\/04\/ramanujan.jpg?w=300&amp;ssl=1 300w, https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2016\/04\/ramanujan.jpg?resize=228%2C300&amp;ssl=1 228w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/>Y\u0131llar \u00f6nce Bilim Teknik dergisinde okudu\u011fum bu hikayeyle tekrar kar\u015f\u0131la\u015f\u0131nca sizlerle de payla\u015fmak istedim. 1729&#8217;un hikayesine ba\u015flamadan \u00f6nce hikayenin kahraman\u0131 hakk\u0131nda biraz bilgi edinelim.<\/p>\n<p>Srinivasa Aiyangar Ramanujan G\u00fcney Hindistan&#8217;da, kast sisteminde en y\u00fcksek tabaka olan Brahman bir ailede do\u011far. Ailesinin maddi durumu pek iyi de\u011fildir. Vefat\u0131ndan \u00e7ok daha sonra hakk\u0131nda bir kitap yazan abisi \u00e7ok zor ve gururlu bir \u00e7ocuk oldu\u011funu s\u00f6yl\u00fcyor. Matemati\u011fe olan ilgisi \u00e7ok k\u00fc\u00e7\u00fck ya\u015f\u0131ndan g\u00f6stermi\u015f kendini. \u00c7ok \u00e7abuk hesap yapabilen, okula ba\u015flad\u0131\u011f\u0131 ilk y\u0131llarda \u00f6d\u00fcller kazanan bir \u00e7ocukmu\u015f.<\/p>\n<p>Matemati\u011fe olan ilgisi, ve sadece matemati\u011fe ve matematikle ilgili olan derslere merak\u0131 \u00fcniversiteye girmesine engel.<\/p>\n<p>Evden ka\u00e7may\u0131 denemi\u015f, \u00fcniversite de\u011fi\u015ftirmi\u015f, di\u011fer derslerden yine kald\u0131\u011f\u0131 i\u00e7in burs hakk\u0131n\u0131 kaybetmi\u015f. Sonunda i\u00e7ine kapan\u0131k olarak tabir edilebilecek birisi olmu\u015f. \u0130ki y\u0131l hi\u00e7 d\u0131\u015far\u0131 \u00e7\u0131kmadan eve kapatm\u0131\u015f kendini. Bu zaman zarf\u0131nda bir \u015fekilde eline ge\u00e7mi\u015f olan ne herhangi bir a\u00e7\u0131klama, ne bir ispat bulunduran bir form\u00fcl kitap\u00e7\u0131\u011f\u0131n\u0131 okumu\u015f durmu\u015f.<\/p>\n<p>20 ya\u015f\u0131na geldi\u011finde annesi onu evlendirmeye karar vermi\u015f. Art\u0131k evli bir adam oldu\u011funda evine ekmek getirmek i\u00e7in i\u015f aramak zorunda kalm\u0131\u015f. Pek dikkat, \u00f6zen gerektirmeyen bir i\u015fe girmi\u015f, bo\u015f vakitlerinde form\u00fcller yaz\u0131p \u00e7izmeye devam etmi\u015f.<\/p>\n<p>Bunlar\u0131 ilk kez 21 ya\u015f\u0131nda \u0130ngiltere&#8217;ye zaman\u0131n \u00fcnl\u00fc matematik\u00e7ilerine g\u00f6ndermi\u015f. Birka\u00e7 cevaps\u0131z mektuptan sonra Godfrey Hardy&#8217;den cevap gelmi\u015f. Hardy ve Littlewood ile birlikte Ramanujan&#8217;in g\u00f6nderdi\u011fi baz\u0131 form\u00fcllerin ispatland\u0131\u011f\u0131n\u0131, ama di\u011ferlerinin ispatlanamayacak kadar zor olduklar\u0131n\u0131 farketmi\u015f ve kendisini \u0130ngiltere&#8217;ye davet etmi\u015f.<\/p>\n<p>\u0130lk ba\u015flarda yine dinsel sebeplerden \u00f6t\u00fcr\u00fc ailesinin kars\u0131 \u00e7\u0131kmas\u0131na ra\u011fmen (Brahmanlar\u0131n su \u00fcst\u00fcnden ge\u00e7me yasa\u011f\u0131, yurtd\u0131\u015f\u0131nda uygulayamayaca\u011f\u0131 rit\u00fcel yemek talimat\u0131 vs.) onlar\u0131 ikna etmesini ba\u015far\u0131r ve 1913 y\u0131l\u0131nda \u0130ngiltere&#8217;ye gider.<\/p>\n<p>Hardy&#8217;nin yard\u0131mlar\u0131yla Trinity College&#8217;de e\u011fitimini en iyi \u015fekilde tamamlar, bir\u00e7ok form\u00fcl alt\u0131na imzas\u0131n\u0131 atar. Ramanujan buldu\u011fu form\u00fcllere gece r\u00fcyas\u0131nda kanl\u0131 harflerle duvara yaz\u0131l\u0131 \u015fekilde g\u00f6rd\u00fc\u011f\u00fcn\u00fc s\u00f6yler, Hardy&#8217;ye bu form\u00fcllere ispatlamak ya da ispatlamaya \u00e7al\u0131\u015fmak kal\u0131r.<\/p>\n<p>Gen\u00e7 ya\u015f\u0131nda yakaland\u0131\u011f\u0131 verem hastal\u0131\u011f\u0131 sebebiyle 18 ay\u0131n\u0131 bir sanatoryumda ge\u00e7irmek zorunda kal\u0131r. \u00c7\u0131kt\u0131ktan sonra kendini hem hastal\u0131\u011f\u0131ndan \u00f6t\u00fcr\u00fc, hem yaln\u0131zl\u0131ktan, memleket hasretinden, hem al\u0131\u015famad\u0131\u011f\u0131 hava ko\u015fullar\u0131ndan, yemeklerden \u00f6t\u00fcr\u00fc olsa gerek kendini o kadar k\u00f6t\u00fc hisseder ki bir Londra&#8217;da metronun \u00f6n\u00fcne atlayarak intihara te\u015febb\u00fcs eder, kurtar\u0131l\u0131r.<\/p>\n<p>Tekrar hastaneye kald\u0131r\u0131l\u0131r. Burada efsanevi 1729 hik\u00e2yesi ya\u015fan\u0131r. Bu numara Hardy&#8217;nin kendisini ziyarete gelirken bindi\u011fi taksinin numaras\u0131d\u0131r ve Ramanujan taksinin numaras\u0131na bak\u0131p, &#8216;\u00e7ok ilgin\u00e7&#8217; demi\u015f. B\u00fcy\u00fck matematik\u00e7i Hardy, Ramanujan&#8217;\u0131n neden s\u00f6z etti\u011fini anlamam\u0131\u015f ve ne demek diye \u00e7\u0131k\u0131\u015fm\u0131\u015f. Akl\u0131n\u0131 rakamlardan ba\u015fka \u015feylerle me\u015fgul etmeyen Ramanujan,<!--more--> 1729&#8217;un iki farkl\u0131 bi\u00e7imde iki say\u0131n\u0131n k\u00fcplerinin toplam\u0131 olan en k\u00fc\u00e7\u00fck say\u0131 oldu\u011fu s\u00f6ylemi\u015f:<\/p>\n<p>1729 = 12<sup>3<\/sup>\u00a0+ 1<sup>3<\/sup>\u00a0= 10<sup>3<\/sup>\u00a0+ 9<sup>3<\/sup><br \/>\nRamanujan evine d\u00f6nmek i\u00e7in I. D\u00fcnya Sava\u015f\u0131n\u0131n bitmesini beklemek zorunda kal\u0131r ve evine d\u00f6nd\u00fckten iki y\u0131l sonra vefat eder.<\/p>\n<p>\u00d6lmeden \u00f6nce bir e\u015fitli\u011fi bulmu\u015f ama ispatlamaya \u00f6mr\u00fc yetmemi\u015f.<\/p>\n<p><strong>Kaynak:<\/strong> https:\/\/tr.wikipedia.org\/wiki\/Srinivasa_Aiyangar_Ramanujan<\/p>\n<p>Bir ba\u015fka hikayeye g\u00f6re ise\u00a0Hintli matematik dehas\u0131 Ramanujan\u00a0hastanede yatarken, \u00fcnl\u00fc \u0130ngiliz\u00a0matematik\u00e7i Hardy onu ziyarete gelir.\u00a0Hardy 1729 numaral\u0131 taksiyle geldi\u011fini\u00a0ve bu numaran\u0131n kendisine \u00f6nemsiz\u00a0g\u00f6z\u00fckt\u00fc\u011f\u00fcn\u00fc ve u\u011fursuz bir \u015fey\u00a0olmas\u0131ndan korktu\u011funu s\u00f6yleyince\u00a0Ramanujan hemen cevap verir: Hay\u0131r,\u00a0bu \u00e7ok ilgin\u00e7 bir say\u0131d\u0131r; iki pozitif tam say\u0131n\u0131n k\u00fcplerinin toplam\u0131 olarak, iki farkl\u0131 \u015fekilde yaz\u0131labilen en k\u00fc\u00e7\u00fck say\u0131 oldu\u011funu a\u00e7\u0131klar:\u00a0Ger\u00e7ekten de\u00a01729 = 12<sup>3<\/sup>\u00a0+ 1<sup>3<\/sup>\u00a0= 10<sup>3<\/sup>\u00a0+ 9<sup>3<\/sup>\u00a0dir.<\/p>\n<p><strong>Cemal Hoca&#8217;n\u0131n Notu :<\/strong> Her evden ka\u00e7\u0131p, intihara te\u015febb\u00fcs eden matematik dahisi olacak veya her okuldan at\u0131lan Edison olacak diye bir kural yok. Bu \u00f6rnekler \u00e7ok d\u00fc\u015f\u00fck olas\u0131l\u0131kla ger\u00e7ekle\u015fen istisnai \u00f6rneklerdir. \u00d6zellikle \u00e7ocu\u011fu \u00e7ok yaramaz ve derslere kar\u015f\u0131 ilgisiz olan bir ka\u00e7 veliden: Hocam benim \u00e7ocu\u011fum \u00e7ok zeki ama da\u011f\u0131n\u0131k, ders \u00e7al\u0131\u015fm\u0131yor, Edison&#8217;da \u00f6yleymi\u015f ama elektri\u011fi bulmu\u015f diye \u00e7ocu\u011funun da Edison olaca\u011f\u0131n\u0131 \u00fcmit etmesi ve \u00e7ok bilmi\u015f baz\u0131 piskologlar\u0131n ve ki\u015fisel geli\u015fim kitab\u0131 yazarlar\u0131n\u0131n da bu u\u00e7 \u00f6rnekleri anlat\u0131p kendilerine \u00f6nem atfetme \u00e7abalar\u0131 bu notu yazmama neden oldu. Unutulmamal\u0131! D\u0131\u015far\u0131s\u0131 zeki ama zekas\u0131n\u0131 kullanmayan insanlarla dolu. Zeka, \u00e7al\u0131\u015fma ve disiplin varsa bir anlam ifade eder.<br \/>\n<strong>Cemal Hoca&#8217;n\u0131n 2. Notu : <\/strong>Bug\u00fcn evlerde kulland\u0131\u011f\u0131m\u0131z<strong>\u00a0<\/strong>Elektri\u011fi Edison de\u011fil Nicola Tesla bulmu\u015ftur. Hatta Edison bug\u00fcn evlerde kulland\u0131\u011f\u0131m\u0131z elektri\u011fin yani alternatif ak\u0131m\u0131n k\u00f6t\u00fc bir \u015fey oldu\u011funu ispat etmek i\u00e7in elektrikli sandalye geli\u015ftirerek halk\u0131n g\u00f6z\u00fc \u00f6n\u00fcnde bizzat canl\u0131 hayvan ve \u00f6l\u00fcm mahkumu insanlara elektrik vererek kendi icad\u0131 olan do\u011fru ak\u0131m\u0131n yayg\u0131nla\u015fmas\u0131n\u0131 sa\u011flamaya \u00e7al\u0131\u015fm\u0131\u015ft\u0131r. Bilgi i\u00e7in\u00a0<a href=\"https:\/\/www.karadenizli.biz\/yaren\/ihanete-ugramis-dahi-nicola-tesla\/\" target=\"_blank\">www.karadenizli.biz\/yaren\/ihanete-ugramis-dahi-nicola-tesla\/<\/a>\u00a0ba\u011flant\u0131s\u0131ndaki yaz\u0131y\u0131 okuyabilirsiniz.<\/p>\n<p><strong>Cemal Hoca&#8217;n\u0131n 3. Notu :<\/strong>Edison&#8217;un ahlaki y\u00f6nden ne kadar zay\u0131f , \u00e7\u0131karc\u0131 biri oldu\u011funu Google&#8217;da Edison ve Tesla sava\u015f\u0131 \u015feklinde ararsan\u0131z net bir \u015fekilde g\u00f6r\u00fcrs\u00fcn\u00fcz.<br \/>\n<strong>Cemal Hoca&#8217;n\u0131n 4. Notu : <\/strong>\u00d6mr\u00fc boyunca<strong>\u00a0<\/strong>40 dakika derse girmeyen ve girmeyecek olan, hi\u00e7 \u00e7ocuk yeti\u015ftirmemi\u015f veya evdeki \u00e7ocu\u011funa s\u00f6z ge\u00e7iremeyen, kontrol edemeyen ki\u015filer, 25 \u00f6\u011frenciyi s\u0131n\u0131fta kontrol ederek e\u011fitim ve \u00f6\u011fretim faaliyetlerini s\u00fcrd\u00fcren \u00f6\u011fretmenlere y\u00f6nelik e\u011fitim psikolojisi, ders nas\u0131l i\u015flenir, zaman y\u00f6netimi, \u00f6\u011frenciye nas\u0131l davranmal\u0131, s\u0131n\u0131f y\u00f6netimi vb. konularda kitap yazmamal\u0131, e\u011fitim ko\u00e7lu\u011fu yapmamal\u0131, deme\u00e7 vermemeli.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Y\u0131llar \u00f6nce Bilim Teknik dergisinde okudu\u011fum bu hikayeyle tekrar kar\u015f\u0131la\u015f\u0131nca sizlerle de payla\u015fmak istedim. 1729&#8217;un hikayesine ba\u015flamadan \u00f6nce hikayenin kahraman\u0131 hakk\u0131nda biraz bilgi edinelim. Srinivasa Aiyangar Ramanujan G\u00fcney Hindistan&#8217;da, kast sisteminde en y\u00fcksek tabaka olan Brahman bir ailede do\u011far. Ailesinin maddi durumu pek iyi de\u011fildir. Vefat\u0131ndan \u00e7ok daha sonra hakk\u0131nda bir kitap yazan abisi \u00e7ok [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1,5],"tags":[410,409,411,412,299],"class_list":["post-6380","post","type-post","status-publish","format-standard","hentry","category-genel","category-vaybee","tag-1729un-hikayesi","tag-3-kuvvet","tag-ramanujan","tag-sayinin-kupu","tag-uslu-sayilar"],"psp_head":"<title>1729'un Hikayesi \u2013 Orijinal Olan Her Bilgi...<\/title>\r\n<meta name=\"description\" content=\"1729&#039;un iki farkl\u0131 bi\u00e7imde iki say\u0131n\u0131n k\u00fcplerinin toplam\u0131 olan en k\u00fc\u00e7\u00fck say\u0131 oldu\u011fu s\u00f6ylemi\u015f:\" \/>\r\n<meta name=\"robots\" content=\"index,follow\" \/>\r\n<link rel=\"canonical\" href=\"https:\/\/www.karadenizli.biz\/yaren\/ramanujan-ve-1729un-hikayesi\/\" \/>\r\n","jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p2X1Qf-1EU","jetpack-related-posts":[{"id":7972,"url":"https:\/\/www.karadenizli.biz\/yaren\/duzgun-onyedigen-matematik-odulleri\/","url_meta":{"origin":6380,"position":0},"title":"D\u00fczg\u00fcn Onyedigen Matematik \u00d6d\u00fclleri","author":"karadenizli","date":"16 Ocak 2023","format":false,"excerpt":"2022 y\u0131l\u0131ndan itibaren \u00f6\u011frencilerime vermeyi d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcm D\u00fczg\u00fcn Onyedigen Matematik \u00d6d\u00fcl\u00fcn\u00fcn birincisini\u00a0 7\/C s\u0131n\u0131f\u0131 \u00f6\u011frencisi Melikenaz \u00d6zdemir ald\u0131. \u00d6d\u00fcl\u00fcn ad\u0131n\u0131n neden D\u00fczg\u00fcn Onyedigen oldu\u011funu ise yaz\u0131m\u0131n devam\u0131nda anlataca\u011f\u0131m. \u00d6d\u00fcl\u00fc uygun g\u00f6rmemde \u00f6\u011frencimin matematik dersine olan ilgisi, sorular\u0131 de\u011fi\u015fik, orijinal ve pratik yollar kullanarak \u00e7\u00f6zmeye \u00e7al\u0131\u015fmas\u0131 ve \u00e7\u00f6zmesi etkili oldu. \u00d6\u011frencimin portre\u2026","rel":"","context":"&quot;Genel&quot; i\u00e7inde","block_context":{"text":"Genel","link":"https:\/\/www.karadenizli.biz\/yaren\/category\/genel\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2023\/01\/17gen2.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":3039,"url":"https:\/\/www.karadenizli.biz\/yaren\/fatih-projesi-egitimde-teknoloji-kullanim-kursu\/","url_meta":{"origin":6380,"position":1},"title":"Fatih Projesi E\u011fitimde Teknoloji Kullan\u0131m\u0131 Kursu","author":"karadenizli","date":"31 Aral\u0131k 2011","format":false,"excerpt":"Etkile\u015fimli tahta i\u00e7in gerekli olan programlar; -\u00a0Audacity : Sesleri keser, ses formatlar\u0131n\u0131n\u0131 birbirine d\u00f6n\u00fc\u015ft\u00fcr\u00fcr -\u00a0Freemake Video Converter :\u00a0Videolar\u0131 de\u011fi\u015fik formatlara d\u00f6n\u00fc\u015ft\u00fcr\u00fcr. Videolar\u0131 birle\u015ftirir. Videonun sesini mp3 olarak ay\u0131r\u0131r. -\u00a0Freemake Video Downloader: Sitelerdeki g\u00f6m\u00fcl\u00fc videolar\u0131 indirir. Tek yapman\u0131z gereken videonun bulundu\u011fu sayfan\u0131n linkini kopyalay\u0131p program\u0131n aray\u00fcz\u00fcne yap\u0131\u015ft\u0131rmak. -\u00a0Eclipse Crossword : G\u00fczel\u2026","rel":"","context":"&quot;Her Telden&quot; i\u00e7inde","block_context":{"text":"Her Telden","link":"https:\/\/www.karadenizli.biz\/yaren\/category\/her-telden\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":676,"url":"https:\/\/www.karadenizli.biz\/yaren\/michael-faraday-ilginc-bir-yasam-ve-etkileyici-birbasari-hikayesi\/","url_meta":{"origin":6380,"position":2},"title":"Michael FARADAY-\u0130lgin\u00e7 Bir Ya\u015fam Ve Etkileyici Bir Ba\u015far\u0131 Hikayesi","author":"karadenizli","date":"24 Mart 2012","format":false,"excerpt":"Bir \u00e7ok bilim adam\u0131n\u0131n ya\u015fam \u00f6yk\u00fcs\u00fcn\u00fc okudum. Ama hi\u00e7 biri beni bu kadar etkilemedi. Bilim Teknik dergisinde okudu\u011fum makale umar\u0131m sizlerin de ilgisini \u00e7eker. Faraday, neredeyse yoksulluktan, yitip gitmek \u00fczere olan bir aileden, yoktan yeti\u015fti. \u015eimdilerin Londra'ya ba\u011fl\u0131 olan Elephant and Castle b\u00f6lgesinde, 22 Eyl\u00fcl 1791\u2019de do\u011fdu. Babas\u0131 a\u011f\u0131r hastal\u0131\u011f\u0131yla\u2026","rel":"","context":"&quot;\u0130lgin\u00e7 Bilgiler&quot; i\u00e7inde","block_context":{"text":"\u0130lgin\u00e7 Bilgiler","link":"https:\/\/www.karadenizli.biz\/yaren\/category\/vaybee\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2012\/03\/faraday.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":6191,"url":"https:\/\/www.karadenizli.biz\/yaren\/umbragram-oyunu-ile-eglenceli-matematik\/","url_meta":{"origin":6380,"position":3},"title":"Umbragram Oyunu \u0130le E\u011flenceli Matematik","author":"karadenizli","date":"18 Ekim 2015","format":false,"excerpt":"Bir bilgisayar dergisinde rastlad\u0131\u011f\u0131m Umbragram adl\u0131 e\u011fitim i\u00e7erikli oyunu \u00a0inceledim. Oyunun \u00f6zellikle 7. s\u0131n\u0131f matematik dersinde, e\u015f k\u00fcplerden olu\u015fan ve farkl\u0131 y\u00f6nlerden g\u00f6r\u00fcn\u00fcmleri verilen yap\u0131lar\u0131 in\u015fa etme konusunu anlat\u0131rken olduk\u00e7a i\u015fime yarayaca\u011f\u0131n\u0131, zamandan tasarruf edece\u011fimi, \u00f6\u011frencilerin daha kolay \u00f6\u011frenece\u011fini d\u00fc\u015f\u00fcnd\u00fcm ve\u00a0 bir e\u011fitim videosu haz\u0131rlad\u0131m. Bu video sayesinde \u00f6\u011frencilerin, farkl\u0131\u2026","rel":"","context":"&quot;E\u011flenceli Matematik&quot; i\u00e7inde","block_context":{"text":"E\u011flenceli Matematik","link":"https:\/\/www.karadenizli.biz\/yaren\/category\/ogrenciler-icin\/eglenceli-matematik\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":6243,"url":"https:\/\/www.karadenizli.biz\/yaren\/matematikle-ilgili-animasyonlar\/","url_meta":{"origin":6380,"position":4},"title":"Matematikle \u0130lgili Animasyonlar","author":"karadenizli","date":"14 Kas\u0131m 2015","format":false,"excerpt":"Bu sayfada sizlere zaman zaman ara\u015ft\u0131rma yaparken ba\u015fta Wikipedi olmak \u00fczere internet sitelerinde rastlad\u0131\u011f\u0131m ve matematikle ilgili olan konular\u0131n a\u00e7\u0131kland\u0131\u011f\u0131 animasyonlar\u0131 ve a\u00e7\u0131klay\u0131c\u0131 bilgileri payla\u015faca\u011f\u0131m. Asal Say\u0131 : Yaln\u0131zca 1'e ve kendine b\u00f6l\u00fcnen say\u0131lara asal say\u0131 denir.\u00a0Ba\u015fka bir ifade ile asal say\u0131lar, sadece iki pozitif tamsay\u0131 b\u00f6leni olan do\u011fal say\u0131lard\u0131r.\u2026","rel":"","context":"&quot;E\u011flenceli Matematik&quot; i\u00e7inde","block_context":{"text":"E\u011flenceli Matematik","link":"https:\/\/www.karadenizli.biz\/yaren\/category\/ogrenciler-icin\/eglenceli-matematik\/"},"img":{"alt_text":"Animation_Sieve_of_Eratosth","src":"https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2015\/10\/Animation_Sieve_of_Eratosth.gif?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":4867,"url":"https:\/\/www.karadenizli.biz\/yaren\/matematik-ogrenmeyi-kolaylastiran-uygulamalar\/","url_meta":{"origin":6380,"position":5},"title":"Matematik \u00d6\u011frenmeyi Kolayla\u015ft\u0131ran Uygulamalar","author":"karadenizli","date":"5 Temmuz 2014","format":false,"excerpt":"Bu yaz\u0131mda, \u00f6\u011frencilere matemati\u011fi sevdiren ve \u00f6\u011frenmelerini kolayla\u015ft\u0131ran interaktif uygulamalar\u0131n oldu\u011fu internet sitelerini tan\u0131taca\u011f\u0131m. http:\/\/www.wolframalpha.com\/ Google arama motoru gibi bir \u00e7ok matematiksel i\u015fleme cevap veren bir uygulama. Kar\u015f\u0131n\u0131za \u00e7\u0131kan metin kutusuna mesela 1\/4+1\/8 yazarak enter tu\u015funa bast\u0131\u011f\u0131n\u0131zda i\u015flemin cevab\u0131n\u0131 ondal\u0131k say\u0131 olarak, kesir olarak, say\u0131 do\u011frusunda ve \u015fekille g\u00f6steriyor. http:\/\/www.fisme.science.uu.nl\/toepassingen\/28432\/\u2026","rel":"","context":"&quot;E\u011flenceli Matematik&quot; i\u00e7inde","block_context":{"text":"E\u011flenceli Matematik","link":"https:\/\/www.karadenizli.biz\/yaren\/category\/ogrenciler-icin\/eglenceli-matematik\/"},"img":{"alt_text":"wolfram","src":"https:\/\/i0.wp.com\/www.karadenizli.biz\/yaren\/wp-content\/uploads\/2014\/07\/wolfram.png?resize=350%2C200","width":350,"height":200},"classes":[]}],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/posts\/6380","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/comments?post=6380"}],"version-history":[{"count":0,"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/posts\/6380\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/media?parent=6380"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/categories?post=6380"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.karadenizli.biz\/yaren\/wp-json\/wp\/v2\/tags?post=6380"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}