{"id":10413,"date":"2011-04-01T19:35:58","date_gmt":"2011-04-01T16:35:58","guid":{"rendered":"http:\/\/109.232.216.219\/~bilimvegelecek\/?p=10413"},"modified":"2017-05-26T19:43:30","modified_gmt":"2017-05-26T16:43:30","slug":"matematigin-mizahi-ii","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2011\/04\/01\/matematigin-mizahi-ii","title":{"rendered":"Matemati\u011fin (m)izah\u0131 II"},"content":{"rendered":"

Bu yaz\u0131da da matematikle mizah\u0131n kesi\u015fti\u011fi yolda y\u00fcr\u00fcyoruz. \u00d6nceki say\u0131da matematik mizah\u0131n\u0131 f\u0131kralardan \u00f6rnekler vererek incelemeye \u00e7al\u0131\u015fm\u0131\u015ft\u0131k. Bu kez de matematik \u00fczerine yap\u0131lm\u0131\u015f olan baz\u0131 \u015faka, espri ve karikat\u00fcrleri ele alaca\u011f\u0131z.<\/p>\n

Matematiksel \u015fakalar\u0131n bir\u00e7o\u011fu say\u0131lar kuram\u0131, fonksiyonel analiz, topoloji gibi matemati\u011fin farkl\u0131 alanlar\u0131na aittir. Merakl\u0131lar\u0131 i\u00e7in matematik d\u00fcnyas\u0131nda ke\u015ffe \u00e7\u0131kabilmenin ilk ad\u0131m\u0131 olabilecek bu esprilerin bir b\u00f6l\u00fcm\u00fc soru yan\u0131t bi\u00e7imindeki bilmecelerle kar\u015f\u0131m\u0131za \u00e7\u0131kar. Matemati\u011fin alt dallar\u0131yla ilgili olan bu \u015fakalar\u0131 anlayabilmek i\u00e7in matematiksel bilgi gerekir. Bu yaz\u0131da b\u00f6ylesi birka\u00e7 \u015fakaya de\u011finece\u011fim, tabii matematikle ilgili baz\u0131 pop\u00fcler bilgileri vererek.<\/p>\n

Geometrik topolojinin inceledi\u011fi b\u00f6l\u00fcmlerden biri olan iki \u015feklin veya iki cismin birbirine\u201cd\u00f6n\u00fc\u015f\u00fcm\u00fc\u201d bir\u00e7ok \u015fakan\u0131n konusu olmu\u015ftur. Bir \u00fc\u00e7genle bir \u00e7ember, kulplu bir kahve kupas\u0131yla bir simit topolojik olarak e\u015fyap\u0131l\u0131d\u0131r. Islak kilden yap\u0131lm\u0131\u015f kulplu bir kahve kupas\u0131n\u0131n par\u00e7alanmadan e\u011filip b\u00fck\u00fclerek, d\u00fczle\u015ftirilip bir simit \u015feklini almas\u0131 topolojik bir d\u00f6n\u00fc\u015f\u00fcmd\u00fcr ve bu d\u00f6n\u00fc\u015f\u00fcm\u00fcn ger\u00e7ekle\u015fmesi kahve kupas\u0131n\u0131n kulplu olmas\u0131na ba\u011fl\u0131d\u0131r. Buradan \u00fcretilmi\u015f bir espride kahve i\u00e7erken simit yiyen bir topolojistin kahve kupas\u0131n\u0131n kulpunu tutarken, kupan\u0131n simide d\u00f6n\u00fc\u015f\u00fcm\u00fcn\u00fc a\u00e7\u0131klayamayaca\u011f\u0131 anlat\u0131l\u0131r. Bu t\u00fcrdeki \u015fakalar matematik k\u00fclt\u00fcr\u00fcn\u00fcn bir par\u00e7as\u0131d\u0131r ve bu k\u00fclt\u00fcre ait ipu\u00e7lar\u0131 veririler.<\/p>\n

Bir\u00e7ok \u00e7e\u015fitlemesi olan \u201cBir ampul\u00fc de\u011fi\u015ftirmek i\u00e7in ka\u00e7 matematik\u00e7iye, ka\u00e7 m\u00fchendise, ka\u00e7 fizik\u00e7iye gerek vard\u0131r?\u201d gibi sorular\u0131n matematikle ilgili de\u011fi\u015fik uyarlamalar\u0131 yap\u0131lm\u0131\u015ft\u0131r:<\/p>\n

S: Bir ampul\u00fc de\u011fi\u015ftirmek i\u00e7in ka\u00e7 topolojiste gerek vard\u0131r?<\/p>\n

Y: Fark etmez,\u00a0 nas\u0131l olsa bir topolojist onu d\u00fc\u011f\u00fcm haline getirecektir.<\/p>\n

S: Ka\u00e7 say\u0131 kuramc\u0131s\u0131 gerekir?<\/p>\n

Y: Bu say\u0131 bilinemez, ancak bu say\u0131n\u0131n kusursuz bir asal say\u0131 oldu\u011fu san\u0131s\u0131 \u00fcnl\u00fc bir matematik\u00e7i taraf\u0131ndan ifade edilmi\u015ftir ve bu san\u0131 hen\u00fcz kan\u0131tlanamam\u0131\u015ft\u0131r.<\/p>\n

S: Ka\u00e7 geometrici gerekir?<\/p>\n

Y: S\u0131f\u0131r, \u00e7\u00fcnk\u00fc bu i\u015f pergel ve cetvelle yap\u0131lamaz.<\/p>\n

S: Ka\u00e7 analizci gerekir?<\/p>\n

Y: \u00dc\u00e7. Biri ampul\u00fc de\u011fi\u015ftirmenin en az bir yolu oldu\u011funu (Varl\u0131k Teoremi),\u00a0 ikincisi ise ampul\u00fcn tek bi\u00e7imde tak\u0131labilece\u011fini kan\u0131tlamak i\u00e7in (Teklik Teoremi);di\u011feri de bu ampul\u00fcn tak\u0131lmas\u0131na ait bir algoritma geli\u015ftirmek i\u00e7in.<\/p>\n

S: Ka\u00e7 matematik\u00e7i gerekir?<\/p>\n

Y: 0,999999\u2026<\/p>\n

Bu \u015faka, 0,999999\u2026 = 1 e\u015fitli\u011finin do\u011frulu\u011fundan ku\u015fku duyanlarla dalga ge\u00e7menin yan\u0131 s\u0131ra, matemati\u011fin tek ba\u015f\u0131na yap\u0131lan bir u\u011fra\u015f oldu\u011funu da anlat\u0131r. \u00d6te yandan bu espri yukar\u0131da topolojist, say\u0131 kuramc\u0131s\u0131, analizci, geometrici gibi matematik\u00e7iler i\u00e7in verilen yan\u0131tlarla \u00e7eli\u015fiyor gibi g\u00f6r\u00fcnse de mizahta mutlak tutarl\u0131l\u0131\u011f\u0131<\/p>\n

 <\/p>\n

aramak do\u011fru olmasa gerek. Bunun g\u00fczel bir \u00f6rne\u011fi a\u015fa\u011f\u0131daki soruda.<\/p>\n

S: Bir ampul\u00fc de\u011fi\u015ftirmek i\u00e7in ka\u00e7 ampul gerekir?<\/p>\n

Y: Bir, e\u011fer bu ampul kendi G\u00f6del say\u0131s\u0131n\u0131 biliyorsa.<\/p>\n

Bu \u015faka, matematikte do\u011frulu\u011fu ya da yanl\u0131\u015fl\u0131\u011f\u0131 kan\u0131tlanamayan \u00f6nemelerin oldu\u011funun kan\u0131t\u0131n\u0131n yap\u0131ld\u0131\u011f\u0131 G\u00f6del\u2019in Eksiklik Teoremleri\u2019ne bir g\u00f6ndermedir. G\u00f6del, ad\u0131na \u201cG\u00f6del say\u0131lar\u0131\u201d denilen her matematiksel t\u00fcmceye, her ime bir say\u0131n\u0131n kar\u015f\u0131l\u0131k getirilebilece\u011finin olanakl\u0131 oldu\u011funu g\u00f6stererek matemati\u011fin \u00e7eli\u015fkisiz oldu\u011funun kan\u0131t\u0131n\u0131n yap\u0131lamayaca\u011f\u0131n\u0131 kan\u0131tlam\u0131\u015ft\u0131r. Eksiklik Teoremleri matemati\u011fin temellerini sarsm\u0131\u015ft\u0131r. Bu \u015fakan\u0131n devam\u0131 olarak bir tavu\u011fun yolun kar\u015f\u0131s\u0131na ge\u00e7mesiyle ilgili olarak \u015fu soru sorulur: Tavuk neden yolun kar\u015f\u0131s\u0131na ge\u00e7ti? G\u00f6del\u2019in Eksiklik Teoremleri\u2019ne g\u00f6re yan\u0131t \u015f\u00f6yledir: Tavu\u011fun yolun kar\u015f\u0131s\u0131na ge\u00e7ip ge\u00e7medi\u011fi kan\u0131tlanamaz.<\/p>\n

Tavu\u011fun yolun kar\u015f\u0131s\u0131na ge\u00e7ip ge\u00e7medi\u011fi kan\u0131tlanabilir mi? Bilemem! Ama matematikte, kan\u0131t olmadan b\u0131rak\u0131n kar\u015f\u0131dan kar\u015f\u0131ya ge\u00e7meyi ad\u0131m atman\u0131n bile olanaks\u0131z oldu\u011fu \u00e7ok iyi bilinir. Kan\u0131t matemati\u011fin hijyenidir ve kan\u0131t\u0131n her a\u015famas\u0131n\u0131n ge\u00e7erlili\u011fi \u00e7ok \u00f6nemlidir. Matematik tarihine bak\u0131ld\u0131\u011f\u0131nda kimi \u00fcnl\u00fc matematik\u00e7ilerin bile yapt\u0131klar\u0131 kan\u0131tlarda gerekli titizli\u011fi g\u00f6stermedi\u011fi g\u00f6r\u00fcl\u00fcr. Bir\u00e7ok matematik\u00e7inin kan\u0131t\u0131, incelemeler sonunda saptanan hatalar nedeniyle ge\u00e7ersizle\u015fmi\u015ftir. Matematikte kan\u0131t bu kadar \u00f6nemliyken, matemati\u011fin g\u00fcnl\u00fck kullan\u0131m\u0131nda bu titizli\u011fe rastlamak her zaman m\u00fcmk\u00fcn olmamaktad\u0131r. A\u015fa\u011f\u0131daki \u015fakalarda, daha \u00e7ok amat\u00f6r matematik\u00e7ilerin ve kimi akademisyenlerin ders verirken matemati\u011fin ihlaline yol a\u00e7an faull\u00fc \u201ckan\u0131t teknikleri\u201d s\u0131ralanm\u0131\u015ft\u0131r.<\/p>\n

Nas\u0131l kan\u0131tlamal\u0131? Ders verenler i\u00e7in rehber<\/strong><\/p>\n

Erteleme yoluyla kan\u0131t: <\/em>\u201cBunu dersin ilerleyen b\u00f6l\u00fcmlerinde kan\u0131tlayaca\u011f\u0131z.\u201d<\/p>\n

Ayartma yoluyla kan\u0131t: <\/em>\u201cKendinizi bunun do\u011fru oldu\u011funa inand\u0131r\u0131n.\u201d<\/p>\n

Savsaklama yoluyla kan\u0131t: <\/em>\u201cOkuyucu rahatl\u0131kla detay\u0131 anlayacakt\u0131r.\u201d<\/p>\n

\u00d6rnek verme yoluyla kan\u0131t: <\/em>\u201cGenel kan\u0131t\u0131n vermek istedi\u011fi fikri n = 2 durumu \u00e7ok iyi anlat\u0131yor.\u201d<\/p>\n

Eri\u015filemeyen literat\u00fcre referans vererek kan\u0131t: <\/em>\u201cSlovenyal\u0131 Filoloji Toplulu\u011fu\u2019nun 1883 y\u0131l\u0131ndaki an\u0131 kitab\u0131nda bu teoremin bir sonucu bulunabilir.\u201d<\/p>\n

G\u00f6zda\u011f\u0131, y\u0131ld\u0131rma yoluyla kan\u0131t: <\/em>\u201c\u00d6nemsiz.\u201d<\/p>\n

Se\u00e7kin otorite yoluyla kan\u0131t: <\/em>\u201cD\u00fcn ak\u015fam telefonda Robert Langlands\u2019la konu\u015ftum, Galois gruplar\u0131yla otomorfik formlar aras\u0131nda bir denkli\u011fin oldu\u011funu s\u00f6yledi.\u201d<\/p>\n

Matematikte ge\u00e7mi\u015fte yap\u0131lm\u0131\u015f \u00e7al\u0131\u015fmalar\u0131n referans g\u00f6sterilmesi yoluyla kan\u0131t: <\/em>\u201cMatematik\u00e7ilerin uzun ve y\u0131lmayan \u00e7al\u0131\u015fmalar\u0131 sonucunda kar\u015f\u0131 bir \u00f6rnek bulunamad\u0131.\u201d<\/p>\n

\u015eekil ve \u015fema kullanarak kan\u0131t: <\/em>\u00d6rnek yoluyla kan\u0131t\u0131n biraz daha ikna edici olan\u0131d\u0131r. Savsaklama yoluyla birlikte \u00e7ok iyi gider.<\/p>\n

Co\u015fkulu el sallama yoluyla kan\u0131t: <\/em>Derste veya seminer d\u00fczeninde iyi i\u015fler.<\/p>\n

Matemati\u011fi \u00f6\u011fretenlerin bu \u201cihlallerine\u201d kar\u015f\u0131l\u0131k, \u00f6\u011frenenler de matematik \u00f6devlerine ili\u015fkin ihlallerini zaman zaman matematik diliyle izah etmi\u015flerdir. Bu b\u00f6l\u00fcmde \u00f6\u011frencilerin \u00f6dev yapmama mazeretlerinden \u00f6rnekler verece\u011fim. \u00d6dev, ad\u0131 \u00fcst\u00fcnde bir otoritenin yapt\u0131r\u0131m\u0131d\u0131r asl\u0131nda. \u00d6\u011frencilere verilen bir\u00e7ok \u00f6devde g\u00f6n\u00fcll\u00fcl\u00fck yok denecek kadar azd\u0131r. B\u00fct\u00fcn bunlar\u0131n \u00fcst\u00fcne matematikle aras\u0131 iyi olmayan bir \u00f6\u011frenciye verilen matematik \u00f6devi o \u00f6\u011frenci i\u00e7in bir i\u015fkenceye d\u00f6n\u00fc\u015f\u00fcr, matemati\u011fin d\u00fcnyas\u0131yla ger\u00e7ekler d\u00fcnyas\u0131n\u0131n \u00e7at\u0131\u015fmas\u0131 ba\u015flar. Her iki d\u00fcnyada ya\u015faman\u0131n zorlu\u011fu i\u00e7inde olan \u00f6\u011frenci, bir\u00e7ok mazeret \u00fcretir. \u00d6dev yapmaman\u0131n esprili matematiksel gerek\u00e7elerinden baz\u0131 \u00f6rnekler:<\/p>\n

– \u00d6devimi yaparken bir tamsay\u0131y\u0131 yanl\u0131\u015fl\u0131kla s\u0131f\u0131ra b\u00f6ld\u00fcm, k\u00e2\u011f\u0131d\u0131m bir anda alev ald\u0131.<\/p>\n

– Bir kahve ve simit molas\u0131 verdim, ama gecenin kalan\u0131nda hangisini hangisine band\u0131raca\u011f\u0131ma karar veremedim.<\/p>\n

– \u00d6dev k\u00e2\u011f\u0131tlar\u0131ma asimptotik olarak yakla\u015f\u0131yor ama dokunam\u0131yordum.<\/p>\n

– \u00d6devimi \u00e7ekmeceye kilitledim ama d\u00f6rt boyutlu bir k\u00f6pek geldi, onu yedi.<\/p>\n

– Teoremi kan\u0131tlayabilirdim ama kan\u0131t\u0131 yazacak yerim yoktu. (Fermat\u2019n\u0131n B\u00fcy\u00fck Fermat Teoremi\u2019nin kan\u0131t\u0131 i\u00e7in \u00e7al\u0131\u015fma k\u00e2\u011f\u0131tlar\u0131ndan birine yazd\u0131\u011f\u0131 \u201cKan\u0131t\u0131 yazacak yerim yok.\u201d notuna bir g\u00f6nderme)<\/p>\n

– \u00d6devimi bir Klein \u015fi\u015fesine koydu\u011fuma dair yemin edebilirim ama onu bu sabah bulmad\u0131m.<\/p>\n

– Carl Friedrich Gauss\u2019un do\u011fum g\u00fcn\u00fcn\u00fc kutlad\u0131\u011f\u0131mdan zaman\u0131m olmad\u0131.<\/p>\n

-D\u00fcnya Kupas\u0131 ma\u00e7lar\u0131n\u0131 izliyordum, topun yak\u0131nsad\u0131\u011f\u0131 noktay\u0131 bulmaya \u00e7al\u0131\u015f\u0131rken ekrana kilitlendim.\"\"<\/p>\n

Kan\u0131t\u0131n\u0131 yapmakta tak\u0131ld\u0131\u011f\u0131m teorem i\u00e7in Matematik D\u00fcnyas\u0131<\/em> dergisine bakt\u0131m g\u00fclmekten \u00f6devimi tamamlayamad\u0131m.<\/p>\n

Farkl\u0131 yay\u0131nlar ve internet ortam\u0131ndan derleyerek yukar\u0131da s\u0131ralad\u0131\u011f\u0131m mazeretlerin sonuncusunu bir \u00f6\u011frencimin esprisinden esinlenerek ben ekledim. S\u00f6z\u00fc, Matematik D\u00fcnyas\u0131<\/em> dergisindeki mizaha getirmek istiyorum. Yar\u0131 akademik nitelikte olan, matemati\u011fin hemen her alan\u0131na ait derinlemesine yaz\u0131larla dolu bir dergide nas\u0131l olur da mizah yap\u0131l\u0131r? Dergiyi okuyanlar bu sorunun yan\u0131t\u0131n\u0131 \u00e7ok iyi bilir. Halkalar, s\u0131ralamalar, sonsuz say\u0131lar, \u00e7izgeler, se\u00e7im beliti, t\u00fcrev gibi kuramsal matemati\u011fin en temel konular\u0131 ak\u0131c\u0131 ve esprili bir dille anlat\u0131l\u0131r. Olduk\u00e7a soyut ve teorik bir konunun bir yerinde adeta birisi sizi g\u0131d\u0131klar, g\u00fclmeye ba\u015flars\u0131n\u0131z. Okur, matematiksel nesnelerin matemati\u011fi suland\u0131rmadan yap\u0131lan mizahi betimlemelerini okuman\u0131n keyfini s\u00fcrer, yap\u0131lan tam anlam\u0131yla matemati\u011fin (m)izah\u0131d\u0131r. E\u011flenceli matematik bu olsa gerek! Ali Nesin\u2019in kaleminden \u00e7\u0131kt\u0131\u011f\u0131n\u0131 zannetti\u011fim bu espri ve betimlemelerden baz\u0131lar\u0131n\u0131 al\u0131nt\u0131l\u0131yorum: \u201cSayfan\u0131n en alt\u0131na \u00e7izdi\u011fimiz bu e\u011friye literat\u00fcrde -\u00e7ok affedersiniz!- sikloid denir.\u201d, \u201cFonksiyonlar\u0131n s\u00fcpnormunun sonsuz olabilmesi baz\u0131 hassas ruhlar\u0131 rahats\u0131z edebilir.\u201d \u201cAcaba bu en g\u0131c\u0131r sonlu k\u00fcme maksimal bir sonlu k\u00fcme mi?\u201d, \u201cf s\u0131ralamaya sayg\u0131 duyuyor\u201d.<\/p>\n

Matematik D\u00fcnyas\u0131<\/em>\u2019n\u0131n \u201cOkurlardan\u201d k\u00f6\u015fesine g\u00f6z att\u0131\u011f\u0131n\u0131zda da tam bir mizah \u015f\u00f6leniyle kar\u015f\u0131la\u015f\u0131rs\u0131n\u0131z. Okurlardan gelen sorular ve edit\u00f6r\u00fcn yan\u0131tlar\u0131na \u00f6rnekler:<\/p>\n

Soru: Hocam, tek say\u0131lar\u0131n olmad\u0131\u011f\u0131n\u0131 kan\u0131tlad\u0131m. Bu konuyu uluslararas\u0131 dergilerde yay\u0131mlamam gerekiyormu\u015f. Onun i\u00e7in size g\u00f6nderdim. Yard\u0131mc\u0131 olursan\u0131z sevinirim. <\/em><\/p>\n

Yan\u0131t: \u015eimdi de \u00e7ift say\u0131lar\u0131n olmad\u0131\u011f\u0131n\u0131 kan\u0131tla da MD\u2019nin kap\u0131s\u0131na kilit vural\u0131m.<\/p>\n

Soru: San\u0131r\u0131m 5 y\u0131ld\u0131r u\u011fra\u015f\u0131p kan\u0131tlayamad\u0131\u011f\u0131m Goldbach san\u0131s\u0131n\u0131 bu sefer kan\u0131tlad\u0131m. Size yolluyorum. \u0130nceleyip beni do\u011fru ya da yanl\u0131\u015f oldu\u011fu konusunda bilgilendirmenizi rica ediyorum.<\/em><\/p>\n

Yan\u0131t: Kan\u0131t\u0131n\u0131z sadece iki sayfa oldu\u011fundan yanl\u0131\u015ft\u0131r.<\/p>\n

Soru: 0 = 1 e\u015fitli\u011fini ispatlayarak matemati\u011fin \u00e7eli\u015fkili oldu\u011funu g\u00f6sterdim. \u015eimdi ne yapay\u0131m?<\/em><\/p>\n

Yan\u0131t: Fizi\u011fe el at\u0131p ba\u015f\u0131m\u0131za ta\u015f ya\u011fmayaca\u011f\u0131n\u0131 kan\u0131tla.<\/p>\n

Soru: 29\u2019un ikilik tabanda asal olmad\u0131\u011f\u0131n\u0131 g\u00f6sterdim. Bu \u00f6nemli bir bulu\u015f mudur?<\/em><\/p>\n

Yan\u0131t: Asall\u0131k tabandan ba\u011f\u0131ms\u0131z bir kavramd\u0131r. Bulu\u015funuz \u00f6nemli olmas\u0131na \u00f6nemli de, bir kusuru var, yanl\u0131\u015f\u2026<\/p>\n

Matematik D\u00fcnyas\u0131<\/em>\u2019nda yap\u0131lan mizah, al\u0131nt\u0131lad\u0131\u011f\u0131m bu \u015fakalarla s\u0131n\u0131rl\u0131 de\u011fil elbette. Dergide mizah\u0131n en \u00f6nemli ismi karikat\u00fcrist Tayfun Akg\u00fcl. Uluslararas\u0131 bilim dergilerinde de karikat\u00fcrleri yay\u0131mlanan Tayfun Akg\u00fcl, Matematik D\u00fcnyas\u0131<\/em> i\u00e7in \u00e7izdi\u011fi karikat\u00fcrlerle matematik (m)izah\u0131ndan \u00e7ok g\u00fczel \u00f6rnekler vermi\u015ftir. Bu y\u00fczden Matematik D\u00fcnyas\u0131<\/em> okurlar\u0131 \u00e7ok \u015fansl\u0131, d\u00fcnyada hi\u00e7bir matematik dergisinin Tayfun Akg\u00fcl gibi bir karikat\u00fcriste sahip oldu\u011funu sanm\u0131yorum.<\/p>\n

Matematik ve mizah\u2026 Her iki etkinlik de soyutlaman\u0131n \u00fcr\u00fcn\u00fc. Mizah matematik d\u00fcnyas\u0131n\u0131 soyutluyor, matematik ise insan\u0131n en m\u00fckemmel soyutlama u\u011fra\u015flar\u0131ndan biri. Matemati\u011fin d\u00fcnyas\u0131 ile ger\u00e7ekler d\u00fcnyas\u0131n\u0131n \u00e7arp\u0131\u015ft\u0131\u011f\u0131 noktada mizah sahne al\u0131yor ve bizlere her iki d\u00fcnyan\u0131n g\u00fczelliklerini g\u00f6rme olana\u011f\u0131n\u0131 sa\u011fl\u0131yor.<\/p>\n

Te\u015fekk\u00fcr:<\/strong> Karikat\u00fcr\u00fcn\u00fc yay\u0131mlamama izin verdi\u011fi i\u00e7in Tayfun Akg\u00fcl\u2019e \u00e7ok te\u015fekk\u00fcr ederim.<\/p>\n

 <\/p>\n

KAYNAKLAR<\/strong><\/p>\n

1) Paul Renteln, Alan Dundes, Notices of theAmerican Mathematical Society, 2005, Volume 52, Number 1.<\/p>\n","protected":false},"excerpt":{"rendered":"

Bu yaz\u0131da da matematikle mizah\u0131n kesi\u015fti\u011fi yolda y\u00fcr\u00fcyoruz. \u00d6nceki say\u0131da matematik mizah\u0131n\u0131 f\u0131kralardan \u00f6rnekler vererek incelemeye \u00e7al\u0131\u015fm\u0131\u015ft\u0131k. Bu kez de matematik \u00fczerine yap\u0131lm\u0131\u015f olan baz\u0131 \u015faka, espri ve karikat\u00fcrleri ele alaca\u011f\u0131z. Matematiksel \u015fakalar\u0131n bir\u00e7o\u011fu say\u0131lar kuram\u0131, fonksiyonel analiz, topoloji gibi matemati\u011fin farkl\u0131 alanlar\u0131na aittir. Merakl\u0131lar\u0131 i\u00e7in matematik d\u00fcnyas\u0131nda ke\u015ffe \u00e7\u0131kabilmenin ilk ad\u0131m\u0131 olabilecek bu esprilerin […]<\/p>\n","protected":false},"author":375,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[123,25,514],"tags":[208,340],"class_list":["post-10413","post","type-post","status-publish","format-standard","hentry","category-86-sayi","category-matematik","category-matematik-sohbetleri","tag-matematik","tag-mizah"],"acf":[],"aioseo_notices":[],"aioseo_head":"\n\t\t\n\t\n\t\n\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t