{"id":10680,"date":"2011-05-01T21:13:47","date_gmt":"2011-05-01T18:13:47","guid":{"rendered":"http:\/\/109.232.216.219\/~bilimvegelecek\/?p=10680"},"modified":"2017-05-29T21:16:04","modified_gmt":"2017-05-29T18:16:04","slug":"matematiksel-semboller","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2011\/05\/01\/matematiksel-semboller","title":{"rendered":"Matematiksel Semboller"},"content":{"rendered":"

1995\u2019te Cahit Arf\u2019\u0131n 85. do\u011fum y\u0131ld\u00f6n\u00fcm\u00fc onuruna d\u00fczenlenen bir sempozyuma kat\u0131lm\u0131\u015ft\u0131m. Toplant\u0131 salonunun lobisinde matematik\u00e7ilerle s\u00f6yle\u015fen Cahit Arf\u2019\u0131n \u015fu s\u00f6zlerini an\u0131ms\u0131yorum: \u201cYa\u015far Kemal\u2019in \u0130nce Memed<\/em>\u2019i \u00e7ok g\u00fczel; e\u011fer edebi bir metin de\u011fil de, matematiksel bir metin olarak yaz\u0131labilseydi, ben onu matematik diliyle iki sayfada yazmak isterdim.\u201d Bu fantastik espri matematik dilinin ekonomik niteli\u011fine vurgu yap\u0131yordu. Ama o g\u00fcn, o ayak\u00fcst\u00fc sohbette bu esprinin ger\u00e7ekle\u015fmesi kurgusu \u00fczerine de konu\u015fulmu\u015ftu. Hi\u00e7bir \u00e7eviriye gerek kalmadan her \u00fclkede, matemati\u011fi bilen herkesin \u0130nce Memed<\/em>\u2019i okuyabilece\u011fi \u015fakas\u0131 yap\u0131lm\u0131\u015ft\u0131. Ku\u015fkusuz bu \u015faka matematik dilinin evrenselli\u011finden kaynaklan\u0131yordu.<\/p>\n

Matemati\u011fin dili d\u00fcnyan\u0131n ortak dilidir. Bir logaritmik denklemin \u00e7\u00f6z\u00fcm\u00fcn\u00fc, bir e\u011frinin \u00e7izimini yapan her ki\u015fi d\u00fcnyan\u0131n neresinde olursa olsun ayn\u0131 matematiksel sembolleri kullanacakt\u0131r. Matemati\u011fin 5000 y\u0131ll\u0131k yaz\u0131l\u0131 tarihinde zenginle\u015ferek bir\u00e7ok de\u011fi\u015fikli\u011fe u\u011frayan bu semboller matematiksel anlat\u0131m\u0131n yap\u0131ta\u015flar\u0131d\u0131r.<\/p>\n

G\u00fcn\u00fcm\u00fcz matematik notasyonu 500 y\u00fczy\u0131ll\u0131k bir ge\u00e7mi\u015fe sahiptir ve \u00f6nemli bir b\u00f6l\u00fcm\u00fc son 250 y\u0131l i\u00e7inde ortaya \u00e7\u0131km\u0131\u015ft\u0131r. Ama matematiksel sembollerin kullan\u0131m\u0131 5000 y\u0131ldan da \u00f6ncesine dayan\u0131r. Babillerin ve muhtemelen onlardan \u00f6nce S\u00fcmerlerin say\u0131larla ilgili baz\u0131 sembolleri kulland\u0131klar\u0131n\u0131 biliyoruz. \u00c7o\u011funlukla say\u0131lar\u0131 60 taban\u0131nda yazm\u0131\u015flar. Kulland\u0131klar\u0131 bu say\u0131 taban\u0131n\u0131n etkisini g\u00fcn\u00fcm\u00fczde de g\u00f6rmek m\u00fcmk\u00fcn. Dakika, saat, y\u0131l gibi zaman \u00f6l\u00e7\u00fc birimlerini, \u00e7emberin \u00e7evresinin 360 dereceye b\u00f6l\u00fcnmesini 60\u2019\u0131n kat\u0131 say\u0131larla ifade ediyoruz. Bug\u00fcn de binlerce y\u0131l \u00f6nce sembolize edilmi\u015f bu say\u0131larla birlikte ya\u015f\u0131yoruz.<\/p>\n

Babillerden \u00e7ok \u00f6nce de say\u0131lar\u0131n g\u00f6sterimi i\u00e7in baz\u0131 semboller kullan\u0131lm\u0131\u015ft\u0131r mutlaka. Bulunan ilk g\u00f6sterim 37000 y\u0131l \u00f6ncesine ait oldu\u011fu bilinen bir hayvan kemi\u011fi par\u00e7as\u0131 \u00fczerindeki 29 adet \u00e7entiktir. Birli sistemde \u00e7al\u0131\u015fm\u0131\u015flar, \u00f6rne\u011fin 5 say\u0131s\u0131n\u0131 g\u00f6stermek i\u00e7in be\u015f \u00e7entik atmak gibi. Tabii ki bu bulgunun say\u0131lar\u0131n ilk g\u00f6sterimi olup olmad\u0131\u011f\u0131 kesin de\u011fil. Uzak tarihe ait g\u00f6sterimleri tam olarak bilmemiz olanaks\u0131z.<\/p>\n

Matemati\u011fin tarihine daha yak\u0131ndan bakarsak g\u00fcn\u00fcm\u00fcz matematik dilinin ortaya \u00e7\u0131k\u0131\u015f\u0131n\u0131n 15. y\u00fczy\u0131l\u0131n sonuna kar\u015f\u0131l\u0131k geldi\u011fini g\u00f6r\u00fcr\u00fcz. 16. y\u00fczy\u0131lda cebir alan\u0131nda yap\u0131lan \u00e7al\u0131\u015fmalar matematik notasyonunun do\u011fmas\u0131na yol a\u00e7m\u0131\u015ft\u0131r. Bug\u00fcn cebirde kullan\u0131lan bir\u00e7ok sembol bu d\u00f6nemde olu\u015fmu\u015ftur.\u00a0 Bilinmeyen \u00e7okluklar\u0131n harflerle g\u00f6sterilmesi, d\u00f6rt i\u015flem i\u00e7in sembollerin kullan\u0131lmas\u0131 problemlerin \u00e7\u00f6z\u00fcm\u00fcnde b\u00fcy\u00fck kolayl\u0131klar getirmi\u015ftir. \u0130lkel bir cebirden sembolik cebire ge\u00e7i\u015f s\u00fcreci, birka\u00e7 y\u00fczy\u0131ll\u0131k bir zaman diliminde ger\u00e7ekle\u015fmi\u015ftir. Daha sonras\u0131nda, matematik dilinde birlik sa\u011flama 19. y\u00fczy\u0131l\u0131n sonlar\u0131na do\u011fru daha \u00e7ok ihtiya\u00e7 haline gelmi\u015ftir.<\/p>\n

Matematiksel geli\u015fmeye ko\u015fut olarak ortaya \u00e7\u0131kan ve y\u00fczy\u0131llar \u00f6ncesinden g\u00fcn\u00fcm\u00fcze dek gelen matematiksel semboller neyi ama\u00e7lar? Bir matematiksel sembol, temsil etti\u011fi<\/p>\n

 <\/p>\n

matematiksel nesneyi a\u00e7\u0131k ve kesin olarak ifade edebilmelidir. Ayr\u0131ca kullan\u0131m kolayl\u0131\u011f\u0131 olmal\u0131, yayg\u0131n bir \u015fekilde kabul g\u00f6rmelidir. Asl\u0131nda matematiksel g\u00f6sterimlerin ba\u015fat amac\u0131 k\u0131saltmad\u0131r. K\u0131saltma olmaks\u0131z\u0131n matematik yapmak adeta olanaks\u0131zla\u015f\u0131r. Bunun en g\u00fczel ve basit \u00f6rne\u011fi say\u0131lar\u0131n g\u00f6steriminde kar\u015f\u0131m\u0131za \u00e7\u0131kar. G\u00fcnl\u00fck dilde bir tane kelime \u201con\u201d i\u00e7in, bir ba\u015fka kelime \u201cy\u00fcz\u201d i\u00e7in ve bir ba\u015fkas\u0131 \u201cbin\u201d i\u00e7in vard\u0131r ve dahas\u0131\u2026 Ama biz biliyoruz ki \u201con\u201d\u2019u \u201cbir ve s\u0131f\u0131r\u201d (10), y\u00fcz\u00fc \u201cbir, s\u0131f\u0131r, s\u0131f\u0131r\u201d (100), bini \u201cbir, s\u0131f\u0131r, s\u0131f\u0131r, s\u0131f\u0131r\u201d (1000) olarak g\u00f6steriyor ve bir rakam\u0131 farkl\u0131 konumlarda tekrar kullanarak farkl\u0131 anlamlar \u00e7\u0131karabiliyoruz. Bu pratik ve ekonomik g\u00f6sterimin ke\u015ffi insanl\u0131\u011f\u0131n binlerce y\u0131l\u0131n\u0131 alm\u0131\u015ft\u0131r.<\/p>\n

Matematik tarihinde sadece birka\u00e7 matematik\u00e7i evrensel olarak kabul edilen sembollerden iki veya \u00fc\u00e7ten fazlas\u0131n\u0131 icat edebilmi\u015ftir. Gottfried Leibniz<\/a> (1646\u20131716), Leonhard Euler<\/a> (1707\u20131783), Giuseppe Peano<\/a> (1858\u20131932) m\u00fckemmel semboller yaratm\u0131\u015flard\u0131r. Leibniz, diferansiyel ve integral hesapta, Peano matematiksel mant\u0131kta g\u00fcn\u00fcm\u00fczde de kulland\u0131\u011f\u0131m\u0131z g\u00f6sterimleri ifade etmi\u015flerdir. Euler ise matemati\u011fin farkl\u0131 alanlar\u0131na ait notasyon yaratmakta \u00e7ok ba\u015far\u0131l\u0131 olmu\u015ftur. Say\u0131lardaki e <\/em>ve i <\/em>simgeleri,ile g\u00f6sterilen toplam sembol\u00fc, f = f(x)<\/em> fonksiyon sembol\u00fc, trigonometrideki sinx, cosx<\/em>, logaritmadaki logx<\/em> sembolleri, \u00fc\u00e7genin kenar uzunluklar\u0131n\u0131n a, b, c<\/em> gibi k\u00fc\u00e7\u00fck, k\u00f6\u015felerinin A, B, C<\/em> gibi b\u00fcy\u00fck harflerle g\u00f6sterilmesi, r<\/em> i\u00e7 te\u011fet \u00e7emberin, R<\/em> \u00e7evrel \u00e7emberin yar\u0131\u00e7aplar\u0131, S<\/em> \u00e7evrenin yar\u0131s\u0131 olmak \u00fczere bir \u00fc\u00e7genin temel alt\u0131 uzunlu\u011fu aras\u0131ndaki ili\u015fkiyi sergileyen 4Rrs = abc<\/em> e\u015fitli\u011fi Euler\u2019e aittir.<\/p>\n

Nitelikli bir matematiksel notasyon nas\u0131l tan\u0131mlan\u0131r? Bu soruyu Amerikal\u0131 matematik\u00e7i Alferd North Whitehead (1861\u20131947) \u015f\u00f6yle yan\u0131tlar: \u201c\u0130yi bir notasyon, beyni b\u00fct\u00fcn gereksiz i\u015flerden kurtarmakla daha ileri problemler \u00fczerinde yo\u011funla\u015fmas\u0131 i\u00e7in \u00f6zg\u00fcr b\u0131rak\u0131r ve sonu\u00e7ta insan\u0131n zihinsel g\u00fcc\u00fcn\u00fc geli\u015ftirir.\u201d Bu tan\u0131ma uygun en g\u00fczel \u00f6rnekleri Leibniz vermi\u015ftir; kulland\u0131\u011f\u0131 g\u00f6sterim sistemi a\u00e7\u0131k, kesin ve zariftir. Bug\u00fcn diferansiyel ve integral hesapta kullan\u0131lan teknik dil b\u00fcy\u00fck \u00f6l\u00e7\u00fcde Leibniz\u2019e aittir. Onun buldu\u011fu sembolleri matematik\u00e7iler, daha ileriki kuramsal \u00e7al\u0131\u015fmalarda kolayl\u0131kla kullanabilmi\u015ftir. Notasyon yaz\u0131m\u0131nda Leibniz\u2019i di\u011fer matematik\u00e7ilerden ay\u0131ran en belirgin yan, sembolleri \u00f6ng\u00f6r\u00fcyle yaratmas\u0131d\u0131r. \u00d6rne\u011fin Newton, bir f <\/em>fonksiyonunun birinci ve ikinci t\u00fcrevlerini \u00f6nce \u00a0olarak g\u00f6stermi\u015f ard\u0131ndan f<\/em>\u2019nin \u00fcst\u00fcndeki noktan\u0131n k\u00e2\u011f\u0131ttaki ba\u015fka bir noktayla veya bir lekeyle kar\u0131\u015ft\u0131r\u0131labilece\u011fi itiraz\u0131 \u00fczerine \u00a0ve \u00a0olarak de\u011fi\u015ftirmi\u015ftir. Leibniz ise , <\/em>\u00a0sembollerini kullanm\u0131\u015ft\u0131r. \u00a0Bu iki g\u00f6sterim aras\u0131nda diferansiyel hesap kuram\u0131na uygunluk bak\u0131m\u0131ndan \u00f6nemli farklar vard\u0131r. yaz\u0131l\u0131m\u0131 yan\u0131lt\u0131c\u0131 olabilir; \u00e7\u00fcnk\u00fc f<\/em>\u2019 nin t\u00fcrevinin hangi de\u011fi\u015fkene (z<\/em>, t<\/em> olabilir) g\u00f6re al\u0131nd\u0131\u011f\u0131 belirsizdir. Leibniz bu sorunu g\u00f6rebildi\u011finden kullanm\u0131\u015ft\u0131r. Ayr\u0131cag\u00f6sterimi, n<\/em> pozitif tamsay\u0131yken ard\u0131\u015f\u0131k t\u00fcrevlerin say\u0131s\u0131n\u0131 ifade eder, bu da bize n<\/em>\u2019nin negatif veya rasyonel say\u0131 de\u011ferleri i\u00e7in\u00a0\u00a0yaz\u0131l\u0131m\u0131na g\u00f6re yorum yapma olana\u011f\u0131 sa\u011flar.<\/p>\n

G\u00fcn\u00fcm\u00fcz matematik dilinde kulland\u0131\u011f\u0131m\u0131z gibi baz\u0131 semboller \u0130talyan matematik\u00e7i Giuseppe Peano<\/a>\u2019ya aittir. Kurucusu oldu\u011fu matematik dergilerinde yay\u0131mlad\u0131\u011f\u0131 makalelerde matematik notasyonunda \u00e7\u0131\u011f\u0131r a\u00e7m\u0131\u015ft\u0131r. Daha \u00f6nce Leibniz\u2019in de hayali olan, \u00f6\u011frenilmesi kolay uluslararas\u0131 bir dil yaratmaya \u00e7al\u0131\u015fm\u0131\u015f ama yayg\u0131nla\u015fmas\u0131n\u0131 sa\u011flayamam\u0131\u015ft\u0131r.<\/p>\n

Bertnard Russell, (1872\u20131970) 1900\u2019deki \u00fcnl\u00fc Paris Konferans\u0131\u2019nda Peano\u2019yla kar\u015f\u0131la\u015fmas\u0131n\u0131 entelekt\u00fcel hayat\u0131n\u0131n d\u00f6n\u00fcm noktas\u0131 olarak g\u00f6rm\u00fc\u015ft\u00fcr. Russell, Peano\u2019nun matematiksel mant\u0131k ve dil \u00fczerine yapt\u0131\u011f\u0131 \u00e7al\u0131\u015fmalara olan hayranl\u0131\u011f\u0131n\u0131 \u015fu s\u00f6zlerle ifade etmi\u015ftir: \u201cOnun yaratt\u0131\u011f\u0131 matematiksel notasyonu\u00a0 inceledik\u00e7e, anlatmak istedi\u011fi \u015feyi azaltmadan, ona zarar vermeden, kulland\u0131\u011f\u0131 sembollerin ortaya koyulan matematiksel d\u00fc\u015f\u00fcnceyi nas\u0131l g\u00fc\u00e7lendirdi\u011fini g\u00f6rd\u00fcm, y\u0131llard\u0131r arad\u0131\u011f\u0131m \u015fey buydu ve yeni bir teknik kazanm\u0131\u015f oldum.\u201d<\/p>\n

Matematiksel semboller, matematik dilinin s\u00f6zc\u00fckleri gibidir. Nas\u0131l ki bir d\u00fc\u015f\u00fcnceyi do\u011fru ve g\u00fczel bir bi\u00e7imde aktarabilmek i\u00e7in \u00f6zenle se\u00e7ilmi\u015f uygun s\u00f6zc\u00fcklere gerek varsa, matematik yapmak i\u00e7in de g\u00fc\u00e7l\u00fc, nitelikli sembollere gerek vard\u0131r. Matematik tarihine bak\u0131ld\u0131\u011f\u0131nda bir\u00e7ok matematik\u00e7inin daha m\u00fckemmel semboller yaratma \u00e7abas\u0131 i\u00e7inde oldu\u011fu g\u00f6r\u00fcl\u00fcr. Belki de Cahit Arf, \u0130nce Memed<\/em>\u2019i iki sayfaya indirgemeyi hayal ederken bu m\u00fckemmel sembollerin g\u00fcc\u00fcne g\u00fcveniyordu! Hakl\u0131yd\u0131, semboller olmasayd\u0131 Cahit Arf ismi matematik tarihine yaz\u0131lamayacakt\u0131 ve yery\u00fcz\u00fcnde tek bir ki\u015fi bile onun matematiksel ke\u015fiflerini ifade edemeyecekti. Oysa bug\u00fcn, matematik literat\u00fcr\u00fcndeki Arf(x), Arf(y)<\/em> k\u0131saltmalar\u0131yla matematik yapan matematik\u00e7iler var.<\/p>\n

Ku\u015fkusuz, matematik sembolleri matematik yapan herkes i\u00e7in gerekli. Onlar olmasayd\u0131 matemati\u011fin b\u00fcy\u00fcl\u00fc d\u00fcnyas\u0131ndaki o g\u00fczel yolculuklara \u00e7\u0131kamayacakt\u0131k. Galile\u2019nin \u201cevrenin dili\u201d dedi\u011fi matematik, d\u00fcnyan\u0131n her yerinde \u0131rk, din, dil fark\u0131 g\u00f6zetmeksizin t\u00fcm insanlar\u0131n ortak dili olamayacakt\u0131.<\/p>\n

Baz\u0131 matematiksel g\u00f6sterimlerin k\u0131sa tarih\u00e7esi<\/strong><\/p>\n

\u00a0(D\u00f6rt i\u015flem i\u015faretleri): <\/strong>Onbe\u015f ve onyedinci y\u00fczy\u0131llar aras\u0131nda ortaya \u00e7\u0131kan bu semboller, Alman ve \u0130ngiliz matematik\u00e7iler taraf\u0131ndan ifade edilmi\u015ftir. ( + ) ve (\u00a0i\u015faretlerini ilk kez Jean Viedman 1489\u2019da yay\u0131mlanan Pratik Matematik<\/em> isimli kitab\u0131nda kullanm\u0131\u015ft\u0131r. Toplama i\u015fareti, Latincede \u201cve\u201d anlam\u0131na gelen ve \u00f6n ek olarak kullan\u0131lan \u201cet\u201d s\u00f6zc\u00fc\u011f\u00fcn\u00fcn ikinci harfi olan \u201ct\u201d den t\u00fcretilmi\u015ftir. B\u00f6lme sembol\u00fc olan () i\u015faretine ilk kez 12. y\u00fczy\u0131lda yaz\u0131lan Arap\u00e7a eserlerde rastlanm\u0131\u015ft\u0131r ve bu i\u015faret s\u00f6z konusu eserlerde kesirli de\u011ferleri g\u00f6stermek amac\u0131yla kullan\u0131lm\u0131\u015ft\u0131r; Avrupal\u0131lar ise \u00f6nceleri bu sembol\u00fc \u00e7\u0131karma i\u015flemini tan\u0131mlayan bir sembol olarak kullanm\u0131\u015flar, daha sonra \u00e7\u0131karma i\u015fareti \u00a0olarak bu g\u00f6sterim g\u00fcn\u00fcm\u00fcze dek gelmi\u015ftir. \u00c7arpma i\u015fareti ilk kez 1631\u2019de William Oughtred taraf\u0131ndan\u00a0olarak kullan\u0131lm\u0131\u015ft\u0131r. Leibniz, John Bernoulli\u2019ye g\u00f6nderdi\u011fi mektupta\u00a0i\u015faretinin yaz\u0131l\u0131\u015f\u0131n\u0131n pratik olmad\u0131\u011f\u0131n\u0131 ve bilinmeyen i\u00e7in kullan\u0131lan x<\/em> harfiyle kar\u0131\u015fabilece\u011fini \u00f6ne s\u00fcrerek, (a\u2219b) bi\u00e7imindeki noktayla olan g\u00f6sterimi kulland\u0131\u011f\u0131n\u0131 yazm\u0131\u015ft\u0131r.<\/p>\n

\u00a0(E\u015fitlik i\u015fareti): <\/strong>1557 y\u0131l\u0131nda Galli matematik\u00e7i Robert Recorde, \u00e7al\u0131\u015f\u0131rken \u201ce\u015fittir\u201d s\u00f6zc\u00fc\u011f\u00fcn\u00fc b\u0131kt\u0131r\u0131c\u0131 bir bi\u00e7imde tekrar tekrar yazman\u0131n zorlu\u011funu belirtmi\u015f, \u201cParalel iki \u00e7izgi koydum,\u00a0 \u00e7\u00fcnk\u00fc paralel iki \u00e7izgiden daha e\u015fit bir \u015fey olamaz.\u201d diyerek bu sembol\u00fc kullanan ilk ki\u015fi olmu\u015ftur.<\/p>\n

\u00a0(Karek\u00f6k sembol\u00fc): <\/strong>Bu sembol ilk kez 1525\u2019te Kristof Rudolff taraf\u0131ndan kullanm\u0131\u015ft\u0131r.\u00a0 Matematik tarih\u00e7ilerinden baz\u0131lar\u0131 Rudolff\u2019un bu sembol\u00fc \u0130ngilizcede \u201ck\u00f6k\u201d anlam\u0131na gelen \u201cradix\u201d s\u00f6zc\u00fc\u011f\u00fcn\u00fcn ilk harfi olan k\u00fc\u00e7\u00fck \u201cr\u201d den t\u00fcretti\u011fini varsaym\u0131\u015flard\u0131r.<\/p>\n

(Fakt\u00f6ryel sembol\u00fc): <\/strong>Bu sembol\u00fc ard\u0131\u015f\u0131k pozitif tamsay\u0131lar\u0131n \u00e7arp\u0131m\u0131n\u0131n g\u00f6sterimindeki zorlu\u011fu a\u015fmak i\u00e7in ilk kez 1808\u2019de Christian Kramp kullanm\u0131\u015ft\u0131r. Say\u0131n\u0131n sa\u011f\u0131na \u00fcnlem i\u015faretinin koyulma nedeni say\u0131 b\u00fcy\u00fcd\u00fck\u00e7e \u00e7arp\u0131mdaki b\u00fcy\u00fcmeye dikkat \u00e7ekmek olarak yorumlanm\u0131\u015ft\u0131r.<\/p>\n

(Niceleyici sembolleri): <\/strong>sembol\u00fcn\u00fc ilk kez, 1897\u2019de Giuseppe Peano<\/a> Matematik Form\u00fclleri<\/em> ismiyle yay\u0131nlad\u0131\u011f\u0131 kitab\u0131nda kullanm\u0131\u015ft\u0131r.sembol\u00fc ise Gerhard Gentzen taraf\u0131ndan sembol\u00fcn\u00fcn ortaya \u00e7\u0131k\u0131\u015f\u0131ndan 38 y\u0131l sonra 1935\u2019te yarat\u0131lm\u0131\u015ft\u0131r. G\u00fcn\u00fcm\u00fcz matemati\u011finde birbirinin tamamlay\u0131c\u0131s\u0131 olan bu sembollerin 38 y\u0131l arayla ifade edilmi\u015f olmas\u0131 matematik notasyonunun geli\u015fimini \u00e7ok iyi anlat\u0131r.<\/p>\n

(Bo\u015f k\u00fcme sembol\u00fc): <\/strong>Norve\u00e7 alfabesinde bir harf olan bu sembol ilk kez N. Bourbaki grubunun 1939\u2019da yay\u0131mlanan Elemanter Matematik<\/em> isimli kitab\u0131nda kullan\u0131lm\u0131\u015ft\u0131r. Bourbaki grubunun \u00fcyesi Frans\u0131z matematik\u00e7i Andr\u00e9 Weil bir yaz\u0131s\u0131nda, k\u0131z\u0131n\u0131n okulda \u201cbo\u015f k\u00fcmeyi\u201d kendilerinin \u00f6nerdi\u011fi bu sembolle \u00f6\u011freniyor olmas\u0131ndan gururland\u0131\u011f\u0131n\u0131 ifade etmi\u015ftir.<\/p>\n

(Sonsuz sembol\u00fc): <\/strong>Bu sembol ilk kez 1665\u2019te \u0130ngiliz matematik\u00e7i John Wallis\u2019in yay\u0131mlad\u0131\u011f\u0131 bir kitapta yer alm\u0131\u015ft\u0131r. Wallis bu sembol\u00fc Yunan alfabesinin son harfi olan \u2019dan (omega)\u00a0 esinlenerek \u201csonsuz<\/em>, son say\u0131 olsayd\u0131 son harfle g\u00f6sterilirdi\u201d d\u00fc\u015f\u00fcncesiyle t\u00fcretmi\u015ftir.<\/p>\n

\u222b (\u0130ntegral sembol\u00fc): <\/strong>Bu sembol\u00fcn yarat\u0131c\u0131s\u0131 Leibniz\u2019dir. E\u011fri alt\u0131nda kalan alan\u0131 \u201csonsuz k\u00fc\u00e7\u00fck alanlar\u0131n\u201d toplam\u0131 olarak ifade etti\u011finden Latincede toplama anlam\u0131na gelen SUMMA s\u00f6zc\u00fc\u011f\u00fcn\u00fcn ilk harfi olan S\u2019nin uzat\u0131lm\u0131\u015f \u015feklini integral sembol\u00fc olarak kullanm\u0131\u015ft\u0131r.<\/p>\n

0 (S\u0131f\u0131r): <\/strong>S\u0131f\u0131r <\/em>kavram\u0131n\u0131n ilk olarak hangi medeniyet i\u00e7erisinde ve kim taraf\u0131ndan kullan\u0131ld\u0131\u011f\u0131 belirsizdir ama s\u0131f\u0131r<\/em> say\u0131 i\u015fareti olarak ilk kez milattan sonra 5. y\u00fczy\u0131lda yaz\u0131l\u0131 Hint eserleri i\u00e7inde g\u00f6r\u00fclm\u00fc\u015ft\u00fcr. Hint D\u00fcnyas\u0131\u2019n\u0131n \u00fcnl\u00fc matematik\u00e7i ve astronomu Brahmaqupta 632 y\u0131l\u0131nda yazd\u0131\u011f\u0131 Siddihanta<\/em> isimli eserinde dokuz ayr\u0131 say\u0131 i\u015faretinin yan\u0131nda s\u0131f\u0131r\u0131 da kullanarak hesaplamalar yapm\u0131\u015ft\u0131r. Hint bilginleri, dokuz ayr\u0131 rakam\u0131n baz\u0131 say\u0131lar\u0131 ifade etmekte yetersiz kald\u0131\u011f\u0131n\u0131 g\u00f6rm\u00fc\u015fler, eksik kalan basama\u011f\u0131 \u00f6nce bo\u015f b\u0131rakm\u0131\u015flar sonra \u201c.\u201d (nokta)\u00a0 koymu\u015flar, sonras\u0131nda da \u201c0\u201d (s\u0131f\u0131r) i\u015faretini kullan\u0131lm\u0131\u015flard\u0131r. \u00a0Bug\u00fcnk\u00fc basamak sistemiyle \u00f6rneklersek, be\u015f y\u00fcz yedi <\/em>say\u0131s\u0131 \u00f6nce \u201c5 7\u201d, sonra \u201c5. 7\u201d ve s\u0131f\u0131r i\u015faretini kullanarak \u201c507\u201d olarak yaz\u0131l\u0131r. Hint bilginleri \u00e7ember \u015feklinde g\u00f6sterdikleri s\u0131f\u0131r<\/em> i\u00e7in bir \u015feyin hi\u00e7li\u011fi ve bo\u015flu\u011fu anlam\u0131na gelen sunya <\/em>s\u00f6zc\u00fc\u011f\u00fcn\u00fc kullanm\u0131\u015flar.<\/p>\n

(Pi sembol\u00fc): <\/strong>Dairenin \u00e7evresinin \u00e7ap\u0131na oran\u0131ndan elde edilen say\u0131y\u0131 g\u00f6steren ,<\/strong> Yunanca \u00e7evre ya da \u00e7evre uzunlu\u011fu anlam\u0131na gelen \u03c0\u03b5\u03c1\u03af\u03bc\u03b5\u03c4\u03c1\u03bf\u03bd( perifereia) s\u00f6zc\u00fc\u011f\u00fcn\u00fcn ilk harfidir. Bu sembol\u00fc ilk kez William Jones 1706\u2019da yay\u0131mlanan Yeni Matemati\u011fe Giri\u015f<\/em> isimli kitab\u0131nda kullanm\u0131\u015ft\u0131r. Ama daha sonra Euler\u2019in analiz kitaplar\u0131nda\u2019yi kullanmas\u0131yla bu sembol evrensel olarak kabul edilmi\u015ftir.<\/p>\n

(Do\u011fal logaritma taban\u0131n\u0131n simgesi): <\/strong>e<\/em> simgesi ilk kez Euler taraf\u0131ndan 1728\u2019de yay\u0131mlanan bir makalede kullan\u0131ld\u0131\u011f\u0131nda, Euler hen\u00fcz 21 ya\u015f\u0131ndayd\u0131. Euler\u2019in do\u011fal logaritman\u0131n taban\u0131 olan say\u0131y\u0131 \u201ce\u201d<\/em> harfiyle g\u00f6stermi\u015f olmas\u0131 birka\u00e7 nedene ba\u011flanm\u0131\u015ft\u0131r. Ad\u0131n\u0131n ilk harfini kullanm\u0131\u015f olabilir, ama Euler\u2019in al\u00e7akg\u00f6n\u00fcll\u00fc ki\u015fili\u011fi d\u00fc\u015f\u00fcn\u00fcld\u00fc\u011f\u00fcnde bu se\u00e7ene\u011fin k\u00fc\u00e7\u00fck bir olas\u0131l\u0131\u011fa sahip oldu\u011fu s\u00f6ylenebilir. Euler\u2019in e<\/em>\u2019yi sembol olarak se\u00e7mesindeki as\u0131l neden, Latince k\u00f6kenli \u201cexponential\u201d (\u00fcs alma) s\u00f6zc\u00fc\u011f\u00fcn\u00fcn ilk harfini kullanmas\u0131 olabilir ki, bu a\u00e7\u0131klama e <\/em>say\u0131s\u0131n\u0131n ortaya \u00e7\u0131k\u0131\u015f\u0131 incelendi\u011finde olduk\u00e7a ger\u00e7ek\u00e7i g\u00f6r\u00fcn\u00fcyor.<\/p>\n

i<\/em><\/strong>( Sanal birim simgesi ): <\/strong>\u0130lk kez 1777 Euler taraf\u0131ndan yay\u0131mlanan bir makalede kullan\u0131lm\u0131\u015ft\u0131r. Euler\u2019in bu simgeyi Latince im\u0101gin\u0101rius <\/em>s\u00f6zc\u00fc\u011f\u00fcn\u00fcn ilk harfi olan i<\/em>\u2019yi \u2019in sanal bir say\u0131 oldu\u011funu belirtmek i\u00e7in kulland\u0131\u011f\u0131 d\u00fc\u015f\u00fcn\u00fclmektedir.<\/p>\n

 <\/p>\n

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

1- Florian Cajori, (1929). A History of Mathematical Notations<\/em>, Dover Publications, 1993.<\/p>\n

2- Davis Philip J.,ReubenHersh, (2005) Matemati\u011fin Seyir Defteri<\/em>, \u00c7ev. Abado\u011flu E, Doruk Yay\u0131mc\u0131l\u0131k<\/p>\n","protected":false},"excerpt":{"rendered":"

1995\u2019te Cahit Arf\u2019\u0131n 85. do\u011fum y\u0131ld\u00f6n\u00fcm\u00fc onuruna d\u00fczenlenen bir sempozyuma kat\u0131lm\u0131\u015ft\u0131m. Toplant\u0131 salonunun lobisinde matematik\u00e7ilerle s\u00f6yle\u015fen Cahit Arf\u2019\u0131n \u015fu s\u00f6zlerini an\u0131ms\u0131yorum: \u201cYa\u015far Kemal\u2019in \u0130nce Memed\u2019i \u00e7ok g\u00fczel; e\u011fer edebi bir metin de\u011fil de, matematiksel bir metin olarak yaz\u0131labilseydi, ben onu matematik diliyle iki sayfada yazmak isterdim.\u201d Bu fantastik espri matematik dilinin ekonomik niteli\u011fine vurgu yap\u0131yordu. […]<\/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":[124,514],"tags":[208,703,704],"class_list":["post-10680","post","type-post","status-publish","format-standard","hentry","category-87-sayi","category-matematik-sohbetleri","tag-matematik","tag-matematik-dili","tag-semboller"],"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