{"id":2541,"date":"2015-03-11T00:44:47","date_gmt":"2015-03-10T22:44:47","guid":{"rendered":"http:\/\/www.ilkkimbuldu.com\/?p=2541"},"modified":"2018-09-28T02:42:38","modified_gmt":"2018-09-28T00:42:38","slug":"cebiri-kim-buldu","status":"publish","type":"post","link":"https:\/\/www.ilkkimbuldu.com\/?p=2541","title":{"rendered":"Cebiri kim buldu"},"content":{"rendered":"

Rakamlar ve semboller kullanarak ve denklemler kurarak aritmetik i\u015flemlerini genelle\u015ftirmi\u015f olan matematik koluna cebir ad\u0131 verilir.\u00a0\u00a0 Tarihte bilinen ilk cebir kitab\u0131 H\u00e2rizm\u00ee\u00a0<\/strong>taraf\u0131ndan 825 y\u0131l\u0131nda yaz\u0131lm\u0131\u015ft\u0131r. Kitab\u0131n ad\u0131 El-Cebru vel-Mukabele\u2019dir. Bu kitaptaki cebir kelimesinin anlam\u0131 “b\u00fct\u00fcnleme” yani denklemin her iki taraf\u0131na ayn\u0131 niceli\u011fin ilave edilmesidir. Avrupa bu kelimeye “b\u00fcy\u00fck sanat” manas\u0131n\u0131 vermi\u015ftir. Matemati\u011fin geni\u015f bir dal\u0131 olan “cebir” kelimesi bu eserden dilimize ge\u00e7mi\u015ftir.<\/p>\n

Latince kar\u015f\u0131l\u0131\u011f\u0131 algebre (Frans\u0131zca); algebra (\u0130ngilizce) olarak bat\u0131 dillerine de yerle\u015fmi\u015ftir. H\u00e2rizm\u00ee\u00a0<\/strong>ad\u0131 da bat\u0131 bilim d\u00fcnyas\u0131nda t\u00fcrl\u00fc t\u00fcrl\u00fc yaz\u0131l\u0131\u015f \u015fekillerine sokulmu\u015ftur. Bunlardan “hesap metodu” anlam\u0131nda olmak \u00fczere Latincede “alkhorizmi<\/strong>” (bundan algoritma<\/strong>), Frans\u0131zcadan “algorithme” \u015feklinde kullan\u0131lm\u0131\u015ft\u0131r. Arap\u00e7aya Mezopotamya dillerinden girdi\u011fi s\u00f6ylenen bu kelime bat\u0131da Arap\u00e7a
\nyaz\u0131l\u0131\u015f \u015feklini hat\u0131rlatacak bi\u00e7imde kullan\u0131lmaktad\u0131r.<\/p>\n

Tarafs\u0131z olarak haz\u0131rlanm\u0131\u015f matematik tarihi eserlerinde “Cebir, 8, y\u00fczy\u0131l ve 16. y\u00fczy\u0131l \u0130slam d\u00fcnyas\u0131 bilim adamlar\u0131<\/a> taraf\u0131ndan ortaya koyulmu\u015f ve geli\u015ftirilmi\u015ftir.” diye yazmaktad\u0131r.<\/p>\n

H\u00e2rizm\u00ee<\/a><\/h2>\n

Harizmi<\/strong>, matematik, astronomi ve co\u011frafya konular\u0131 ile ilgili olarak \u00e7e\u015fitli eserler ortaya koymu\u015ftur. Matemati\u011fin geni\u015f bir dal\u0131 olan “Cebir”in temellerini at\u0131p geli\u015ftirmi\u015ftir. \u00c7e\u015fitli kaynaklar “H\u00e2rizm\u00ee\u00a0<\/strong>\u2019nin kurdu\u011fu cebir ilmi Bat\u0131n\u0131n Euckleides (\u00d6klid)inden 1000 y\u0131l ileridir.” \u015feklinde bahsederler.<\/p>\n

H\u00e2rizm\u00ee\u00a0<\/strong>, x2+21= 10x tipindeki denklemleri \u00e7\u00f6zerken, bilinmeyenin bir de\u011feri i\u00e7in (cez\u00eer=k\u00f6k) terimini kullanm\u0131\u015ft\u0131r. H\u00e2rizm\u00ee\u00a0<\/strong>\u2019nin “Al-Cebr” terimi 1202\u2019de Leonardo Pisano taraf\u0131ndan “Algebra” \u015feklinde Avrupa\u2019ya sokulmu\u015ftur.<\/p>\n

Cebir kaynaklar\u0131 i\u00e7inde temel olarak bilinen, t\u00e2rif, izah ve form\u00fcllerin bir k\u0131sm\u0131n\u0131 cebire ilk kazand\u0131ranlar\u0131n ba\u015f\u0131nda \u00d6mer Hayy\u00e2m\u00a0gelmektedir. \u00d6mer Hayy\u00e2m \u00fclkemizde zevk ve e\u011flence \u015f\u00e2iri olarak s\u00e2dece edeb\u00ee y\u00f6n\u00fcyle bilinmektedir. Halbuki Bat\u0131da ise \u00fcnl\u00fc bir matematik ve astronomi bilgini olarak tan\u0131n\u0131r.<\/p>\n

Bat\u0131da yay\u0131nlanan ilk cebir kitab\u0131 on be\u015finci y\u00fczy\u0131l \u0130talyan matematik\u00e7isi Luca Pocioli\u2019nin Summa de Arithmetica adl\u0131 eseridir. On alt\u0131nc\u0131 y\u00fczy\u0131lda Frans\u0131zlardan Fran\u00e7ois Viete, nicelikleri harflerle g\u00f6steren sembolik bir cebir kitab\u0131 yazm\u0131\u015ft\u0131r. Bat\u0131 matematik\u00e7ileri, cebirle ilgili eserlerini H\u00e2rizm\u00ee\u00a0<\/strong>\u2019nin El-Cebr ve\u2019l-Muk\u00e2bele eserini \u00f6rnek alarak yazm\u0131\u015flard\u0131r.<\/p>\n

Cebir\u00a0T\u00fcrleri<\/h2>\n

Elemanter Cebir<\/h3>\n

Pozitif ve negatif say\u0131lar: 1,2,3, …, n… gibi do\u011fal say\u0131lar ile toplama i\u015flemi her zaman yap\u0131labilir. Fakat \u00e7\u0131karma i\u015flemi her zaman m\u00fcmk\u00fcn de\u011fildir. Negatif say\u0131lar kavram\u0131na ge\u00e7ilmesi bu sebepten olmu\u015ftur. Pozitif, negatif ve s\u0131f\u0131r say\u0131s\u0131n\u0131n meydana getirdi\u011fi say\u0131lar k\u00fcmesi tam say\u0131lar k\u00fcmesini te\u015fkil eder.<\/p>\n

Modern Cebir<\/h3>\n

Temeli \u00e7ok eskilerde at\u0131lmas\u0131na ra\u011fmen geli\u015fmesi 20. as\u0131rda \u00e7ok s\u00fcratli oldu\u011fu i\u00e7in yeni bulunan bir matematik sistem gibi g\u00f6r\u00fclen, k\u00fcmeler, elemanter cebirde m\u00fcmk\u00fcn olmayan baz\u0131 i\u015flemleri ve kolayl\u0131klar\u0131 i\u00e7ermektedir. Bunlara en basit bir \u00f6rnek olarak cinsleri farkl\u0131 elemanlar\u0131n birle\u015ftirilmesi (toplanmas\u0131) verilebilir. K\u00fcme (c\u00fcmle); ortak \u00f6zellikleri h\u00e2iz elemanlar\u0131n toplulu\u011fudur. Bir k\u00fcme parantezler i\u00e7inde elemanlar aras\u0131nda virg\u00fcl (,) konulmak s\u00fbretiyle veya Venn diyagramlar\u0131 ile (kapal\u0131 bir e\u011fri i\u00e7erisinde elemanlar\u0131 g\u00f6stermek s\u00fbretiyle) if\u00e2de edilir.<\/p>\n","protected":false},"excerpt":{"rendered":"

Rakamlar ve semboller kullanarak ve denklemler kurarak aritmetik i\u015flemlerini genelle\u015ftirmi\u015f olan matematik koluna cebir ad\u0131 verilir.\u00a0\u00a0 Tarihte bilinen ilk cebir kitab\u0131 H\u00e2rizm\u00ee\u00a0taraf\u0131ndan 825 y\u0131l\u0131nda yaz\u0131lm\u0131\u015ft\u0131r. Kitab\u0131n ad\u0131 El-Cebru vel-Mukabele\u2019dir. Bu…<\/p>\n","protected":false},"author":1,"featured_media":9006,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[92],"tags":[1346,188,929,1493,910,1479,2697],"class_list":["post-2541","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bilim","tag-algoritma","tag-cebir","tag-harizmi","tag-luca-pocioli","tag-matematik","tag-oklid","tag-omer-hayyam"],"_links":{"self":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/2541"}],"collection":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2541"}],"version-history":[{"count":12,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/2541\/revisions"}],"predecessor-version":[{"id":12062,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/posts\/2541\/revisions\/12062"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=\/wp\/v2\/media\/9006"}],"wp:attachment":[{"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2541"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2541"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ilkkimbuldu.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2541"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}