{"id":201,"date":"2008-12-14T01:52:40","date_gmt":"2008-12-13T23:52:40","guid":{"rendered":"http:\/\/www.umitcanli.com\/school\/?p=201"},"modified":"2025-05-31T14:51:32","modified_gmt":"2025-05-31T12:51:32","slug":"bir-cokgen-sorusu-1","status":"publish","type":"post","link":"http:\/\/www.umitcanli.com\/school\/index.php\/2008\/12\/14\/bir-cokgen-sorusu-1\/","title":{"rendered":"Bir \u00c7okgen Sorusu 1"},"content":{"rendered":"

\u00c7okgen konusunu i\u015flerken, derste akl\u0131ma a\u015fa\u011f\u0131daki soru gelmi\u015fti. “Sabah incileri” \u015feklinde, do\u011fa\u00e7lama olarak soruyu yaz\u0131p hemen derste \u00e7\u00f6zd\u00fck.<\/p>\n

K\u00f6\u015feleri, d\u00fczg\u00fcn bir 36-genin k\u00f6\u015feleri \u00fczerinde olan ka\u00e7 d\u00fczg\u00fcn \u00e7okgen \u00e7izilebilir ?<\/p><\/blockquote>\n

Soruyu sevdim. \u00c7\u00fcnk\u00fc, (\u00e7ok ilgin\u00e7 olmasa da), d\u00fc\u015f\u00fcnmeye sevk eden, \u00e7izmeyi, denemeyi ve yorumlamay\u0131 gerektiren bir soru. Beta testini yapmas\u0131 i\u00e7in, soruyu bir \u00f6\u011frencime verdi\u011fimde soru daha da ba\u015fka yerlere gitti. \u00c7\u00fcnk\u00fc ilk d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcm\u00fczde bir noktay\u0131 atlam\u0131\u015f\u0131z ki, o da bizi simetri olay\u0131na y\u00f6neltti. G\u00e2yet g\u00fczel oldu. Soru, d\u00fczeltilip derste (bir daha) do\u011fru \u015fekilde \u00e7\u00f6z\u00fclm\u00fc\u015f olsa da, kimse pek ilgilenmedi\u011finden, s\u0131navda sormay\u0131 d\u00fc\u015f\u00fcn\u00fcyordum. Fakat bu soru s\u0131navda yer almad\u0131, o y\u00fczden detayl\u0131 olarak a\u00e7\u0131klanmas\u0131nda bir sak\u0131nca g\u00f6rm\u00fcyorum.\u00a0 L\u00e2f\u0131 daha fazla uzatmadan, sorunun (yukar\u0131dakinden farkl\u0131) d\u00fczeltilmi\u015f halini soral\u0131m.<\/p>\n

K\u00f6\u015feleri, d\u00fczg\u00fcn bir 36-genin k\u00f6\u015feleri \u00fczerinde ve birbirine e\u015f olmayan ka\u00e7 d\u00fczg\u00fcn \u00e7okgen \u00e7izilebilir ?<\/p><\/blockquote>\n

Soruyu anlamaya \u00e7al\u0131\u015fal\u0131m. D\u00fczg\u00fcn bir 36-gen var. Bu 36-genin k\u00f6\u015feleri \u00fczerinde olan ba\u015fka d\u00fczg\u00fcn \u00e7okgenler \u00e7izilecek. \u00c7izilmesi ve dolay\u0131s\u0131yla g\u00f6rmesi de kolay olaca\u011f\u0131ndan, d\u00fczg\u00fcn bir 6-gen ile ba\u015flayabiliriz. Bir 6-gen \u00e7izin ve deneyin, yani tavsiyemiz ve “olmazsa olmaz”\u0131m\u0131z, bizzat kalemi elinize al\u0131p \u00e7izmeniz.<\/p>\n

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Yukar\u0131daki \u015fekilden de g\u00f6r\u00fclece\u011fi \u00fczere, k\u00f6\u015feleri 6-genin \u00fczerinde\u00a0 olacak bi\u00e7imde \u00e7izilebilen d\u00fczg\u00fcn \u00e7okgenler, 3-gen ve 6-genin kendisidir. Sadece iki tane varm\u0131\u015f. Bu y\u00fczden, 6-gen sorunun i\u00e7eri\u011fini kavramak i\u00e7in biraz yetersiz gibi. Bu y\u00fczden kenar say\u0131s\u0131n\u0131 artt\u0131ral\u0131m. Ama daha \u00f6nce, \u00f6rnek basit de olsa, olu\u015fturdu\u011fumuz bu \u015fekilden g\u00f6r\u00fclecek sonu\u00e7, tabii ki\u00a0 “3” ile “6”n\u0131n ili\u015fkisi. 6-genin i\u00e7ine 3-gen\u00a0 \u00e7izebiliyoruz. \u00c7\u00fcnk\u00fc, “3”, “6”y\u0131 (kalans\u0131z) b\u00f6ler. Dolay\u0131s\u0131yla, 6-genin ard\u0131\u015f\u0131k kenarlar\u0131n\u0131, her birinin say\u0131s\u0131 e\u015fit olacak \u015fekilde gruplayabiliriz. Burada, 3 grup olu\u015ftu ve herbirinde 2 kenar var ( 6:3 = 2).<\/p>\n

\n

Baz\u0131lar\u0131n\u0131n, “a\u00e7\u0131klanmas\u0131 uzun ve gereksiz” diye d\u00fc\u015f\u00fcnebilece\u011fi, “Herbirinin say\u0131s\u0131 e\u015fit olacak bi\u00e7imde gruplayabiliriz” k\u0131sm\u0131 asl\u0131nda \u00f6nemli. Bu a\u00e7\u0131klama, “Bir d\u00fczg\u00fcn \u00e7okgende, bir k\u00f6\u015feden, e\u015fit say\u0131da kenar atlayarak \u00e7izece\u011finiz her\u00a0 k\u00f6\u015fegenin hep ayn\u0131 uzunlukta olaca\u011f\u0131n\u0131” im\u00e2 ediyor. Bu e\u015fit uzunluktaki k\u00f6\u015fegenler de, tabii ki arad\u0131\u011f\u0131m\u0131z d\u00fczg\u00fcn \u00e7okgenin … lar\u0131 olacak. (Anlad\u0131n sen onu). “\u00c7evrel \u00e7ember” ve “D\u00fczg\u00fcn \u00e7okgen”in ili\u015fkisini ger\u00e7ekten anlam\u0131\u015f olanlar i\u00e7in, bu yaz\u0131 gayet a\u00e7\u0131k ve anla\u015f\u0131l\u0131r olmal\u0131. “O da ne demek ?” diyorsan\u0131z, \u015fu<\/a> uygulama \u00fczerinde biraz oynayarak soruyu kendiniz i\u00e7in daha a\u00e7\u0131k hale getirebilirsiniz.<\/p>\n<\/blockquote>\n

\u015eimdi ayn\u0131 olay\u0131, d\u00fczg\u00fcn bir 12-gen ile deneyelim. K\u00f6\u015feleri de adland\u0131rarak 12-geni olu\u015ftural\u0131m.<\/p>\n

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Onikigenin i\u00e7ine d\u00fczg\u00fcn 3-gen \u00e7izilebilir. \u00c7\u00fcnk\u00fc “3”, “12”yi (kalans\u0131z bi\u00e7imde) b\u00f6ler. Bir di\u011fer deyi\u015fle 12-genin kenarlar\u0131n\u0131, her birinin say\u0131s\u0131 e\u015fit olacak \u015fekilde gruplayabiliriz. Burada, 3 grup olu\u015ftu ve herbirinde 4 kenar var ( 12:3 = 4 \/ \u00d6rne\u011fin, A1’den A5’e kadar bir grup vb.)<\/p>\n

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Onikigenin i\u00e7ine d\u00fczg\u00fcn 4-gen de \u00e7izilebilir. \u00c7\u00fcnk\u00fc “4”, “12”yi (kalans\u0131z bi\u00e7imde) b\u00f6ler. Bir di\u011fer deyi\u015fle 12-genin kenarlar\u0131n\u0131, her birinin say\u0131s\u0131 e\u015fit olacak \u015fekilde gruplayabiliriz. Burada, 4 grup olu\u015ftu. ( 12:4 = 3)<\/p>\n

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Onikigenin i\u00e7ine d\u00fczg\u00fcn 6-gen de \u00e7izilebilir. \u00c7\u00fcnk\u00fc “6”, “12”yi (kalans\u0131z bi\u00e7imde) b\u00f6ler. Burada, 2 grup olu\u015ftu. ( 12:6 = 2). Yine ayn\u0131 \u00e7er\u00e7evede, “12”, “12” yi b\u00f6ler ve dolay\u0131s\u0131yla bir 12-gen de \u00e7izilebilir (ilk \u00e7okgenin kendisi). Yani arad\u0131\u011f\u0131m\u0131z \u00e7okgenlerden biri, k\u00f6\u015feleri \u00fczerine \u00e7okgen olu\u015fturdu\u011fumuz \u00e7okgenin kendisi.<\/p>\n

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Bu durumda, \u015fekilden de g\u00f6r\u00fclebilece\u011fi \u00fczere;<\/p>\n

K\u00f6\u015feleri, d\u00fczg\u00fcn bir 12-genin k\u00f6\u015feleri \u00fczerinde ve birbirine e\u015f olmayan 4 d\u00fczg\u00fcn \u00e7okgen \u00e7izilebiliyormu\u015f. Bunlar, 3-gen, 4-gen, 6-gen ve 12-gen. Bunu hesap yoluyla bulmak istersek, a\u00e7\u0131klamalardan g\u00f6r\u00fclece\u011fi \u00fczere 12-genin b\u00f6lenlerine bak\u0131lmal\u0131. Bu durumda 12-genin pozitif b\u00f6lenlerinin say\u0131s\u0131na ihtiyac\u0131m\u0131z var. \u00c7\u00fcnk\u00fc 12’yi b\u00f6lebilen bir say\u0131, 12 adet kenar\u0131 da e\u015fit par\u00e7alara ay\u0131r\u0131r. 12’nin pozitif b\u00f6lenleri; 1,2,3,4,6,12.\u00a0Etti 6. Demek ki bulmam\u0131z gereken say\u0131n\u0131n 2 fazlas\u0131n\u0131 bulduk. Bunlar da, kolayl\u0131kla anla\u015f\u0131laca\u011f\u0131 \u00fczere, 1-gen (nokta) ve 2-gen (do\u011fru par\u00e7as\u0131).<\/p>\n

\u015eimdi as\u0131l sorumuza d\u00f6nelim. 36-gen i\u00e7in ayn\u0131 hesab\u0131 yapacak olursak, 36’n\u0131n pozitif b\u00f6lenlerini (bu kez hesap yoluyla) bulal\u0131m. 36’y\u0131 asal \u00e7arpanlar\u0131na ay\u0131r\u0131yoruz. 36 = 22<\/sup><\/span>. 32<\/sup><\/span> ve hat\u0131rlanacak olursa; Pozitif b\u00f6lenlerin say\u0131s\u0131 da (2+1).(2+1) = 3.3 = 9. Ve de, 1-gen ile 2-geni de \u00e7\u0131kart\u0131rsak\u00a0 9 – 2 = 7 tane imi\u015f. (Yani, 3\/36,4\/36, 6\/36, 9\/36, 12\/36, 18\/36, 36\/36)<\/p>\n

Ba\u015flang\u0131\u00e7ta, basit (ya da baz\u0131lar\u0131 i\u00e7in zor) gibi g\u00f6r\u00fcnen bu sorunun detayl\u0131 olarak a\u00e7\u0131kland\u0131\u011f\u0131n\u0131 san\u0131yorum. Bu sorudan ileriye gidilecek daha bir \u00e7ok yer var. Bu y\u00fczden yan\u0131t\u0131n\u0131 bir sonraki yaz\u0131da vermek \u00fczere, ilgilenenler i\u00e7in, soruyu, akla ilk gelen haliyle tekrar soral\u0131m. Bu sorudan yola \u00e7\u0131karak, yukar\u0131da yapt\u0131\u011f\u0131m\u0131z \u00fczere, her durumda uygulayabilece\u011fimiz bir y\u00f6ntem bulmaya da \u00e7al\u0131\u015fabilirsiniz.<\/p>\n

K\u00f6\u015feleri, d\u00fczg\u00fcn bir 36-genin k\u00f6\u015feleri \u00fczerinde olan ka\u00e7 d\u00fczg\u00fcn \u00e7okgen \u00e7izilebilir ?<\/p><\/blockquote>\n

Bu arada, madem ki soruyu 12-gen \u00fczerinden a\u00e7\u0131klad\u0131k. M\u00fczik ve armoniyle u\u011fra\u015fanlar i\u00e7in de akl\u0131ma hemen \u015fu soru geldi<\/p>\n

\n

\u00c7evrimlerinin her biri ayn\u0131 olan ka\u00e7 akor vard\u0131r ?<\/p>\n<\/blockquote>\n

\u015eekiller haz\u0131rlan\u0131rken olu\u015fturulan son \u00e7izim de buydu ve olduk\u00e7a ho\u015f g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc d\u00fc\u015f\u00fcnd\u00fc\u011f\u00fcm i\u00e7in buraya koymadan edemedim. Anlamad\u0131\u011f\u0131n\u0131z k\u0131s\u0131m veya buradan yola \u00e7\u0131karak akl\u0131n\u0131za gelen ba\u015fka sorular varsa yorum olarak buradan payla\u015fabilirsiniz…<\/p>\n

\"\"<\/p>\n\"1\"2\"3\"4\"5 (16<\/strong> ki\u015finin oyu ile 5<\/strong> \u00fczerinden ortalama 4,63<\/strong> verilmi\u015f)<\/span>Loading...<\/span>\n

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\u00c7okgen konusunu i\u015flerken, derste akl\u0131ma a\u015fa\u011f\u0131daki soru gelmi\u015fti. “Sabah incileri” \u015feklinde, do\u011fa\u00e7lama olarak soruyu yaz\u0131p hemen derste \u00e7\u00f6zd\u00fck. K\u00f6\u015feleri, d\u00fczg\u00fcn bir 36-genin k\u00f6\u015feleri \u00fczerinde olan ka\u00e7 d\u00fczg\u00fcn \u00e7okgen \u00e7izilebilir ?<\/p>\n

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