{"id":62135,"date":"2024-05-17T09:15:53","date_gmt":"2024-05-17T06:15:53","guid":{"rendered":"https:\/\/bilimvegelecek.com.tr\/?p=62135"},"modified":"2024-05-17T09:15:53","modified_gmt":"2024-05-17T06:15:53","slug":"kalansiz-bolunebilme-delisi","status":"publish","type":"post","link":"https:\/\/bilimvegelecek.com.tr\/index.php\/2024\/05\/17\/kalansiz-bolunebilme-delisi","title":{"rendered":"Kalans\u0131z b\u00f6l\u00fcnebilme delisi"},"content":{"rendered":"

Ender Helvac\u0131o\u011flu<\/strong><\/p>\n

B\u0131rak\u0131n bilgisayarlar\u0131, hesap makinelerinin bile yayg\u0131n olmad\u0131\u011f\u0131 d\u00f6nemdi. O zamanlar \u00fcniversiteli bir gen\u00e7tim. Mahallemizin s\u00fcrekli elinde kalem-k\u00e2\u011f\u0131tla dola\u015f\u0131p birtak\u0131m hesaplar yapan bir delisi vard\u0131. Mahallenin \u00e7ocuklar\u0131na \u00f6\u011fretmenlerinin \u00f6dev olarak verdi\u011fi matematik problemlerini \u00e7\u00f6zmeyi kendine i\u015f edinmi\u015fti. Ama amac\u0131, problemleri bilinenden daha kolay yolla \u00e7\u00f6zmenin y\u00f6ntemlerini bulmakt\u0131.<\/p>\n

Hani \u00fcnl\u00fc matematik\u00e7i Gauss\u2019un \u00e7ocukken buldu\u011fu bir y\u00f6ntemden s\u00f6z edilir ya\u2026 \u00d6\u011fretmen yorgundur, ders yapmak istememektedir. \u00d6\u011frencilerden 1\u2019den 100\u2019e kadar olan say\u0131lar\u0131n toplam\u0131n\u0131 bulmalar\u0131n\u0131 ister. B\u00f6ylece \u00e7ocuklar ders boyu u\u011fra\u015facak, o da kafa dinleyecektir. Fakat k\u00fc\u00e7\u00fck Gauss buldu\u011fu y\u00f6ntemle birka\u00e7 dakika sonra sonucu s\u00f6yleyiverir.<\/p>\n

\u0130\u015fte bizim deli de b\u00f6yle y\u00f6ntemler pe\u015findeydi. Bu u\u011fra\u015f\u0131n\u0131n nedenini sordu\u011fumda, \u201c\u00e7ocuklar\u0131n matematik hamal\u0131 de\u011fil matematik a\u015f\u0131\u011f\u0131 olmalar\u0131n\u0131 istiyorum\u201d demi\u015fti. Bu yan\u0131t kar\u015f\u0131s\u0131nda, ona deli dedi\u011fimiz i\u00e7in \u00e7ok utanm\u0131\u015ft\u0131m. Ama deliydi; delilik k\u00f6t\u00fc bir \u015fey de\u011fil ki\u2026 Bir alanda fazla derinle\u015fmenin (tak\u0131nt\u0131 da diyebiliriz) sonucu belki. \u00c7ocuklar da ona deli derdi, ama \u00e7ok severlerdi.<\/p>\n

Neyse, uzatmayay\u0131m; \u201ckalans\u0131z b\u00f6l\u00fcnebilme delisi\u201d lakab\u0131n\u0131 nas\u0131l ald\u0131\u011f\u0131n\u0131 anlatay\u0131m.<\/p>\n

\u00d6\u011fretmenleri \u00f6\u011frencilerden bir say\u0131n\u0131n 3\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcp b\u00f6l\u00fcnmedi\u011fini anlaman\u0131n bir y\u00f6ntemini bulmalar\u0131n\u0131 istemi\u015f. Eskiden b\u00f6yle \u00f6\u011fretmenler vard\u0131; \u00e7ocuklar\u0131 ezbere de\u011fil kafa \u00e7al\u0131\u015ft\u0131rmaya y\u00f6nelten\u2026<\/p>\n

Bir say\u0131n\u0131n 2\u2019ye, 5\u2019e, 10\u2019a kalans\u0131z b\u00f6l\u00fcn\u00fcp b\u00f6l\u00fcnmedi\u011fini saptamak kolayd\u0131r. Ama 3 i\u00e7in biraz kafa \u00e7al\u0131\u015ft\u0131rmak icap eder. Mahallenin \u00e7ocuklar\u0131 hemen bizim deliye ba\u015fvurmu\u015flar: Aman bize bir y\u00f6ntem\u2026 Delinin can\u0131na minnet. Yar\u0131m saatte bulmu\u015f \u00e7\u00f6z\u00fcm\u00fc. Toplam\u0131\u015f \u00e7ocuklar\u0131: Bir say\u0131n\u0131n rakamlar\u0131n\u0131n toplam\u0131 3\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcyorsa o say\u0131 da 3\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcr. \u00c7ocuklarda bir sevin\u00e7\u2026 Hemen 3\u2019e b\u00f6l\u00fcnebilme oyunu oynamaya ba\u015flam\u0131\u015flar.<\/p>\n

\u00c7ocuklar\u0131n bu \u015fen-\u015fakrak halinden \u00e7ok etkilenen deli kalans\u0131z b\u00f6l\u00fcnebilme meselesine kafay\u0131 takar. \u00d6rne\u011fin 11\u2019e, 13\u2019e vb. kalans\u0131z b\u00f6l\u00fcnebilme kurallar\u0131 da yok mudur?<\/p>\n

Gece boyu u\u011fra\u015f\u0131r, 11 i\u00e7in bir y\u00f6ntem geli\u015ftirir. Okul \u00e7\u0131k\u0131\u015f\u0131 mahallenin \u00e7ocuklar\u0131n\u0131 toplar. Al\u0131n size bir say\u0131n\u0131n 11\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcp b\u00f6l\u00fcnmedi\u011fini bulman\u0131n y\u00f6ntemi: Say\u0131n\u0131n son iki rakam\u0131ndan \u00f6nceki rakamlar\u0131ndan olu\u015fan say\u0131y\u0131 son iki rakama ekle, \u00e7\u0131kan sonu\u00e7 11\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcyorsa o say\u0131 da 11\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcr. \u00c7ocuklarda bir sevin\u00e7\u2026 \u0130\u00e7lerinden biri h\u0131nz\u0131rl\u0131k pe\u015findedir: \u201cBiz de 11\u2019e b\u00f6l\u00fcnebilme kural\u0131n\u0131 \u00f6\u011fretmene soral\u0131m!\u201d<\/p>\n

Deli h\u0131z\u0131n\u0131 alm\u0131\u015ft\u0131r. \u0130ki g\u00fcn sonra 13\u2019e kalans\u0131z b\u00f6l\u00fcnebilme kural\u0131yla gelir: Say\u0131n\u0131n son iki rakam\u0131ndan \u00f6nceki rakamlar\u0131ndan olu\u015fan say\u0131y\u0131 9 ila \u00e7arp\u0131p son iki rakama ekledi\u011finizde \u00e7\u0131kan sonu\u00e7 13\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcyorsa o say\u0131 da 13\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcr. \u00c7ocuklar elde kalem-k\u00e2\u011f\u0131t y\u00f6ntemin do\u011frulu\u011funu denemeye ba\u015flarlar.<\/p>\n

Matematikten nefret eden \u00e7ocuklar\u0131n\u0131n ne\u015fe i\u00e7inde hesap yapmaya ba\u015flad\u0131\u011f\u0131n\u0131 g\u00f6ren mahalle sakinleri i\u015fin s\u0131rr\u0131n\u0131 ara\u015ft\u0131r\u0131rlar. Tabii bizim deliye ula\u015f\u0131rlar. O noktadan sonra b\u00fct\u00fcn mahalle hesap yapmaya ba\u015flar. Kahvede art\u0131k tavla oynanm\u0131yor; 17\u2019ye kalans\u0131z b\u00f6l\u00fcnebilme kural\u0131 aran\u0131yor. Deli iki g\u00fcn sonra yan\u0131tla geliyor: Say\u0131n\u0131n son iki rakam\u0131ndan \u00f6nceki rakamlar\u0131ndan olu\u015fan say\u0131y\u0131 2 ile \u00e7arp\u0131p son iki rakamdan \u00e7\u0131kard\u0131\u011f\u0131n\u0131z zaman \u00e7\u0131kan sonu\u00e7 17\u2019ye kalans\u0131z b\u00f6l\u00fcn\u00fcyorsa o say\u0131 da 17\u2019ye kalans\u0131z b\u00f6l\u00fcn\u00fcr.<\/p>\n

Mahallenin kad\u0131nlar\u0131 topland\u0131klar\u0131nda dedikodu yapmak yerine 19\u2019a kalans\u0131z b\u00f6l\u00fcnebilme y\u00f6ntemini bulmaya \u00e7al\u0131\u015f\u0131yorlar. Yan\u0131t k\u0131sa bir s\u00fcre sonra deliden geliyor: Say\u0131n\u0131n son iki rakam\u0131ndan \u00f6nceki rakamlar\u0131ndan olu\u015fan say\u0131y\u0131 5 ile \u00e7arp\u0131p son iki rakama ekledi\u011finizde \u00e7\u0131kan sonu\u00e7 19\u2019a kalans\u0131z b\u00f6l\u00fcn\u00fcyorsa o say\u0131 da 19\u2019a kalans\u0131z b\u00f6l\u00fcn\u00fcr.<\/p>\n

Art\u0131k deliyi durdurabilene a\u015fkolsun. \u00c7ocuklar dahil b\u00fct\u00fcn mahalleyi toplar, 23\u2019e kalans\u0131z b\u00f6l\u00fcnebilme kural\u0131n\u0131 a\u00e7\u0131klar: Say\u0131n\u0131n son iki rakam\u0131ndan \u00f6nceki rakamlar\u0131ndan olu\u015fan say\u0131y\u0131 8 ile \u00e7arp\u0131p son iki rakama ekledi\u011finizde \u00e7\u0131kan sonu\u00e7 23\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcyorsa o say\u0131 da 23\u2019e kalans\u0131z b\u00f6l\u00fcn\u00fcr.<\/p>\n

Delimizin lakab\u0131 art\u0131k \u201ckalans\u0131z b\u00f6l\u00fcnebilme delisi\u201dne \u00e7\u0131km\u0131\u015ft\u0131r. Ama mesele sadece bizim deli de\u011fil ki. Mahallemiz \u201cKalans\u0131z B\u00f6l\u00fcnebilme Mahallesi\u201dne d\u00f6n\u00fc\u015fecek\u2026<\/p>\n

En son 29\u2019a kalans\u0131z b\u00f6l\u00fcnebilme kural\u0131yla (Say\u0131n\u0131n son iki rakam\u0131ndan \u00f6nceki rakamlar\u0131ndan olu\u015fan say\u0131 13 ile \u00e7arp\u0131l\u0131p son iki rakama eklendi\u011finde \u00e7\u0131kan sonu\u00e7 29\u2019a kalans\u0131z b\u00f6l\u00fcn\u00fcyorsa o say\u0131 da 29\u2019a kalans\u0131z b\u00f6l\u00fcn\u00fcr) geldi\u011finde deliye art\u0131k durmas\u0131 s\u00f6ylenir.<\/p>\n

\u201cPeki\u201d der deli. B\u00f6ylece mahallenin matematik d\u00f6nemi son bulur. Deli i\u00e7ine kapan\u0131r. Art\u0131k pek insan i\u00e7ine \u00e7\u0131kmaz.<\/p>\n

Ben bu deliye sayg\u0131 duyar\u0131m. Zaman zaman onu ziyaret ederdim. Son ziyaretimde, art\u0131k \u00e7ok ya\u015flanm\u0131\u015ft\u0131, san\u0131r\u0131m 90\u2019lar\u0131n\u0131 s\u00fcr\u00fcyordu; ama yine de \u201cbak, Ender\u201d dedi, \u201c743\u2019e kalans\u0131z b\u00f6l\u00fcnebilme kural\u0131n\u0131 anlatay\u0131m sana\u201d.<\/p>\n

Kalans\u0131z b\u00f6l\u00fcnebilme delisi ge\u00e7ti\u011fimiz ay \u00f6ld\u00fc. Tek ba\u015f\u0131na ya\u015fad\u0131\u011f\u0131 evde masas\u0131n\u0131n \u00fczerinde buldu\u011fumuz tamamen dolu defterinin son sayfas\u0131nda \u015f\u00f6yle bir nota rastlad\u0131k:<\/p>\n

\u201cB\u00f6yle teker teker nereye kadar? Genel bir kalans\u0131z b\u00f6l\u00fcnebilme teoremi geli\u015ftirdim. Ama burada yerim yok. Sonraki defterde kan\u0131t\u0131 yazaca\u011f\u0131m.\u201d<\/p>\n

Bir sonraki deftere ba\u015flayamadan hayat\u0131n\u0131 kaybetti bizim deli. Teoreminin kan\u0131t\u0131n\u0131 yazmaya ne defteri yetti ne de \u00f6mr\u00fc. Daha onlarca defteri var. \u0130ncelersek baz\u0131 ipu\u00e7lar\u0131 bulabiliriz belki.<\/p>\n

Cenazesinde tahmin etti\u011fimden fazla ki\u015fi vard\u0131. \u00c7o\u011fu mahallenin anlatt\u0131\u011f\u0131m d\u00f6nemdeki \u00e7ocuklar\u0131ndan olu\u015fan 10-15 ki\u015fi. Art\u0131k 50\u2019li ya\u015flar\u0131n\u0131 s\u00fcr\u00fcyorlar. Biliyor musunuz, i\u00e7lerinden \u00fc\u00e7 tanesi matematik\u00e7i olmu\u015f. Kalans\u0131z b\u00f6l\u00fcnebilme delisini onlar defnetti. Mezar ta\u015f\u0131na \u015f\u00f6yle yazm\u0131\u015flar Cemal S\u00fcreya\u2019dan esinlenerek:<\/p>\n

\u201c\u00dcst\u00fc kals\u0131n\u2026\u201d<\/p>\n","protected":false},"excerpt":{"rendered":"

Ender Helvac\u0131o\u011flu B\u0131rak\u0131n bilgisayarlar\u0131, hesap makinelerinin bile yayg\u0131n olmad\u0131\u011f\u0131 d\u00f6nemdi. O zamanlar \u00fcniversiteli bir gen\u00e7tim. Mahallemizin s\u00fcrekli elinde kalem-k\u00e2\u011f\u0131tla dola\u015f\u0131p birtak\u0131m hesaplar yapan bir delisi vard\u0131. Mahallenin \u00e7ocuklar\u0131na \u00f6\u011fretmenlerinin \u00f6dev olarak verdi\u011fi matematik problemlerini \u00e7\u00f6zmeyi kendine i\u015f edinmi\u015fti. Ama amac\u0131, problemleri bilinenden daha kolay yolla \u00e7\u00f6zmenin y\u00f6ntemlerini bulmakt\u0131. Hani \u00fcnl\u00fc matematik\u00e7i Gauss\u2019un \u00e7ocukken buldu\u011fu bir […]<\/p>\n","protected":false},"author":493,"featured_media":62136,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[19,2313],"tags":[9531,5247,9703],"class_list":["post-62135","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-bilim-gundemi","category-degirmen","tag-degirmen","tag-ender-helvacioglu","tag-kalansiz-bolunebilme-delisi"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/62135","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/users\/493"}],"replies":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/comments?post=62135"}],"version-history":[{"count":0,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/posts\/62135\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media\/62136"}],"wp:attachment":[{"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/media?parent=62135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/categories?post=62135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bilimvegelecek.com.tr\/index.php\/wp-json\/wp\/v2\/tags?post=62135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}