altin oran

belli bi anlamda "en irrasyonel sayi"'dir bu. pek "kuul" da sonuclari vardir bunun.(bkz: andrey nikolaevich kolmogorov) (bkz: vladimir igorevich arnold) (bkz: jurgen kurt moser)

(bkz: baskın oran)

finonacci sayılarının genel çözümünün köklerinden biridir altın oran

mimarlık öğrencilerine daha "aa burda ne güzel kızlar varmış" demeye fırsat bile vermeden hap gibi yutturulan kavram. eğer biraz konu ile ilgiliyseniz ikinci senenin sonuna doğru hakkaten bir anlamı olduğunu farkedebilirsiniz. dört yılda okulu başarı ile bitirip ne olduğu hakkında en ufak bir bilgisi olmayanları bile bilirim.

aynı zamanda dini bir sembol olan ve iki eşkenar üçgenden oluşan altı köşeli yıldız üzerinde, kesişen doğruların ortaya doğal bir biçimde çıkardığı oran...

iltifat cümlesi olarak kullanılması tavsiye edilmeyen cümledir. hoş karşılanmaz.

da vinci şifresinden mi çıktı nedir, son dönemde bütün televizyonların, gazetelerin mal bulmuş mağribi gibi üstüne atladıkları bir konu oldu bu. yok efendim hülya avşarın yüzü, yok tarkanın kıçı. bir yerde gördüm, ufaktan fibonacciyi de anlatmaya çalışmışlar ama kasılmışlar, anca tavşan kısmını anlayabildiklerinden ve anlatabilecek olmalarından olsa gerek. burayı okuyan medya mensubu varsa kendilerine sesleniyorum buradan, yeni bir şey değil altın oran, bayağı bi zamandır var yani, 5000 sene kadar. delirtmeyin adamı.

bir bitkinin hangi oransal hizda buyuyecegi sorusuna cevap bulma gorevinin sizeverildigini farzedin. her yeni dalin 2 nin katlari seklinde mi buyumesini uygun gorurdunuz,bitki cok hizli buyuyup besinsizlikten olmesin...yoksa 0.5 mi olsun da cok siki duran yapraklar birbirinin isigini kessin.bu az cok probleminin denge noktasi altin oran dir. bu sayede bitki govdesinde her parcaninbir onceki kucuk parca ile bir sonraki buyuk parcaya olan orani ayni olur. buna ister ilahikardes payi diyin ister dogal optimizasyon... (bkz: fraktal geometri)

"tanrısal oran" olarak da anılan irrasyonel sayı : 1.61... olarak süregider ve sanata uygulanımı dışında ve eveliyatında doğada rastlanabilir. örneğin bir insanın vücudunun yerden yüksekliğinin göbeğinin yerden yüksekliğine oranı yaklaşık olarak bu sayıya tekabül eder.

güzelliğin matematiksel tanımı.

fotgrafta kullanılan bır terımdır.anlamak ıcın orta format veya genıs format bır fotograf makınasının vızorunden ısın ehlı kısılerın gozetımı altında acıklamalı olarak bakılması gerekır.leonardo da vinci'nin man power adlı calısmasında ayrıntılı olarak gozlemlenebılır

bide insan bu altın oran hakkında bilgi edindikçe ürperiyo kendi kendine "nooluyo mına goyim??" yada "s.ktir lan" diyesi geliyo

da vinci şifresi'nden sonra meraklısı artan oran... halbuki hep vardı.

bela bartok´un "music for strings, percussion and celesta" adli eserinin birinci bölümünün yapisinda mükemmel olarak kullandigi matematiksel orandir. bu eser, bati müzigi tarihindeki yapisal acidan en tutarli ve mükemmel eserlerden biri olarak kabul edilir. parcanin analizinde bütünde ve detaylarda her yerinde karsiniza altin oran cikar.

ingilizcede altin oran.. antik yunanda evlerin pencereleri, kapilar vs gibi dikdortgen sekiller tasarlanirken kullanilan ve goze en hos gorunen en/boy orani.

mimarlarin projelerine koyabilmek icin kasmasi gerektigi halde deniz minaresinin, salyangozun, cicegin, bocegin hic zorlanmadan uyguladigi oran.muhendis mimar savaslarina neden olabilecek oranlardandir. ayni nitelikte bir diger oran ise narinlik oranidir.

ideal insanın boyu x birim olsun. göbeğinden ayak ucuna olan uzaklık da y birim olsun. bu durumda göbeğinden başucuna olan uzaklık da x - y birim olacak. iddiaya göre ideal insandaki ölçüler şu denklemi sağlamalı:x / y = y / (x - y).ideal insanda sağlanması istenen bu orana yani x / y oranına altın oran denir.kök bes artı bir bölü 2'dir

aslında soyle bir orandır: bir dogru alın. iki parcaya bolun. buyuk parcanini kucuk parcaya oranının, dogrunun buyuk parcaya oranına esit oldugu orandır. 1.618... diye gider. anatomide, botanikte bolca vardır. da vincinin en cok kullanan kisi oldugu soylenir.

kısa kenarı a, uzun kenari b olan bi dikdörtgen a/b = b/(a+b) eşitliğini sağlıyorsa o dikdörtgen altınoranlı bi dikdörtgendir, dikdörtgen işte diyip geçiştirilemez

bir kitap adi ve lise2'deki dönem ödevimin konusu..

bilim technique de okumuştum, tam hatırlamıyorum ama iyi bişhi galiba, doğada da böle bi oran var mesela kamasutra da (yani kamasutranın doğal ve doğada yane dört duvar arasında olmayanında qaplan/geyique = geyique/(qaplan+geyique) aynı zevki veriyosa altın oran vardır vermiyosa altın oran yoktur, ama bi olup bi olmuyosa kaplanda, hiç olmuyosa geyique de sorun vardır, telafi edilmeli gereği yapılmalıdır)...

bi fibonacci serisinde bulunan iki ardisik fibonacci sayisinin arasindaki oran ki bu sabittir ve yaklasik 1.618 tir

(bkz: fibonacci sayilari)

altin oran, fibonacci dizisinin n->sonsuz'a giderken i(n)/i(n-1) ifadesinin limitine denir.

sin(666)*(-2)=1,61803398874989484820458683436564

da vinci şifresi kitabında da değinilen ilahi oran. olduk olmadık her yerde karşılaşılınca insan ister istemez huzursuz oluyor...

ao = 1 + 1/(1 + 1/(1 + 1/( ... ))) ao = sqrt(1 + sqrt(1 + sqrt(1 + ... )))

günlük hayatimizda bize estetik ve güzel görünen her nesnede bulunan orandir,örnegin kibrit kutusu,tv ekrani,fotograf basilan kagitlar,ari kovani,papatyanin içindeki sarmal...

altın oran a uygun bir penis ihtişamlı ve lüzumsuzca kalın olabilecekken, altın oran kukuya uygulandığında, follofoş olabilme ihtimaline sahiptir, bu meyanda kuku da oran aranmaz gibi bir çıkarıma ulaşabiliriz.

kulaklarımızın oranı da buymuş...(by melatonin)

resim tekniginde kullanilan bir terimdir ayni zamanda. örn: dilzerini bkerek oturmus bir adam önden görüldügünde diz eklemleriyle kalcalari arasinda bir derinlik farki vardir. buna altin oran denir

"altın ne renk?" sorusuna verilebilecek terbiyesiz yanıtlardan biridir.. (bkz: ilkokul esprileri)

(bkz: canon)

1.618 daha dogru bi orandir. (bkz: fibonacci sayilari)

tam olarak (sqr(5) + 1) / 2 ye eşittir, carpimsal tersi ise sayinin bir cikarilmiş halidir ayni zamanda ve sayilardan biri de 1/x=x/(1-x) denkleminin kokudur. (yani ya carpimsal ters olan yada bu sayi) 1,61803398874989484820458683436564.... (bkz: daha gider bu)

zamaninda hatunlara bakarken "vaay bu hakkat 1.1618 mis", "bu da cok sekermis, bir nevi 1.1613", "yok abi bu 1.1602'lerde kalmis" seklinde bol bol geyigini yaptigimiz evrensel guzellik olcutu. aslinda "evrensel guzellik" veya mukemmellik dedigimiz olay matematigin icinde sakli ama biz nesnelere veya kisilere atfetmeye calisiyoruz israrla. (bkz: olmaz)

(bkz: golden shower)

(bkz: golden section) (bkz: altin kesim) (bkz: golden goal)

sayfa da kabaca 5/2'lik kisima gelen alandan faydalanilma durumu, oraya onemli saydigimiz objemizi yerlestirdik, ve ne oldu, cok guzel bir tasarim oldu...

biz programcilar bir algoritma bulduk mu hevesle hep onun uzerinden yazmaya calisiriz her b.ku. paso kullaniriz. allah da bi oran bulmus paso onla yazmis evreni. bi angut da cikmis kirmis bunu bulmus da is yapmis. kaldi ki hulya yavsarin surati bu oranlara uyuyormus. bi oran var diye guzel mi olacak illa, kaldi ki paralelkenar da kendi icinde bir suru orana sahip bi geometrik hadise. simdi kari paralel kafa olsa guzel mi olacakti. saten programlarinde yatay sikistirma kullandiklari icin paralel kenara baya benziyo <b>bazen</b>.

yaratıcının varlığının çok sade ispatı.zırt pırt karşılaşıldığında, huzursuz olmak yerine; huzurla dolmak gerekir.

doğadaki herşeyin oranıdır bu.. 1.618 gibi bir sayıdır.. bizim vücudumzda da vardır bu.. mesela boyumuzu ölçüp bunu bacaklarımızın uzunluğuna bölersek bu oran çıkar... bacaklarımızın uzunluğunu dizimize kadar olan uzunluğa bölersek de bu çıkar... kollarımızda, parmaklarımızda da aynı şey geçerlidir.. ayrıca doğadaki pekçokşeyde de bu oran tespit edilmiştir.. baya ilginç doğrusu...

fi sayısı "altın oran" denilen şey. 1,618033... diye sürüp gidiyor.yaklaşık 2/3 oranı altın oran, mesela bir dikdörtgenin göze en estetik görünmesi için uzun kenarı ile kısa kenarı arasında olması gereken oran. kate moss'un ve hülya avşar'ın yüzlerinin altın orana uygun olduğu için "güzel" olduğu söyleniyor. leonardo da vinci amca mesela mona lisa'da kullanmış bu oranı. mona lisa'nın başının etrafına bir dikdörtgen çizdiğinizde ortaya çıkan dört kenar bir altın dikdörtgenmiş. bu dikdörtgeni, göz hizasında çizeceğiniz bir çizgiyle ikiye ayırdığınızda yine bir altın oran elde ediyormuşsunuz. resmin boyutları da altın oran oluşturmaktaymış. stanley kubrick'in filmlerindeki hemen her karenin de bu orana göre çekildiği rivayet ediliyor. bu da işte sanatın matematiği... aşkın matematiği olmaz mı dersiniz, sekste estetik aranmaz mı; orası size kalmış.

hülya'nın güzelliğine bilimsel onay http://arsiv.hurriyetim.com.tr/.../31/yasam/08yas.htm ideal güzellikte altin oran 1,6180339887... http://www.sabah.com.tr/2004/04/01/gny103.html

fotoğrafta altin oranfotoğraf bir yüzey sanatıdır. eni ve boyu olan bir yüzey üzerinde gerçekleşir. bu yüzeye görüntü ne kadar iyi ve dengeli yerleştirilirse algılama o kadar iyi olur. aksi taktirde görüntü gözü tırmalar veya akılda kalmaz. insan gözünün algılamadaki uyumunda altın oran söz konusudur. fotoğraf karemizi enden ve boydan üç eşit parçaya böldüğümüzde çizgilerin kesiştiği noktalar altın noktalardır. ilgi merkezimizin bu noktalara yerleştirilmesi daha başarılı sonuç verir. bu üç parçaların üçte birlik bölümü de (hangi taraftan olursa olsun) altın oranı teşkil eder. ufuk çizgisinin veya gökyüzünün bu oranlarda kullanılmasıyla doğru ve başarılı fotoğraflar elde ederiz. ( http://www.enversengul.betlis.com/...graf_estetik.htm ) sitesinden alıntı

bir uzunluğu ikiye böldüğünüzde kısa parçanın uzun parçaya olan oranıyla uzun parçanın bütüne olan oranının aynı olması şıklığı.1.6 küsürle ifade ediliyor ve karesini almakla sayıya 1 eklemek aynı şey. insanın ağzında yüzünde parmaklarında falan da bu oran varmış.

yüzünde ve vücudunda bu oranı taşıyan insanlara halk arasında güzel denir. ayriyetten tavan ya da dip yaptıktan sonra yön değiştiren bi borsanın muhtemel destek direnç noktaları bu oranla hesaplanır ve batmanıza sebep olur. (bkz: piyasaya kalkan eller kirilsin)

1.61803399 www.google.com

sadece fibonacci sayılarıyla değil, aynı kuralla oluşturulacak her dizide bu oran elde edilir. (yani bir dizide n. ve (n+1). terimler toplanarak (n+2). terim elde ediliyorsa, terimler arasında altın oran bulunur.)bir örnekle açıklayalım, iki sayı seçerek dizimizi oluşturmaya başlayalım. hesaplama kolaylığı açısından bu sayılar 2 ve 3 olsun. böylece dizimiz 2, 3, 5, 8, 13, 21, 34... olur. hımm, bu fibonacci dizisi oldu zaten. "bizi mi kandırıyosun lan it oğlu it" dediğinizi duyar gibiyim, bir daha deniyorum. sayılarımız 1 ve 5 olsun. sayı dizimizin ilk 10 terimi şu şekilde olur: (10 terim kullanmanın bir faydası var, birazdan açıklayacağım) 1, 5, 6, 11, 17, 28, 45, 73, 118 ve 191. son iki terimi birbirine bölelim: 191/118=1.618... bu işlem ilk terimlerde yapılırsa sonuç tabiki altın orandan uzaklaşır ama terim sayısı büyüdükçe, elde edilen oran altın orana ((sqr(5) + 1) / 2) yaklaşır.şimdi gelelim 10 terim meselesine, 1, 5, 6, 11, 17, 28, 45, 73, 118 ve 191'den oluşan dizide 10 terim var. bu terimlerin toplamı da: 495. 495 aynı zamanda 7. terimin (45) 11 katı.n. ve (n+1). terimlerin toplanarak (n+2). terimin elde edildiği dizilerde, 10 terimin toplamı her zaman 7. terimin 11 katıdır.peki bu ne işe yarar? ne bileyim, sözlüğe falan yazılabilir.

diş hekimlerinin protez yaparken dişlerin birbirleri ve yüz ile uyumunu sağlamak için kullandıkları oran.ancak en bariz rehber oranlar dışındaki oranlar pek kaale alınmaz.örneğin, köpek dişinin genişliği , zygomalar (elmacık kemiği) arası mesafenin 1/19'u kadardır. bunun gibi bir sürü incik cıncık oranı diş hekimi eline cetveli alıp, milimetrik ölçümler yaparak sağlamaz.göze dişler güzel gözüktüğü anda diş hekimi bilir ki altın oranı yakalamıştır.

bir pentagram'ı oluşturan en uzun çizgilerden birini alıp, bu çizgiye murtaza adını verelim. murtaza'nın pentagramın tabanına oranı altın oran'dır; başka bir deyişle cos(pi/2.5)*2 = 0.618...ispatı söz konusu üçgenlerin benzerliği üzerinden (tabanın murtaza ile kesişmeyen ucundan murtaza'nın pentagramın içindeki beşgene dokunduğu noktaya bir çizgi çekiyorsunuz ve bu uzunlukları birbiri ile altın oran ilişkisi içinde olduğunu gösteriyorsunuz).bunun sonucu olarak, pentagram'ın içine/dışına doğru çizilen daha büyük eşkenar beşgenler ve yıldızlar da birbirlerine altın oran ile bağlı.

fibonacci sayilarinin sonsuzdaki d'alembert constanti. yani fibonacci dizisine a(n) dersek lim(n->sonsuz) a(n+1)/a(n) şu şekilde kolayca bulunur (tum limitler n->sonsuz)q(n) = (a(n+1) / a(n)) diye tanimlayalim. lim q(n)'i ariyoruzq(n) = lim ( a(n)+a(n-1)/a(n) ) = lim ( 1+ (a(n-1)/a(n)) = 1 + lim( 1 / [a(n)/a(n-1)] ) = 1 + 1/ lim q(n-1).şimdi eger bi limit varsa n sonsuza giderken lim q(n) = lim q(n-1) = ko vakit k = 1 + 1/k, k^2 = k+1, k^2-k-1=0bunun cozumunu de ortaokulda ogrenmiştik, k=(1+sqrt(5))/2.

klasik sanatta çok kullanılan altın dikdörtgenin özelliği,kenarlarının birbirine oranının içinden bir kare atılarak elde edilen dikdörtgenin kenarlarının oranına eşit olmasıdır.kalan dikdörtgen de altın dikdörtgen olduğu için ondan da bir kare atılırsa tekrar bir altın dikdörtgendir geriye kalan..(bkz: fibonacci)

(bkz: esas oğlan altın oran)

dogada var olan, ressamlarin, muzisyenlerin, mimarlarin da sanatlarina tasidiklari oran. bir brokolinin o minicik ucgenimsi tanesinde bile bu oran gizlidir. bilimin ve sanatin kesisim noktasi leonardo da vinci gibi ustun bir gozlemleme yetenegi olan birisi de resimlerinde bol miktarda bu orani kullanmistir. mona lisa ve diger iki portresinde(birisi washington dc 'de national gallery of art'da, birisi polonya'da sanirim) de bu oran mevcuttur. ayrica insanlarin basindan ayak ucuna kadar olan uzunlugunun basindan yaklasik gobek kismina kadarina orani da golden ratio'yu verir derler, denemedim, math and mona lisa kitabinin yazari bulent atalay sectigi kucuk olcekli bir orneklem uzerinde bunu her subje icin olcmustur ve ortalamanin golden ratio'ya cok yakin oldugunu gostermistir. salvador dali'nin last supper'inin da eninin boyuna orani bu orandir yine. ayrica malezya'nin kuala lumpur'undaki o buyuk ticari binanin mimarisi de bu orana dayanmaktadir. ayrica tavsanlarin uremesi de bu oranla aciklanir.

phi sayısı da denir, yunan heykeltraş phidias'tan gelmektedir bu ad. mısır piramitlerinden tutun da, mona lisa'nın suratına dek birçok yerde mevcuttur. o yüzden güzeldir bu şeyler.

hatta luca pacioli isimli kimse "ilahi oran" adında bir kitap yazmıştır.ayrıca iddia edildiğine göre buna ilk defa leonardo da vinci "altın bölge" demiştir.

gunumuzde kredi kartlari, sigara paketleri, ankara'daki otobus biletleri, izmir'in kentkarti, ogrenci kartlari hep bu orana gore uretilip sinir bozmaktadır.

(bkz: ilahi oran)

baskin oran'in abisi.

yüzünde altın oran bulunan kişi evrensel bir güzelmiş. mesela hülya avşar'ın suratı altın orana uyuyormuş.

sayinin bulunusunun ispatinin hem lineer cebir hem de z-transformla yapildigini gordugumde koptugum olay.

...camel paketi altin oranlidir...

kar kristallerinin budaklanma noktaları arasındaki uzaklıklarda da bulunur. bişey tasarlarken ardışık fibonacci sayılarını kullanmamın nedenidir.

(bkz: goldmember)

da vinci sifresi isimli kitabin populer hale getirdigi yillardir bilinmekte olan ve hayatin her yerinde varlik gosteren oran.modern sanatlarda en iyi ornegini mondrian babamiz vermistir.ayrica piyasa ornekleri icin http://goldennumber.net/

kimilerine göre matematiğin keşif olduğunun kanıtı. eğer insanoglu var olmadan önce doğada çeşitli altın oranlar varsa, insanoglunun piskolojisi bu oranlardan etkileniyorsa, ve doğa olarak isimlendirilen atomlar bütünü bilince sahip değilse, matematik yavaş yavaş keşfedilen bir icattır.

bir nevi (bkz: aurea mediocritas)

1 1 2 3 5 8 13 21 34 55 89 144... diye giden sayi dizisinden bulunur.. 1den baslayip her sayiyi kendisinden bir öncekiyle toplayarak gidersiniz.. serinin her elemanının bir öncekine bölümünün sonsuza limiti altın oranı verir.. dogadaki her türlü kus, çiçek, böcekte altin oran yani tanrisal oran vardir.. takdiri ilahidir iste.. yaraticiligin dogayi taklit etmekten baska bisey olmadiginin nefis kanitidir..

görsel anlatımlı sanatların hepsi için geçerli olan oran (sinema,resim,fotoğraf.vs..) eserin estetik açıdan göze en hoş şekilde görünmesi için kulanılır..stanley kubrick in filmlerindeki hemen her kare bu oran a göre çekilmiştir mesela,işinde mükemmelliyetçi insanların takıntısıdır.

eger bi kadin / erkek guzelse bu orana sahiptir. mesela kate moss ve tom cruise bu orana yuz olarak en yakin insanlardan. 1.618.1 diye olculur kisaca. eger on disinizle kopek disiniz arasinda bu oran varsa mukemmelsiniz. (bkz: reynaldo gianecchini)

lezzetli tabir edilen bir balığın eninin boyuna bölümü bu oranı verir.(gelişmişlik ve olgunluğa ulaşmış bir balık olduğunu anlamanın yolu.aynı zamnda düzgün diye nitelendirilebilcek bir yaprağın (sayfanın) eninin boyuna oranıda da altın orandır.

leonardo da vinci'nin resimlerinde bolca kullandığı matematiksel rasyo.

ankara'da oran semti semalarındaki uçak içerisinde gecen diyalog parcası...

kemal unakıtan: altın oranı tarihten silecegiz.

ticari hiçbir kaygisi olmayan pi filminde "hayat sarmallardan olusmaktadir" repliginin altinda pusuda yatmakta olan kavram

yerçekimi ya da elektromanyetizma kadar doğal olduğunu düşündüğüm, dahası evreni yöneten kuvvetlerin etkileşimlerinin kaçınılmaz sonuçlarından biri olduğuna inandığım oran.bileşik alanlar kuramı'nın çözüldüğü gün kendiliğinden bir açıklama bulmasını beklediğimiz sabit.

yunanlıların m.ö. 5.yüzyılda geliştirdikleri bi sistem.yatay ve düşey ölçülerin birbiriyle uyumu demek.

(bkz: levent oran)

mimar sinan'in butun camilerinin kubbeleri altin oran kanununa gore insaa edilmistir..

yunanlıların geliştirmediği, tesadüfen kullandığı oran.. çok uzun yıllar sonra bu oranı tesadüfen kullandıkları farkedilmiştir, böylece bu oranın göze hoş gözüktüğü gerçeği doğrulanmıştır bir kez daha.. galaksilerin şekillerinden çiçeklere kadar doğada birçok yerde bulunur altın oran..

her şeyi bu oranda yapıcam falan diye çok kaptirip eserini şekilciliğe boğan bir bir sanatçının sanatının altın oran yapıp öldüğünü söyleyebiliriz.

sevgili arkadasimizin bir uzvu hizla altina donusurse sasirip altin bolgeye isaret ederek "aaa! altin oran!" diye baarmamiza izin veren kelime obegi..

(bkz: phi)

fazla bulaşmayınekg grafiklerinde bile tonlarca altın oran bulunmasından tutun da, ayçiçeğinin üzerindeki sprial hatlar üzerindeki çekirdeklerin fibonacci serisine nasıl bağlandığına kadar öğrenince çıldırır gibi oluyo insan. ben daha yeni kurtuldum.geometrik bulunuşu, cebirselden daha eğlencelidir bence bakın kasıp anlatıcam.yatay bir [ab] doğru parçası çizin 1 birim uzunluğunda.b'den yukarıya dik bir [bd] doğru parçası çizin 1 birim uzunluğunda[ab]'nin orta noktası (e mesela) ile d'yi birleştirerek [ed] elde edin e merkezli [ed] yarıçaplı çemberi çizin[ab]'yi sağdan çembere değene kadar uzatın. kesişme noktasına c deyin.[ab]/[bc] altın oran

ayrıca bir de aristo'nun altın oranı vardır. matematiksel altın oranla bir şekilde bağlantılı olabileceği mümkünse de farklı bir terimdir. aristo insanlara hayatlarını altın orana göre düzenlemelerini tavsiye eder. bu altın oran duygusal, düşünsel ve yaşamsal her olayda aşırılıklardan sakınmak gerektiği söyler. misal bir insan ne çok sevilmeli ne de ondan nefret edilmelidir. bir olaya gözleri kapalı atlamamalıdır insan, ne de korkaklık edip kaçmalıdır. insanın tavrı iki extremin arasında bir yerlerde olmalıdır.

tahin pekmez için de vardır bu olay. daha tutturabilene rastlamadım. ya pekmezi çok olur fazla tatlı olur ya da tahini fazla olur tatsız olur. bu oranı tutturanlara buradan sözlük aracılığıyla helal olsun demek istiyorum.altın oranı tutturabilmek için (bkz: #6567482)(bkz: tahin ve pekmez arasındaki altin oran)

(bkz: keops)

klasik ipod'larda ekranın navigatöre oranıdır aynı zamanda...bilinen bir çok büyük markanın tasarımlarında dikkat ettiği orandır...uzuuuun bir altın oran versiyonu:1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475408807538689175212663386222353693179318006076672635443338908659593958290563832266131992829026788067520876689250171169620703222104321626954862629631361443814975870122034080588795445474924618569536486444924104432077134494704956584678850987433944221254487706647809158846074998871240076521705751797883416625624940758906970400028121042762177111777805315317141011704666599146697987317613560067087480710131795236894275219484353056783002287856997829778347845878228911097625003026961561700250464338243776486102838312683303724292675263116533924731671112115881863851331620384005222165791286675294654906811317159934323597349498509040947621322298101726107059611645629909816290555208524790352406020172799747175342777592778625619432082750513121815628551222480939471234145170223735805772786160086883829523045926478780178899219902707769038953219681986151437803149974110692608867429622675756052317277752035361393621076738937645560606059216589466759551900400555908950229530942312482355212212415444006470340565734797663972394949946584578873039623090375033993856210242369025138680414577995698122445747178034173126453220416397232134044449487302315417676893752103068737880344170093954409627955898678723209512426893557309704509595684401755519881921802064052905518934947592600734852282101088194644544222318891319294689622002301443770269923007803085261180754519288770502109684249362713592518760777884665836150238913493333122310533923213624319263728910670503399282265263556209029798642472759772565508615487543574826471814145127000602389016207773224499435308899909501680328112194320481964387675863314798571911397815397807476150772211750826945863932045652098969855567814106968372884058746103378105444390943683583581381131168993855576975484149144534150912954070050194775486163075422641729394680367319805861833918328599130396072014455950449779212076124785645916160837059498786006970189409886400764436170933417270919143365013715766011480381430626238051432117348151005590134561011800790506381421527093085880928757034505078081454588199063361298279814117453392731208092897279222132980642946878242748740174505540677875708323731097591511776297844328474790817651809778726841611763250386121129143683437670235037111633072586988325871033632223810980901211019899176841491751233134015273384383723450093478604979294599158220125810459823092552872124137043614910205471855496118087642657651106054588147560443178479858453973128630162544876114852021706440411166076695059775783257039511087823082710647893902111569103927683845386333321565829659773103436032322545743637204124406408882673758433953679593123221343732099574988946995656473600729599983912881031974263125179714143201231127955189477817269141589117799195648125580018455065632952859859100090862180297756378925999164994642819302229355234667475932695165421402109136301819472270789012208728736170734864999815625547281137347987165695274890081443840532748378137824669174442296349147081570073525457070897726754693438226195468615331209533579238014609273510210119190218360675097308957528957746814229543394385493155339630380729169175846101460995055064803679304147236572039860073550760902317312501613204843583648177048481810991602442523271672190189334596378608787528701739359303013359011237102391712659047026349402830766876743638651327106280323174069317334482343564531850581353108549733350759966778712449058363675413289086240632456395357212524261170278028656043234942837301725574405837278267996031739364013287627701243679831144643694767053127249241047167001382478312865650649343418039004101780533950587724586655755229391582397084177298337282311525692609299594224000056062667867435792397245408481765197343626526894488855272027477874733598353672776140759171205132693448375299164998093602461784426757277679001919190703805220461232482391326104327191684512306023627893545432461769975753689041763650254785138246314658336383376023577899267298863216185839590363998183845827644912459809370430555596137973432613483049494968681089535696348281781288625364608420339465381944194571426668237183949183237090857485026656803989744066210536030640026081711266599541993687316094572288810920778822772036366844815325617284117690979266665522384688311371852991921631905201568631222820715599876468423552059285371757807656050367731309751912239738872246825805715974457404842987807352215984266766257807706201943040054255015831250301753409411719101929890384472503329880245014367968441694795954530459103138116218704567997866366174605957000344597011352518134600656553520347888117414994127482641521355677639403907103870881823380680335003804680017480822059109684420264464021877053401003180288166441530913939481564031928227854824145105031888251899700748622879421558957428202166570621880905780880503246769912972872103870736974064356674589202586565739785608595665341070359978320446336346485489497663885351045527298242290699848853696828046459745762651434359050938321243743333870516657149005907105670248879858043718151261004403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23774246171...

bir hesap makinasinda bu orana ulaşmak icin iki işlemi yorulana kadar tekrarlamak gereklidir.başlamak icin oncelikle sifirdan buyuk bir sayi ekrana yazilip karekoku alinir ve sonra ;a. sonuc 1 ile toplanir,b. sonucun karekoku alinir.bu dongu ne kadar cok yapilirsa altin orana o kadar yakin olunur.

bir zamanlar milk'in isim alternatiflerinden biri olan sayı.

hakkında çok şey var:http://goldennumber.net/

müzikteki ilk kullanımı bela bartok tarafından yapılmıştır.(bkz: bartok orkestra konçertosu)