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Ya da bu esrarengiz sayının ardındaki gerçeği çözmek evrene, varlığımıza ve hatta tanrıya bakışımızı değiştirebilir mi? 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Bu videoda pi sayısının tarihsel hikayesine...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4562667/a7ff7b2322a8ee9ba77faf01f379c807/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/VBB5BQEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"5","reqid":"1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=videoid:16953214189798364145","teaser":[{"list":{"type":"unordered","items":["Bu video, bir konuşmacının pi sayısının kavramsal anlamını ve evrenin geometrisi ile ilişkisini açıklayan eğitici bir içeriktir.","Video, pi sayısının irrasyonel bir sayı olduğunu ve evrenin genişlemesiyle doğrudan ilişkili olduğunu anlatmaktadır. İçerik, pi'nin tanımı ve Arşimet'in hesaplamalarıyla başlayıp, evrenin Big Bang'den başlayarak şişme ve genişleme sürecini geometrik modellerle açıklamaktadır. Konuşmacı, pi'nin zaman parametreli ve çok boyutlu değişim fonksiyonunu bulamadığımız sürece evrenin geleceği hakkında şansımızın olmadığını vurgulamaktadır.","Video ayrıca evrenin ilk anlarından günümüze kadar olan tarihsel hikayesini pi sayısının basamaklarının nasıl kodladığını, evrenin ideal küresel formuna ulaşmasıyla pi'nin sabitleşebileceği ve pi'nin evrenin dijital hafızası olabileceği sorusunu ele almaktadır. Gelecek videoda kompleks ve irrasyonel sayıların pi ile ilişkileri inceleneceği belirtilmektedir."]},"endTime":1786,"title":"Pi Sayısı ve Evrenin Geometrisi","beginTime":0}],"fullResult":[{"index":0,"title":"Pi Sayısının Tanımı ve Önemi","list":{"type":"unordered","items":["Bu video pi sayısının tarihsel hikayesine değinmek yerine, pi sayısının neye benzediğini kavramsal olarak anlamaya odaklanacak.","Pi sayısı, dar anlamda ortogonal ve düz bir uzayda çemberin çevre uzunluğunun çapına bölünmesiyle bulunan irrasyonel bir sayıdır.","Pi sayısının evrende etkilemediği bir kavram hemen hemen yoktur."]},"beginTime":15,"endTime":94,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=15&ask_summarization=1"},{"index":1,"title":"Uzayın Geometrisi ve Pi Sayısı","list":{"type":"unordered","items":["Matematiksel kavramların geçerli olduğu uzayın belirtilmesi önemlidir, çünkü örneğin Pisagor teoremi sadece ortogonal ve düz uzaylarda geçerlidir.","Pi sayısı evrensel bir sayı olmasına rağmen bulunduğu uzayın geometrisi ile doğrudan ilişkilidir.","Evren o kadar büyük ki, eğri bile olsa en azından bizim yaşadığımız kısmı düz ve ortogonal kabul edilebilir."]},"beginTime":94,"endTime":177,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=94&ask_summarization=1"},{"index":2,"title":"İrrasyonel Sayılar ve Pi","list":{"type":"unordered","items":["Matematikçiler irrasyonel sayıları basit olarak iki tam sayının birbirine bölümü şeklinde gösterilemeyen sayılar olarak tanımlarlar.","Evrende çevresi ve çapı tam sayı olan dairesel formda bir nicelik henüz rasyonel olarak yok gibidir.","Evrendeki en ideal görünen dairesel formların bile yeterince küçük bir parçası düz olarak alınabilir."]},"beginTime":177,"endTime":251,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=177&ask_summarization=1"},{"index":3,"title":"Evrenin Geometrisi ve Pi Sayısı","list":{"type":"unordered","items":["Kırmızı altıgen yapı evrenin bebeklik halini temsil eder ve evren genişledikçe ideal küresel şekle yaklaşır.","Evren ideal şekline ulaşmak istedikçe pi sayısı sürekli değişmek zorundadır.","Muhtemelen çok boyutlu genişleyen evrenin üçüncü boyuta izdüşümü küredir ve pi sınırlı bir aralık içinde değişir."]},"beginTime":251,"endTime":319,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=251&ask_summarization=1"},{"index":4,"title":"İrrasyonel Nicelikler ve Pi","list":{"type":"unordered","items":["İrrasyonel nicelikler sınırlı bir aralık içindeki ideal değerlerine doğru hep bir hareket ve değişim içindedirler.","İrrasyonel bir yapıyı tanımlamak için pay ve paydanın her ikisinin de veya herhangi birinin sınırlı bir aralıkta sürekli değişimi yeterlidir.","İrrasyonel bir sayı, en azından pi gibi sınırlı bir aralıkta sonsuza kadar devam ediyormuş gibi görünür ve sürekli değişim bize canlı bir şeyi hatırlatır."]},"beginTime":319,"endTime":426,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=319&ask_summarization=1"},{"index":5,"title":"Evrenin Genişlemesi ve Pi Sayısı","list":{"type":"unordered","items":["Evren muhtemelen çok boyutlu bir genişleme ve dönme hareketi yapmaktadır.","Evrenin çok boyutlu genişlemesinin ikinci boyuttaki izdüşümü düzlemdeki her yöne hareketi temsil eden dairesel hareketten kaynaklanır.","Evrenin genişlemesine direnç gösteren maddenin evrenin dokusunu bükerek eğmesi, çekim kuvvetinin bu çukurlar sonucu oluşmasını sağlar."]},"beginTime":426,"endTime":516,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=426&ask_summarization=1"},{"index":6,"title":"Yerçekimi ve Evrenin Genişlemesi","list":{"type":"unordered","items":["Yerçekimi bizi sadece tek yöndeki hareketimize karşı koyar ve dünya yüzeyinde tutarak evrenin genişlemesine karşı korur.","Güneş, Samanyolu'nun çekim çukurundadır ve Samanyolu da kendi yerel galaksi kümesinin çukurundadır.","Evrenin genişlemesinin etkisini küresel ya da dairesel olarak, yerçekimine dik eksende ve yerçekiminden fazla etkilenmeyen hareketlerde gözlemleyebiliriz."]},"beginTime":516,"endTime":590,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=516&ask_summarization=1"},{"index":7,"title":"Eşitsizlik ve Eşitsizlikler","list":{"type":"unordered","items":["Eşitsizlikler, evrenin genişleme yapısını tanımlayan önemli bir kavramdır.","Eşitsizlikler, evrenin genişleme yapısını tanımlayan önemli bir kavramdır.","Eşitsizlikler, evrenin genişleme yapısını tanımlayan önemli bir kavramdır."]},"beginTime":599,"endTime":623,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=599&ask_summarization=1"},{"index":8,"title":"Merkezkaç Kuvveti ve Evrenin Genişlemesi","list":{"type":"unordered","items":["Merkezkaç kuvveti, evrenin küresel formda genişlemesine karşı gösterilen direnç etkisidir.","Bir ipe bağlı dönen cisim, evrenin genişlemesine karşı yarıçapı ipin boyuna eşit olan dairesel hareketler yapar.","İpteki gerilim, evrenin büyümeye çalışan çemberi korumak için oluşur."]},"beginTime":623,"endTime":679,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=623&ask_summarization=1"},{"index":9,"title":"Dönen Cisimlerin Fiziksel Özellikleri","list":{"type":"unordered","items":["Dönen cismin hız vektöründeki anlık yön değiştirme hızı arttıkça, merkezcil kuvvet vektörü artar ve yerçekimi vektörünün etkisi azalır.","Yeterince hızlı bir dönüşte yerçekimi vektörü ihmal edilebilir seviyeye kadar küçülür, ancak hiçbir zaman sıfır olmaz.","Bu sistemde çok küçük bir kuvvetle yerçekimini yenebiliriz."]},"beginTime":679,"endTime":714,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=679&ask_summarization=1"},{"index":10,"title":"Dönen Cisimlerin Momentumu","list":{"type":"unordered","items":["Dönen cismin momentumunun yönünü, hız vektörünün teğet ve normal bileşenleri belirler.","Sabit yarıçapta dönen cismin momentumunu açısal hız belirler.","Merkezden geçen, iki vektöre de dik açısal momentum, iki vektörün vektörel çarpımıdır."]},"beginTime":714,"endTime":754,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=714&ask_summarization=1"},{"index":11,"title":"Dönen Diskler ve Yerçekimi","list":{"type":"unordered","items":["Dönen disklerin yerçekimini yenmesi, açısal momentum vektöründen kaynaklanır.","Disklerin ideal bir eksende dönmemesi, dönme eksen açılarının değişmesi ve açısal momentum vektöründeki değişimler bir tork oluşturur.","Bu tork, kütle ve yerçekiminden kaynaklanan mgl torkunu yener ve sistem dengede kalır."]},"beginTime":754,"endTime":793,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=754&ask_summarization=1"},{"index":12,"title":"Dönen Cisimlerin Fiziksel Özellikleri","list":{"type":"unordered","items":["Dönen cisimler, tek yönlü çekim kuvvetinden bağımsız yönlerde de hareket ve yer değiştirebilir.","Evrende, dış müdahale olmadıkça dairesel hareketini koruyabilen, çapı değişmeden sabit kalmayı başarabilen reel bir nicelik yoktur.","Isı, ışık, ses, su ve elektromanyetik dalgaların dairesel veya küresel yayılması, evrenin genişleme yapısından kaynaklanır."]},"beginTime":793,"endTime":830,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=793&ask_summarization=1"},{"index":13,"title":"Katı Cisimlerin Şekilleri","list":{"type":"unordered","items":["Katı cisimlerin dairesel bir formda yayılmasını önleyen, mevcut şekillerini koruyan şey, atom ve moleküller arasındaki bağ kuvvetleridir.","Eğer bu kuvvetler olmasaydı, katı cisimler de atomlarına veya moleküllerine ayrışarak dairesel veya küresel formda dağılırdı.","Kağıt üzerinde çizilen şekiller, maddeyi bir aradatan moleküler kuvvetler sayesinde korunur."]},"beginTime":830,"endTime":858,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=830&ask_summarization=1"},{"index":14,"title":"Pi Sayısı ve Evren","list":{"type":"unordered","items":["Pi sayısının canlılık, zamana ve geometriye göre her an sürekli değişim göstermesi ve bu değişimin evrenle paralel bir başlangıcı ve sonu olmasıdır.","Yerçekim vektörü, bizi evrenin genişleme etkilerinden tek yönlü olarak korur ve dünyanın çekim çukurunda tutar.","Atom ve moleküller arasındaki bağ kuvvetleri, bizi diğer yönlerde genişlememizi ve dairesel veya küresel yayılmamızı önler."]},"beginTime":858,"endTime":928,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=858&ask_summarization=1"},{"index":15,"title":"Pi Sayısının Değişkenliği","list":{"type":"unordered","items":["Pi sayısının bir an bile sabit kalamamazlığı, evrenin küresel formda genişlemesiyle doğrudan bağlantılıdır.","Pi'nin herhangi bir andaki değeri, evrenin o andaki çap ve çevre büyüklüğünün kodlarını verir.","Evren genişlediği sürece pi sabittir demek hatalıdır; pi sabit bir sayı değil, zaman ve geometriye bağlı bir fonksiyon gibi çalışır."]},"beginTime":928,"endTime":984,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=928&ask_summarization=1"},{"index":16,"title":"Pi ve Evrenin Çapı","list":{"type":"unordered","items":["Evrenin çevre çapı, evrenin bebeklik halinden genişlemenin duracağı son haline kadar olan çevre çap değerlerinden oluşan bir aralıktır.","Evrenin şimdiki çevre çap değeri ile bir an sonraki değeri farklıdır, ancak aradaki fark çok küçüktür ve dünyadaki en hassas hesaplamaları bile değiştirmez.","Pi, irrasyonel sayıların anası olarak tanımlanabilir ve bundan sonraki videoda irrasyonel ve kompleks sayıların neye benzettiği incelenecektir."]},"beginTime":989,"endTime":1033,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=989&ask_summarization=1"},{"index":17,"title":"Arşimet'in Pi Hesaplaması","list":{"type":"unordered","items":["Arşimet, binlerce yıl önce geometrik modelleme yaparak pi için 3,141 ile 3,142 arasında değişen değerler bulmuştur.","Arşimet, üçgen, dörtgen ve altıgen çizerek pi'nin gerçek değerini bulmaya çalışmış, üçgen için yaklaşık 2,59, dörtgen için 2,82 ve altıgen için 3 değerini bulmuştur.","Arşimet, günümüzün teknolojik imkanlarından ve güncel kozmolojik bilgilerden mahrum olarak yaklaşık 96 kenarlıya kadar çokgen çizebilmiştir."]},"beginTime":1033,"endTime":1082,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1033&ask_summarization=1"},{"index":18,"title":"Çap Kavramı ve Pi Hesaplaması","list":{"type":"unordered","items":["Çap sadece çember için değil, cisimlerin genişliği, büyüklük, ölçü, ölçek, sınır ve değer gibi pek çok anlamda kullanılır.","Arşimet, üçgenin çevresini çapa bölerek pi'yi yaklaşık 2,59 olarak, dörtgen için 2,82 ve altıgen için 3 olarak hesaplamıştır.","Bizden binlerce yıl önce yaşamış Arşimet, big bang, tekillik ve sıfırıncı boyut gibi bilinmeyen kavramlardan habersiz pi hesaplamasına ikizkenar üçgenden başlamıştır."]},"beginTime":1082,"endTime":1180,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1082&ask_summarization=1"},{"index":19,"title":"Evrenin Şişmesi ve Pi","list":{"type":"unordered","items":["Evrenin küresel formda şişmesi ve genişlemesi farklı kavramlardır; şişme evrenin her noktasını büyütürken, genişleme evrenin boyutlarını genişletir.","Evren henüz tekil bir noktayken boyut kavramı yoktur ve pi'nin değeri başlangıçta sıfıra eşittir.","Şişme teorisine göre, 10 üzeri eksi 36 ile 10 üzeri eksi 34 saniyeler arasındaki kısa dönemde evren katlanarak büyümüştür."]},"beginTime":1180,"endTime":1248,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1180&ask_summarization=1"},{"index":20,"title":"Evrenin Gelişimi ve Pi Değerleri","list":{"type":"unordered","items":["Evren bir kat şişene kadar pi değeri 1'den 3'e ulaşana kadar bazı ara aşamalardan geçer.","Birinci aşamada çap ve çevre birbirine eşit, pi değeri 1'dir; ikinci aşamada 2,59, üçüncü aşamada 2,82, dördüncü aşamada 2,93 ve beşinci aşamada pi 3'tür.","Evrenin çapı iki kat artarken hacmi sekiz kat artmıştır ve beşinci aşamaya gelene kadar evren sadece şişme değil, genişleme de yapmıştır."]},"beginTime":1248,"endTime":1343,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1248&ask_summarization=1"},{"index":21,"title":"Pi Sayısı ve Evrenin Hikayesi","list":{"type":"unordered","items":["Pi sayısı evrenin tüm hikayesinin kodlarını anbean vermektedir.","Evrenin geleceği ile ilgili şansımız olabilmesi için pi'nin zaman parametreli ve çok boyutlu değişim fonksiyonunu bulmak gerekmektedir.","Evrenin genişleme ve şişme teorileri pi sayısının şekillenmesiyle doğrulanmaktadır."]},"beginTime":1360,"endTime":1475,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1360&ask_summarization=1"},{"index":22,"title":"Evrenin Gelişimi ve Pi Sayısı","list":{"type":"unordered","items":["Evren 10 üzeri eksi 36 saniyeden 10 üzeri eksi 34 saniyeye kadar az genişleme ve çok şişme yaparken, 10 üzeri eksi 34 ile 10 üzeri eksi 32 saniye aralığında hem şişme hem de genişleme yapmaktadır.","Evren 10 üzeri eksi 32 saniyeden sonra şişme etkisinin neredeyse tamamen bitip günümüze kadar etkin olan genişleme evresine geçmiştir.","Evren ne kadar büyürse büyüsün çok küçük bir parçası düz alınabilir, gerçek bir daire ile değil, çokgen ile karşılaşırız."]},"beginTime":1475,"endTime":1524,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1475&ask_summarization=1"},{"index":23,"title":"Pi Sayısının Değişmesi ve Evrenin Geleceği","list":{"type":"unordered","items":["Pi sayısının değişmesinin temelinde evrenin henüz ideal küresel formuna ulaşamaması yatar.","Evren ideal küresel formunu alıncaya kadar sorunsuz genişleyebilir, ancak ideal bir küre şekline ulaştığında artık genişlemesi için cidarlarının zorlanması veya yırtılması gerekecektir.","Pi'nin durması, evrenin kalbinin durması, ölümü veya çöküşü olabilir."]},"beginTime":1524,"endTime":1571,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1524&ask_summarization=1"},{"index":24,"title":"Çok Boyutlu Evren ve Pi Sayısı","list":{"type":"unordered","items":["Evren günümüzde etkin olarak şişmiyor ama genişliyor ve muhtemelen çok boyutlu genişlemektedir.","Çok boyutlu bir evreni anlamamızda küremsi geometri çok önemlidir çünkü kürenin yarıçapı veya çapı birçok farklı boyutta değişmez ve doğru temsil edilebilir.","Evrenin genişlemesi küremsi değil de elipsoit olsaydı, çok boyutlu genişleyen bir evreni doğru anlayamazdık."]},"beginTime":1571,"endTime":1624,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1571&ask_summarization=1"},{"index":25,"title":"Pi Sayısının Evrenin Hikayesi","list":{"type":"unordered","items":["Kadim pi değiştiği sürece evrenin hiçbir yerinde ideal bir çembersel, dairesel veya küresel geometriden bahsedilemez.","Evren ideal bir küresel form bulana kadar pi'nin basamakları ilerlemeye devam edecektir.","Evrenin tam bir küresel forma ulaşmasıyla pi'nin rasyonelleşmesi beklenir, ancak evrenin cidarları tam küresel formdan sonra genişlemeye devam ederse gerilip patlayabilir."]},"beginTime":1624,"endTime":1698,"href":"/video/preview/16953214189798364145?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1624&ask_summarization=1"},{"index":26,"title":"Pi Sayısının Evrenin Dijital Hafızası","list":{"type":"unordered","items":["Pi sayısı içinde evrenin genişlemeye başladığı andan itibaren geçmişteki yapısı, davranışları hakkında tüm bilgileri barındırır.","Pi, evrenin varoluşundan bu yana hüzünlü hikayesini anlatan evrensel bir masal mühendisidir.","Pi, evrenin geçmiş tarihini kodlamış, şimdiki anı kodlayan ve geleceğini de kodlayacak olan bir 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Simgesini yada yaklaşık değerini(3.14). Peki pi sayısı nedir ? adını nereden almıştır ? bu adı kim vermiştir ?","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1966710/4797e790ffa91973c48a1d7cdfcbc105/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/YQlLTwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"10","reqid":"1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D34hwfdNQ_9g","linkTemplate":"/video/preview/2310186374413046254?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Gizemli sayı: Pi nedir ?","related_orig_text":"Say, Pi","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Say, 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kullandığımız 3,14 yada 3 tam 1/7 yada 22/7 gibi bir sayı… Bir dairenin çevresinin çapına bölümü ile elde edilen sayıdır. Bu oran her daire için aynı değeri aldığından, π sayısı bir...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/1962635/81c31f8bd37d87c3ef0c18b9b3d9ede9/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/I8DUBgEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"12","reqid":"1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=videoid:11916559435823734615","teaser":[{"list":{"type":"unordered","items":["Bu video, pi sayısının tarihsel gelişimini anlatan eğitici bir içeriktir. Video, pi sayısının keşfi ve hesaplanması sürecini kronolojik olarak sunmaktadır.","Video, pi sayısının ilk keşfinden başlayarak Ahmet'in Ryan Papirüs'teki hesaplamalarından, Arşimet'in çokgenlerle pi sayısını bulma yöntemine, Liu Hui'nin çokgenlerle yaklaşımına ve daha sonra William Jones, Legendre, Euler gibi matematikçilerin pi sayısını hesaplama çalışmalarına kadar uzanan bir tarihçesi sunmaktadır. Ayrıca pi sayısının irrasyonel olduğu, 1949'da Larry Shaw tarafından ilk kez kutlandığı ve günümüzde dünya çapında 14 Mart'ta kutlandığı bilgisi de paylaşılmaktadır. Video, pi sayısının günlük hayattaki yeri ve önemi hakkında da bilgiler içermektedir."]},"endTime":448,"title":"Pi Sayısının Tarihi ve Önemi","beginTime":0}],"fullResult":[{"index":0,"title":"Pi Sayısının Tarihi","list":{"type":"unordered","items":["İnsanlar ilk tanıştığılar şekil muhtemelen daireydi ve güneşi, mehtabı gözlemleyerek mükemmel şekli kopyalamak istediler.","Pi sayısının bilinen en eski kaydı, MÖ 1650'larda Ahmet adlı Mısırlı katip tarafından yazılmış Ryan Papirüsündedir.","Ryan Papirüsünde pi sayısının yaklaşık değeri 3,16 olarak hesaplanmış ve Ahmet'in bulduğu değer doğru değerden %1'den daha az hata içeriyordu."]},"beginTime":1,"endTime":76,"href":"/video/preview/11916559435823734615?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=1&ask_summarization=1"},{"index":1,"title":"Arşimet ve Pi Sayısı","list":{"type":"unordered","items":["Arşimet, pi sayısını hesaplamak için çemberin içine ve dışına çizdiği çokgenler kullanmıştır.","Arşimet, 96-gen çizerek pi sayısının 3,1408'den büyük, 3,1429'dan küçük olduğunu hesaplamıştır.","263 yılında Çinli Liu Hui de pi sayısını bulmak için kenar sayılarını arttıran çokgenler kullanmıştır."]},"beginTime":76,"endTime":138,"href":"/video/preview/11916559435823734615?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=76&ask_summarization=1"},{"index":2,"title":"Pi Sayısının Hesaplanması","list":{"type":"unordered","items":["1593 yılında Adrian van Rooman, 2 üzeri 30 kenarlı düzgün çokgen kullanarak 17 ondalık basamağı doğru hesaplamıştır.","1596 yılında Ludof van Seulen, 6×2 üzeri 33 kenarlı düzgün çokgen kullanarak 20 ondalık basamağı hesaplamıştır.","1610 yılında Ludof, 2 üzeri 62 kenarlı düzgün çokgen kullanarak 35 ondalık basamağı doğru hesaplamıştır."]},"beginTime":138,"endTime":178,"href":"/video/preview/11916559435823734615?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=138&ask_summarization=1"},{"index":3,"title":"Pi Sayısının Sembolü ve Özellikleri","list":{"type":"unordered","items":["1748 yılında Leonardo Euler ilk kez pi sembolünü kullanmıştır.","1706 yılında William Jones, pi sembolünü dairenin çevresinin çapına olan oranını ifade etmek için kullanmıştır.","1800'lerde Fransız matematikçi Legendra, pi sayısının irrasyonel olduğunu ispatlamıştır."]},"beginTime":178,"endTime":236,"href":"/video/preview/11916559435823734615?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=178&ask_summarization=1"},{"index":4,"title":"Pi Sayısının Hesaplanan Basamakları","list":{"type":"unordered","items":["1847 yılında Alman matematikçi Thomas Klaussen, pi sayısının 248 ondalık basamağını doğru hesaplamıştır.","1853 yılında İngiliz William Rutherford, pi sayısının 440 ondalık basamağını doğru hesaplamıştır.","1874 yılında William Sharks, pi sayısının 707 ondalık basamağını doğru hesaplamıştır."]},"beginTime":236,"endTime":260,"href":"/video/preview/11916559435823734615?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=236&ask_summarization=1"},{"index":5,"title":"Pi Sayısının Modern Hesaplamaları","list":{"type":"unordered","items":["İlk elektrikli bilgisayar olarak bilinen ENIAC, 2037 haneyi 70 saatte hesaplamıştır.","1989 yılında pi sayısının yaklaşık 13,30 trilyon basamağı biliniyordu.","1988'de San Francisco'da Larry Show ilk kez Pi Günü'nü kutlamıştır."]},"beginTime":260,"endTime":286,"href":"/video/preview/11916559435823734615?parent-reqid=1769373680310507-11449023066365168380-balancer-l7leveler-kubr-yp-vla-227-BAL&text=Say%2C+Pi&t=260&ask_summarization=1"},{"index":6,"title":"Pi Günü ve Pi Sayısının 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