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Ayrıca, Pisagor'un okulu ateşe verilmesi ve ölümü gibi trajik olaylar da videoda yer almaktadır."]},"endTime":802,"title":"Pisagor: Matematiğin Antik Dahisi","beginTime":0}],"fullResult":[{"index":0,"title":"Pisagor'un Hayatı ve Okulu","list":{"type":"unordered","items":["Pisagor, Samos adasında yaşayan antik Yunan matematiğin doğduğu yerde yaşayan bir matematik dahisidir.","Pisagor matematiği analitik bir yapıya kavuşturmuş ve 6. yüzyılda Samos'ta bir okul kurmuştur.","Pisagor'un matematikle ilgili günümüze ulaşan yazılı bir çalışması yoktur, ancak ünlü üçgenini (a² + b² = c²) herkes bilmektedir."]},"beginTime":5,"endTime":52,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=5&ask_summarization=1"},{"index":1,"title":"Pisagor Akademisi ve Yaşam Biçimi","list":{"type":"unordered","items":["Pisagorcuların okulları olduğuna dair yeterli kanıt mevcuttur ve Pisagor Akademisi'nde sadece bilgi değil, yaşam biçimi de paylaşılırdı.","Pisagorcular komün halinde yaşayıp mistik bir yaşam biçimi sürdürdüler ve aralarında kadınlar da bulunuyordu.","Kendilerine \"matematik koi\" diyen kadın ve erkekler, \"bir lokma bir hırka\" düsturuyla yaşayıp günümüzün vejeteryan diyetine benzer bir beslenme şekli benimsediler."]},"beginTime":52,"endTime":99,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=52&ask_summarization=1"},{"index":2,"title":"Sayıların Anlamı","list":{"type":"unordered","items":["Pisagor'a göre sayıların özel anlamları vardı: 1 bütün varlıkların sonsuz kaynağı ve sarsılmaz ilkesiydi.","2 dişiliği, 3 uyum ve düzenle maddenin kapsadığı üçlü öğeleri (ateşi, suyu, havayı) sembolize ediyordu.","4 tanrısal güce, 5 evlenmeyi, 6 nesillerin devam etmesini, 7 akıl ve ışık kuvvetini, 8 ahlak ve erdemi, 9 adaleti temsil ederken, 10 ise kutsal kareye denk geliyordu."]},"beginTime":99,"endTime":156,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=99&ask_summarization=1"},{"index":3,"title":"Eğitim ve Kariyeri","list":{"type":"unordered","items":["Pisagor, temel eğitimini tamamladıktan sonra Thales'in tavsiyesiyle Mısır ve Babil'e giderek fen ve dini bilimler tahsili gördü.","Mısır'da kahin ve rahiplerden aldığı eğitimin ardından Babil'e gitti ve burada aldığı eğitim matematiğin kutsallığına olan inancını pekiştirdi.","Mısır kahinleri ve Babil'deki rahiplerin ayinlerini müzik eşliğinde yapmaları ile müzik de Pisagor felsefesindeki yerini aldı."]},"beginTime":156,"endTime":203,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=156&ask_summarization=1"},{"index":4,"title":"Kroton'daki Dönemi ve Sonu","list":{"type":"unordered","items":["Otuzdört yılını eğitimleri alarak geçiren Pisagor, ülkesine dönünce dersler vermeye başladı.","Yönetimin baskısı ile MÖ 529 yılında Güney İtalya'da Yunanlıların yaşadığı bir liman kenti olan Kroton'a göç etmek zorunda kaldı.","Kroton'da ünü çok daha çabuk yayılan Pisagor, kendi adıyla Pisagor ve müritlerine göre sayılar arasında tesadüfi olmayacak kadar mükemmel bir harmoni vardı."]},"beginTime":203,"endTime":246,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=203&ask_summarization=1"},{"index":5,"title":"Pisagor'un Ölümü ve Mirası","list":{"type":"unordered","items":["Pisagor'un hem bilimsel çalışmaları ve açılımlarından hem de dini alandaki çalışmalarından rahatsız olan halk bir süre sonra okulu ateşe verdi.","Pisagor ve öğrencileri yanarak can verdiler ve ona ve kurucusu olduğu ekole ait pek çok belgede yangında kül olup gitti.","Bu yüzden Pisagor'un günümüzde çok fazla kaynağı kalmamıştır."]},"beginTime":246,"endTime":274,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=246&ask_summarization=1"},{"index":6,"title":"Sayıların Önemi","list":{"type":"unordered","items":["Pisagor, sayılara tanrılık atfediyor ve matematiğin ilkelerini dünya üzerindeki tüm sistemlerin temeli olarak kabul ediyordu.","Ona göre her şey sayılarla ve matematikle açıklanabilirdi.","Pisagor, evrendeki bazı kavramların karşılığını sayılarla ifade etmişti; örneğin 5 rengin, 6 soğuğun, 7 sağlığın, 8 aşkın sayısıydı."]},"beginTime":274,"endTime":333,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=274&ask_summarization=1"},{"index":7,"title":"Geometri ve Sayılar","list":{"type":"unordered","items":["Sayılarla kavramlar ve nesneler arasında bağlantı kuran Pisagor, düzgün geometrik şekillerle kavramlar ve nesneler arasında da bir eşleştirme yaptı.","Ateşin piramitten, yeryüzünün altı yüzlüden, havanın düzgün sekiz yüzlüden ve suyun yirmi yüzlüden yaratıldığına inanıyordu."]},"beginTime":333,"endTime":360,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=333&ask_summarization=1"},{"index":8,"title":"Müzik ve Matematik","list":{"type":"unordered","items":["Pisagor'un sayılarla matematiğin dışında hayatın diğer alanları arasında kurduğu bağlantılar somut bir şekilde müzikte karşımıza çıkar.","Pisagor, telli çalgıda telin kısalmasıyla çıkardığı sesin inceldiğini fark etmişti; iki telden birinin uzunluğu diğerinin iki katı ise kısa telin çıkardığı ses, uzun telin çıkardığı sesin bir oktav üstündeydi.","Tellerin uzunluklarının oranı üçte iki oranındaysa iki tenin çıkardığı sesler beşli aralıklıydı."]},"beginTime":360,"endTime":435,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=360&ask_summarization=1"},{"index":9,"title":"Pisagor'un Müzikteki Buluşu","list":{"type":"unordered","items":["Pisagor'un müzikteki bu önemli buluşu, demircilerden ilham almıştı.","Çarşıda beş ayrı demirci dükkanı bulunmaktaydı ve hepsinden de ayrı sesler geliyordu çünkü demircilerin kullandıkları çekiçlerin boyutları birbirinden farklıydı.","Pisagor, çekiçlerin örse vuruşu sırasında çıkan düzenli seslerin bir müzik parçasını andırdığını fark etti ve çekiçlerin ağırlıkları bir sayı dizisi oluşturacak şekilde sıralanıyordu."]},"beginTime":435,"endTime":533,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=435&ask_summarization=1"},{"index":10,"title":"Matematikte İspat Fikri","list":{"type":"unordered","items":["Matematiğin piri sayılan Pisagor, matematikte ispat fikrini ortaya atan ilk bilim adamıydı.","Ona göre aksiyonlar ve postulatlar her şeyden önce gelmeliydi ve başka bir önermeye götürülmeyen ve onunla kanıtlanmayan böyle bir geri götürme ve kanıtı da gerektirir.","Pisagor, kendiliğinden apaçık olan ve böyle olduğu için öteki önermelerin temeli ve ön dayanağı olan temel önerme anlamına gelen aksiyon kavramını getirmiş ve sonuçların bu aksiyon ve postulatlardan yararlanılarak elde edilmesi gerektiği düşüncesini yerleştirmişti."]},"beginTime":533,"endTime":584,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=533&ask_summarization=1"},{"index":11,"title":"Pisagor Teoremi ve İrrasyonel Sayılar","list":{"type":"unordered","items":["Çarpım cetvelinin bulunuşu ve geometriye uygulanması da Pisagor'a mal edilir.","Pisagor teoremi, bir dik üçgende dik kenarlar üzerine kurulan karelerin alanları toplamı hipotenüsün üstüne kurulan karenin alanına eşittir düşüncesinden alan teorem matematiksel olarak da c² = a² + b² şeklinde ifadelendirilir.","Pisagor teoremi sonucunda matematikte sadece tam sayılar ve rasyonel sayılar olmadığı önermesini ortaya koyan bir dik üçgende dik kenarlar üzerine kurulan karelerin alanları toplamı hipotenüs üstüne kurulan karenin alanına eşittir teoreminden yola çıkarsak, hipotenüs uzunluğu karekök onbir ifadesiyle kendini bulur."]},"beginTime":584,"endTime":707,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=584&ask_summarization=1"},{"index":12,"title":"İrrasyonel Sayıların Keşfi","list":{"type":"unordered","items":["O zamanki matematikte ortaya konduğu şekliyle, yani rasyonel sayılar arasında karekök onbir ifadesi yer almıyordu.","Bu ayrı bir sayı grubunun üyesidir ve irrasyonel sayıdır.","Hipotenüs ya da diğer adıyla karenin köşegeni, Pisagor'un doğal sayılar kümesini alt üst etmişti ve bu sonuçla birlikte hiçbir zaman tekrar etmeyen sonsuz ondalıklı irrasyonel sayı keşfedildi."]},"beginTime":707,"endTime":754,"href":"/video/preview/11537723072783691208?parent-reqid=1769626025597740-3285550890443716399-balancer-l7leveler-kubr-yp-vla-18-BAL&text=Mathematikoi&t=707&ask_summarization=1"},{"index":13,"title":"Pisagor'un Son Yılları","list":{"type":"unordered","items":["Meşhur matematikçi, tarihteki birçok bilim adamı ile aynı korkunç akıbeti paylaştı.","Bir rivayete göre politikacılarla ters düşünce okuluyla birlikte yakıldı, bir başka söylentiye göre ise Pisagor önce Tarentum'a sürgün edildi.","Onaltı yıl kadar sonra kendisine bağlılığını sürdüren idealist bir grup ile daha kuzeydeki bir sahil kasabası olan Metapontium'a kaçtı ve Mısırlı kahinlere verdiği söze sadık kalarak, hiçbir şey yazmadan öğrencileriyle sohbetler ederek yaşadı ve 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