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Fibonacci dizisinin altın oranla ilişkisi ve bu oranın doğadaki yerleri, insan vücudundan çam kozalaklarına kadar çeşitli örneklerle açıklanmaktadır."]},"endTime":301,"title":"Leonardo Fibonacci ve Altın Oran","beginTime":0}],"fullResult":[{"index":0,"title":"Leonardo Fibonacci'nin Hayatı ve Matematiksel Keşifleri","list":{"type":"unordered","items":["Leonardo Fibonacci, doğanın kanunlarını matematiksel düşüncelerle açıklamaya çalışan ve matematiğin sırlarını Araplardan Avrupa'ya aktaran ortaçağ Avrupası'nın en önde gelen matematikçisiydi.","İtalya'nın Pisa şehrinde bir tüccarın oğlu olarak dünyaya gelen Fibonacci, çocuk yaştayken babasının gümrük memurluğu yaptığı Kuzey Afrika'daki Bugia şehrine taşındı.","Burada İslam bilginlerinden Doğu matematiğindeki tüm gelişmeleri öğrenen Fibonacci, Hint-Arap sayıları ile aritmetik işlemler yapmanın Roma rakamları ile hesap yapmaktan çok daha basit ve verimli olduğunu gördü."]},"beginTime":31,"endTime":86,"href":"/video/preview/17725496443804245816?parent-reqid=1769593391303666-6041010485534168502-balancer-l7leveler-kubr-yp-klg-19-BAL&text=Leonardo+Math&t=31&ask_summarization=1"},{"index":1,"title":"Hint-Arap Sayı Sisteminin Avrupa'ya Yayılması","list":{"type":"unordered","items":["Fibonacci, öğrendiklerini \"Liber Abaci\" (Hesaplama Kitabı) isimli eserinde toplayarak Hint-Arap sayı sistemini Avrupalılara tanıttı.","O yıllarda Avrupa'da egemen olan Roma sayı sistemine karşı çıkan Fibonacci, dokuz Hint rakamını ve işaretini kullanarak herhangi bir sayı yazılabilir ifadesini kullandı.","Bu yeni sayılar kilisenin yasaklamasına karşın İtalyan tüccarlar arasında hızla yayıldı ve sonunda 0'dan 9'a kadar uzanan Hint-Arap sayı sistemi Avrupa'da yaygınlaştı."]},"beginTime":86,"endTime":144,"href":"/video/preview/17725496443804245816?parent-reqid=1769593391303666-6041010485534168502-balancer-l7leveler-kubr-yp-klg-19-BAL&text=Leonardo+Math&t=86&ask_summarization=1"},{"index":2,"title":"Fibonacci Dizisi ve Altın Oran","list":{"type":"unordered","items":["Fibonacci, dört bir yanı duvarla çevrili bir ortamda bir çift tavşandan yılda kaç tavşan türeyeceğini bilmek istedi ve çözüm üzerinde çalışırken ilginç bir tablo fark etti.","Tavşan sayısı her ay kesin bir mantık sisteminde artmaktaydı: 1, 2, 3, 5, 8, 13, 21 gibi ve serideki her sayı kendinden önce gelen iki sayının toplamından oluşmaktaydı.","Fibonacci, dizideki her sayının kendinden bir önceki sayıya bölümünün yaklaşık olarak 1,618'e (altın orana) eşit olduğunu fark etti ve bu sayıyı keşfetmesi nedeniyle altın orana adının ilk iki harfi olan fi sayısı denildi."]},"beginTime":144,"endTime":235,"href":"/video/preview/17725496443804245816?parent-reqid=1769593391303666-6041010485534168502-balancer-l7leveler-kubr-yp-klg-19-BAL&text=Leonardo+Math&t=144&ask_summarization=1"},{"index":3,"title":"Altın Oranın Doğada ve Sanatta Yeri","list":{"type":"unordered","items":["Doğada yaratılan güzelliğin ölçüsü olarak bilinen altın oran, evrende eşi benzeri olmayan tek sayıdır ve görsel alanda güzelliğin tahtı bu harika sayı üzerine kuruludur.","Altın oran, insan vücudundan çam kozalaklarındaki tanelere, salyangoz kabuklarından ayçiçeğine kadar doğanın pek çok detayında saklıdır.","Leonardo da Vinci, Mimar Sinan ve Christopher Wren gibi birçok mimar, ressam ve heykeltıraş yapıtlarında bu muhteşem sayıyı kullandı."]},"beginTime":235,"endTime":301,"href":"/video/preview/17725496443804245816?parent-reqid=1769593391303666-6041010485534168502-balancer-l7leveler-kubr-yp-klg-19-BAL&text=Leonardo+Math&t=235&ask_summarization=1"}],"linkTemplate":"/video/preview/17725496443804245816?parent-reqid=1769593391303666-6041010485534168502-balancer-l7leveler-kubr-yp-klg-19-BAL&text=Leonardo+Math&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Matematik Hikayeleri 6. 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Uydu benzeri harita, makineli tüfek, mekanik şövalye, paraşüt, helikopter, dalgıç giysisi ve araba gibi icatlarını detaylı şekilde anlatıyor. Her bir icatın nasıl tasarlandığı, neden yapıldığı ve günümüzdeki etkileri hakkında bilgiler veriliyor. Video, Leonardo'nun hayalperestliğini ve yaratıcılığını vurgulayarak, onun icatlarının günümüz dünyasını nasıl şekillendirdiğini gösteriyor."]},"endTime":402,"title":"Leonardo da Vinci'nin Zamanının Ötesinde İcatları","beginTime":0}],"fullResult":[{"index":0,"title":"Leonardo da Vinci'nin Çok Yüzlülüğü","list":{"type":"unordered","items":["Leonardo da Vinci, Mona Lisa tablosu ile tanınan Rönesans sanatçısı olup, matematikçi, yazar, tarihçi, aşçı ve mucit olarak da bilinir.","Da Vinci, 1502 yılında dünyanın ilk gerçek uydu fotoğrafının çekildiği 1959'dan yüzyıllarca önce uydu görüntüsüne benzeyen bir harita ortaya çıkarmıştır.","Bu harita tamamen el çizimiydi ve Leonardo, yaratıcı ve açılarla mesafeyi hesaplamak için bir yol (tekerlekli mesafe ölçer) 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