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Video, Pascal'ın bilime katkılarının şerefine verilen isimlerle sonlanmaktadır."]},"endTime":344,"title":"Blaise Pascal'ın Hayatı ve Bilimsel Katkıları","beginTime":0}],"fullResult":[{"index":0,"title":"Blaise Pascal'ın Hayatı ve İlk Çalışmaları","list":{"type":"unordered","items":["1623 yılında dünyaya gelen Blaise Pascal, Fransız mucit, matematikçi, fizikçi, yazar ve filozoftur.","Vergi tahsildarı olan babası tarafından eğitilen Pascal, ilk çalışmaları doğa bilimleri ve uygulamalı bilimler alanındaydı.","Pascal, akışkanlar ile ilgili çalışmalara katkılarda bulunmuş, basınç ve vakum kavramlarını açıklığa kavuşturmuştur."]},"beginTime":15,"endTime":46,"href":"/video/preview/8217912020040511810?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=15&ask_summarization=1"},{"index":1,"title":"Mekanik Hesap Makinesi ve Matematiksel Katkıları","list":{"type":"unordered","items":["1642 yılında genç yaşta hesap makineleri üzerine çalışmalara öncülük etmiş ve mekanik hesap makinesinin ilk iki mucidinden biri olmuştur.","On altı yaşındayken izdüşümsel geometri konusunda kayda değer bir bilimsel eser yazmıştır.","Pascal Teoremi, bir hexagonun çemberin içine çizilmesi durumunda zıt taraflardaki üç kesişim noktasının bir düz çizgi üzerinde olduğunu belirtir."]},"beginTime":46,"endTime":152,"href":"/video/preview/8217912020040511810?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=46&ask_summarization=1"},{"index":2,"title":"Bilimsel ve Teknik İcatları","list":{"type":"unordered","items":["1642 yılında, henüz on dokuz yaşındayken, babasının vergi hesaplamalarına yardımcı olmak için toplama ve çıkarma yapabilen mekanik bir hesap makinesi geliştirmiştir.","Pascal, hidrodinamik ve hidrostatik alanındaki çalışmaları hidrolik akışkanlar konusunda yoğunlaşmıştır.","Hidrolik pres ve şırınga icatları yapmış, hidrostatik basıncın sıvının ağırlığına değil, yükselti farkına bağlı olduğunu kanıtlamıştır."]},"beginTime":152,"endTime":91,"href":"/video/preview/8217912020040511810?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=152&ask_summarization=1"},{"index":3,"title":"Felsefi ve Teolojik Çalışmaları","list":{"type":"unordered","items":["1654 yılının sonlarında felsefe ve teoloji alanında etkileyici çalışmalarda bulunmuştur.","Pascal'ın ölümünden sonra düşünceler olarak anılacak olan en etkileyici teolojik eseri ölümünden önce tamamlanmamıştı.","Pascal'ın son büyük başarısı, mekanik dahili sayesinde ilk otobüs hattını açarak insanların Paris içinde taşıtla yolculuk etmesini sağlamaktır."]},"beginTime":91,"endTime":275,"href":"/video/preview/8217912020040511810?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=91&ask_summarization=1"},{"index":4,"title":"Pascal'ın Vefatı ve Mirası","list":{"type":"unordered","items":["1662 yılında Pascal'ın hastalığı şiddetlendi ve duygusal durumu kardeşinin ölümünden beri kötüleşmiştir.","Pascal 18 Ağustos 1662'de Paris'te vefat etmiş ve otuz dokuz yaşında olmuştur.","Pascal'ın bilime katkılarının şerefine pascal adı basınç birimine, bir programlama diline ve Pascal kuralına verilmiştir."]},"beginTime":275,"endTime":326,"href":"/video/preview/8217912020040511810?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=275&ask_summarization=1"}],"linkTemplate":"/video/preview/8217912020040511810?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"Pascal (Blaise Pascal) Kimdir? 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Pekiştirmek İçin 👇 0'dan 10'a Matematik: https://bit.ly/2ZGkHtr Dinamo Matematik: https://bit.ly/39l119b Tonguç Plus Üyeliğini İncelemek İçin : https://bit.ly/3ihGmOR 📌Eylül ayı...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4266379/ce1cb7c04f286421176e2b47963da99f/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/GKqqPgIAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"1","reqid":"1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=videoid:4262797571639949768","teaser":[{"list":{"type":"unordered","items":["Bu video, bir matematik öğretmeninin Pascal üçgeni ve binom açılımı konusunu anlattığı kapsamlı bir eğitim içeriğidir. Öğretmen, 29 Eylül Çarşamba günü bu konuyu ele almaktadır.","Video, Pascal üçgeninin tanımı ve özellikleriyle başlayıp, binom açılımının temel prensiplerini adım adım açıklamaktadır. Öğretmen, (x+y)² açılımını örnek olarak göstererek kombinasyonların nasıl yerleştirileceğini, terimlerin nasıl hesaplanacağını ve binom açılımının özellikleri (terim sayısı, x kuvvetlerinin toplamı, ortanca terim) hakkında bilgi vermektedir. Ayrıca katsayılar toplamı, sabit terim ve belirli terim bulma gibi konulara da değinilmektedir.","Videoda ÖSYM tarzı sorular üzerinden konu pekiştirilmekte ve öğrencilerin ezber yerine mantığı anlaması vurgulanmaktadır. Dersin sonunda öğrencilere ödev verilmekte ve bir sonraki derste olasılık konusunun işleneceği belirtilmektedir."]},"endTime":1534,"title":"Pascal Üçgeni ve Binom Açılımı Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Pascal Üçgeni ve Binom Açılımı Tanıtımı","list":{"type":"unordered","items":["Pascal üçgeni ve binom açılımı konusu, 29 Eylül Çarşamba günü anlatılmaktadır.","Yarın felsefe tanımlama konusu ve Ekim ayı programı için hazırlıklar yapılıyor.","Bu hafta pascal üçgeni tanımı, işlevi, pascal-kombinasyon ilişkisi, pascal özdeşliği ve binom açılımı konuları ele alınacaktır."]},"beginTime":0,"endTime":52,"href":"/video/preview/4262797571639949768?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=0&ask_summarization=1"},{"index":1,"title":"Pascal Üçgeni Tanımı ve Yapısı","list":{"type":"unordered","items":["Pascal üçgeni, bir ile başlayan ve başında ve sonunda bir olan üçgen şeklinde yayılan bir sistemdir.","Pascal üçgeninde, her sayı üstteki iki sayının toplamı olarak hesaplanır.","Pascal üçgeni, binom açılımında katsayıları belirlemek için kullanılır."]},"beginTime":52,"endTime":151,"href":"/video/preview/4262797571639949768?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=52&ask_summarization=1"},{"index":2,"title":"Binom Açılımının Pascal Üçgeni ile İlişkisi","list":{"type":"unordered","items":["Binom açılımı, iki terimli ifadelerin kuvvetlerinin açılımlarıdır (x+y)ⁿ şeklinde.","Pascal üçgenindeki sayılar, binom açılımındaki katsayıları belirler: (x+y)⁰=1, (x+y)¹=x+y, (x+y)²=x²+2xy+y², (x+y)³=x³+3x²y+3xy²+y³.","Pascal üçgeni, kombinasyon değerlerinden türetilir: 0C0, 1C0+1C1, 2C0+2C1+2C2 şeklinde."]},"beginTime":151,"endTime":338,"href":"/video/preview/4262797571639949768?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=151&ask_summarization=1"},{"index":3,"title":"Pascal Özdeşliği","list":{"type":"unordered","items":["Pascal özdeşliği, Pascal üçgenindeki ardışık kombinasyon değerlerinin toplamının bir sonraki satırda aynı konumda bulunan kombinasyon değerine eşit olduğu özelliğidir.","Örneğin: nCk + nC(k+1) = (n+1)C(k+1) formülü geçerlidir.","Pascal özdeşliği, işlem sorularında ve sınavlarda önemli bir kısayol olarak kullanılır."]},"beginTime":338,"endTime":421,"href":"/video/preview/4262797571639949768?parent-reqid=1769428222866407-123957556399570832-balancer-l7leveler-kubr-yp-vla-211-BAL&text=Pascal+BLNC&t=338&ask_summarization=1"},{"index":4,"title":"Binom Açılımı Kavramı","list":{"type":"unordered","items":["Her şeyin bir kuvveti kendisiydi, ikinci kuvveti ise x² şeklinde ifade edilir.","Binom açılımında 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