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if you enjoyed this! Thank you to @3Blue1Brown for providing the mathematical animation software (Manim) to make this video. Before you enter your graph theory class, watch this video!","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/4441180/a041683923b18876a2b01660354b5f88/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/KyJycwEAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"8","reqid":"1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL","summary":{"fullTextUrl":"/int_search_summary?data=http%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DmMUfbPUxfgE","linkTemplate":"/video/preview/13575406869933632883?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"What is Graph Theory?","related_orig_text":"Graph The General - Topics","related_porno":false,"related_less_3m_off":true,"client":"d2d","no_cnt":1,"related_src":"serp","related":"{\"porno\":false,\"vfp\":1,\"orig_text\":\"Graph The General - Topics\",\"url\":\"http:\\/\\/www.youtube.com\\/watch?v=mMUfbPUxfgE\",\"src\":\"serp\",\"rvb\":\"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-v38BQDwCwwC-gP_AfgMAPr5_f0A-v4B-QQD_wAB-QD3-gEAAP4LBwIAAAAA-AoFAfn_AAADC_b_BAAAAAb0_fsEAAAABgv6_f4BAAAL_AgDA_8AABIEAf3_AAAAAAD6BAUAAAD5D_0GAAAAABL7AAH89f4AIAAtU2bdOzgTQAlITlACKoQCEAAa8AF87SAB0PvR_-8G2ADWD8MAgSIK_gIjCgDy_RwB0t7sAB0tGADa3zL-EfLjAKTwCQAE-N__OPP2ACoBA_9A4voAzwQFABPdFwEX9hMBA9nZAe0zD_71FAsA9eTmAukLB_4q6QL-GiH1_QrsvQgi_CwBGTfzASTuAAEVERoC_AwS_RTz9_wYCfn8_wATAO0UNwHnA-IBB-8RB_NI5wcP_BsF-ff9BCYC5wIa-hkH0_sH-gLuAPYhAw342O___vUyFgPm1BH88NgP8uwY-v4P6PMF8-EDAQQB8wzV5fYGKP3r-ukC9wHUNvX-Fw8R9hcD_QAgAC3_IR07OBNACUhhUAIqcxAAGmAlAgAt3SIK_vv07e2e0w3uANoy7dfn_-zbAPQL4f7x-M7ZN-EALdQ-CqwAAAD8ygTz9AAScfPT2ywM_urunfcdJ38UEyi73BcGsOLL4-fx4CnzH0AAtfS_AyC64_3OPxogAC3OkyQ7OBNACUhvUAIqrwYQDBqgBgAASEIAADDCAADQQQAAQMAAANjBAAAQQQAA6kIAAEBAAAA4QgAAAMAAAAxCAAAsQgAAMEEAAAjCAADAQQAAHEIAABDBAAAAwQAAFEIAAITCAACgQAAAUEEAAMBAAAAEwgAAJMIAAMhBAACwwQAAFEIAALBBAAA8QgAAwEAAACxCAAC0wgAAoEAAABjCAAAAwQAAcEIAALBBAAAMQgAAsEEAAEDAAABEQgAADEIAABDBAACowQAAoMIAAHhCAACAwQAAgEIAAKDBAAAQwQAAIMIAAILCAACWwgAAAEAAALBCAACMwgAAXMIAAABAAACIQQAAQMEAAIbCAABQwgAAgL8AAGDCAAAcwgAAGMIAABjCAAAgQgAAMMIAANBBAAAMQgAAQMEAADxCAACAwAAA-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_AABwQQAAiEEAALDBAABMwgAA0sIAAIBAAAA0QgAAoMAAAILCAACsQgAAisIAAHDBAAAMwgAALEIAAAxCAACQQQAAIMEAAGDBAACwwQAAFEIAAEDBAAAUQgAAUEEAAPBBAABgwQAA8EEAAIZCAACgwQAAgMAAANjBIAA4E0AJSHVQASqPAhAAGoACAAC2vgAApr4AAKg9AAAsPgAAML0AAKI-AAC4vQAAJb8AAFS-AADYPQAAkj4AAIg9AAA8PgAA-D0AAIq-AAA8vgAAxj4AAOA8AAAwPQAA3j4AAH8_AAA8vgAAND4AADw-AAC4vQAAqD0AAAQ-AABQPQAARD4AAMg9AABsPgAAiL0AANa-AABsPgAAHD4AAJi9AABEPgAAnr4AANi9AABAvAAAiL0AAJK-AACiPgAAFD4AADC9AACAOwAA-L0AAJi9AAC4vQAAcL0AACy-AACIvQAAND4AAFw-AACCPgAAMD0AAFM_AADIPQAAQLwAAEC8AACIvQAA-D0AAEA8AADovSAAOBNACUh8UAEqjwIQARqAAgAAFL4AAOi9AAAUvgAAR78AAJg9AABAvAAA9j4AAIq-AADIPQAAQDwAAEC8AADovQAAuD0AAAy-AABEPgAAML0AAEC8AAAbPwAAJL4AALo-AAAQPQAAMD0AAKA8AAAwvQAAED0AAOA8AABAvAAAcD0AAMi9AAAQPQAAmD0AANg9AACovQAAZL4AAIg9AAC4vQAAVD4AAEC8AACOvgAAQLwAAGQ-AABAPAAAuD0AADw-AABwvQAAiL0AAH-_AAAsvgAAyL0AALg9AADgPAAAPD4AADA9AABAvAAA6D0AAOg9AADgvAAAoDwAABQ-AACIvQAAbD4AAFQ-AACAuwAAqL0gADgTQAlIfFABMAk4AUoAUgkIDxCSAhgAMAFgAGgA\"}","related_url":"http://www.youtube.com/watch?v=mMUfbPUxfgE","parent-reqid":"1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL","related_vfp":1,"relatedVideo":"yes"},"cwidth":1920,"cheight":1080,"cratio":1.77777,"dups":["13575406869933632883"],"episode":0,"season":0,"isEmbedOnly":false,"greenHost":"YouTube","hasTranslation":true,"contentTypeId":null,"censored":false,"videoContentId":"1913863281"},"10575151389641245791":{"videoId":"10575151389641245791","docid":"34-10-3-Z5618604555E150EC","description":"Genel olarak Graf teorisine ve kavramlarına giriş yapılmıştır. Bazı konu başlıkları: Graf (Şekil, ağ, network) nedir, düğüm (node, vertex), kenar (Edge, arc) kavramları Grafların küme teorisi ile...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3482714/7f6d76cf27335bd7dac10f2e38501dba/564x318_1","videoSrc":"https://video-preview.s3.yandex.net/dhZkuQAAAAA.mp4","videoType":"video/mp4"},"target":"_self","position":"9","reqid":"1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=videoid:10575151389641245791","teaser":[{"list":{"type":"unordered","items":["Bu video, Şadi Evren Şeker tarafından \"Bilgisayar Kavramları\" kanalında sunulan, graf teorisi hakkında kapsamlı bir eğitim içeriğidir. Eğitmen, graf teorisinin temel kavramlarını ve uygulamalarını detaylı şekilde anlatmaktadır.","Video, graf teorisinin tanımı ve temel kavramlarıyla başlayıp, düğümler (node/vertices) ve kenarlar (edge) üzerinden grafın yapısal özelliklerini açıklamaktadır. Ardından Königsberg Köprüleri Problemi gibi tarihsel gelişim, yönlü ve yönsüz graf, ağırlıklı graf, bağlantılı graf kavramları, düğüm dereceleri, yürüyüş, yol ve döngü gibi temel kavramlar ele alınmaktadır. Son olarak, ağaç, düzenli graf, iki parçalı graf, tam graf, düzlemsel graf gibi özel graf türleri ve graf gösterim yöntemleri (küme, matris, kenar listesi, düğüm listesi) anlatılmaktadır.","Video, graf teorisinin gerçek hayattaki uygulamalarını da içermekte olup, sosyal ağlar, bilimsel katkılar, tedarik zinciri, biyoinformatics, internet ve ekolojik ağlar gibi alanlardaki graf modelleri örneklerle gösterilmektedir. Ayrıca en kısa yol problemi, gezgin satıcı problemi gibi önemli graf teorisi problemleri de açıklanmaktadır."]},"endTime":3041,"title":"Graf Teorisi Eğitim Videosu","beginTime":0}],"fullResult":[{"index":0,"title":"Graf Teorisi Tanıtımı","list":{"type":"unordered","items":["Konuşmacı Şadi Evren Şeker, \"Bilgisayar Kavramları\" kanalında graf teorisini anlatacaklarını belirtiyor.","Graf (şekil) kavramı, network veya a teorisi olarak da adlandırılabilir ve arkasında küme teorisi yatar.","Graf teorisi, düğümler (node) ve kenarlar (edge) olarak adlandırılan iki temel bileşenden oluşur."]},"beginTime":1,"endTime":71,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=1&ask_summarization=1"},{"index":1,"title":"Graf Teorisinin Gerçek Hayatta Kullanımı","list":{"type":"unordered","items":["Gerçek hayatta hemen hemen her şey graflarla modellemek mümkün olabilir; bir varlık birden fazla varlıkla ilişkiliyse orada bir graf vardır.","Kenarlar genelde ilişkiyi, düğümler ise varlıkları gösterir; örneğin arkadaşlar arasındaki güven ilişkileri bir graf olarak gösterilebilir.","Düğümler genellikle isimlerle (sayılar, harfler, şehir isimleri gibi) etiketlenebilir."]},"beginTime":71,"endTime":149,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=71&ask_summarization=1"},{"index":2,"title":"Graf Teorisinin Uygulamaları","list":{"type":"unordered","items":["Sosyal ağlar (Facebook, Twitter, LinkedIn) arkadaşlık ağı olarak graf teorisine örnek verilebilir.","Farklı çevrelerden tanıdığınız kişiler farklı renklerle (renklendirme) gösterilebilir.","Bilimsel çalışmalar, makale atıfları, kurumlar arası ilişkiler, tedarik zinciri ve protein geçişlilik ağı gibi çeşitli alanlarda graf teorisi kullanılır."]},"beginTime":149,"endTime":293,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=149&ask_summarization=1"},{"index":3,"title":"Graf Teorisinin Tarihi","list":{"type":"unordered","items":["Graf teorisi, çözümlenmesi gereken problemlerden ortaya çıkmıştır.","Bu problemlerin çözümü için geliştirilen yöntemler ve tanımlar graf teorinin temelini oluşturmuştur."]},"beginTime":293,"endTime":314,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=293&ask_summarization=1"},{"index":4,"title":"Konigsberg Köprüleri Problemi","list":{"type":"unordered","items":["Konigsberg'de yedi köprü bulunuyor ve bu köprüler bir adadan ve yarımada arasında akan nehirlerle bağlanıyor.","Euler'in ilk teorisi, bu yedi köprüden sadece bir kere geçerek tümünü dolaşabilme problemine odaklanıyor.","Euler, düğümlerin derecesi kavramını ortaya atarak, bir grafa en fazla iki tek sayıda düğüm olabilir veya tamamı çift sayıda düğüm olabilir durumunda tüm kenarlardan bir kere geçilerek bir yol çizilebileceğini ispatladı."]},"beginTime":321,"endTime":454,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=321&ask_summarization=1"},{"index":5,"title":"Graf Teorisinin Uygulamaları","list":{"type":"unordered","items":["Kirşof'un elektrik devreleri üzerindeki teorisi, döngüler ve geçişleri içeren bir graf teorisi örneğidir.","Harita boyama (map coloring) teorisi, komşu bölgeleri aynı renkle boyamamak şartıyla en az sayıda renk kullanma problemidir.","Taşımacılıkta en kısa yol (shortest path problem), gezgin satıcı problemi (travelling salesman problem) gibi çeşitli problemler graf teorisine dayanmaktadır."]},"beginTime":454,"endTime":608,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=454&ask_summarization=1"},{"index":6,"title":"Graf Teorisinin Temel Tanımları","list":{"type":"unordered","items":["Graf (graph), genellikle büyük G harfiyle gösterilir ve düğümler (vertex veya node) ve kenarlar (edge) olmak üzere iki kümeden oluşur.","Graf teorisinde self-loop (kendine dönen bağlantı) kavramı vardır ve bazı düğümler kendi üzerine bağlantıya sahip olabilir.","Yönlü graf (directed graph) içinde, bir düğümden diğerine giden bağlantılar yönüne göre belirlenir ve bir düğümden kendisine dönülemez."]},"beginTime":608,"endTime":773,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=608&ask_summarization=1"},{"index":7,"title":"Yönlü ve Ağırlıklı Graf Kavramları","list":{"type":"unordered","items":["Yönlü graf (directed graph veya degraf olarak da bilinir) içinde, düğümler arasında hem 5'ten 4'e hem de 4'ten 5'e gidilebiliyor, ancak 3'ten 4'e doğrudan gidilemiyor.","Ağırlıklı graf, kenarların üzerinde ağırlık değerleri bulunur; ağırlık mesafe, maliyet veya bir kişi diğerinin paylaşımını beğenen sayı gibi farklı fonksiyonlar olabilir.","Ağırlık fonksiyonları tamamen isteğe bağlıdır ve reel sayılar veya tam sayılar üzerinden tanımlanabilir."]},"beginTime":774,"endTime":883,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=774&ask_summarization=1"},{"index":8,"title":"Graf Bağlantı Türleri","list":{"type":"unordered","items":["Yönsüz graflar, her iki yönde de bağlantı olan çift yönlü yönlü graf olarak da düşünülebilir.","Bağlı graf, her düğümden diğer her düğüme bir şekilde ulaşılabildiği graf türüdür.","Kuvvetli bağlı (strongly connected) graf, her düğümden diğer her düğüme doğrudan gidilebildiği graf türüdür."]},"beginTime":883,"endTime":969,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=883&ask_summarization=1"},{"index":9,"title":"Graf Teorisi Kavramları","list":{"type":"unordered","items":["Component (bileşen) kavramı, tamamen bağlı olmayan bir graf için kullanılır ve birbirinden kopuk olan her bir ada parçası olarak düşünülebilir.","Connected (bağlı) bir grafta sadece bir bileşen vardır, tamamı tek bir bileşen olarak düşünülebilir.","Derece tanımı, her bir düğümden çıkan kenar sayısı veya bir düğümün kaç tane komşusu olduğu olarak tanımlanır."]},"beginTime":974,"endTime":1056,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=974&ask_summarization=1"},{"index":10,"title":"Yönlü ve Yönsüz Graf Teorisi","list":{"type":"unordered","items":["Yönlü graf teorisinde derece ikiye ayrılır: in-degree (gelen derece) ve out-degree (çıkan derece).","Yönlü graf teorisinde toplam derece, in-degree ve out-degree'nin toplamıdır.","Bir graftaki kenar sayısı, düğümlerin toplam derecelerinin yarısıdır (2 × kenar sayısı = toplam dereceler)."]},"beginTime":1056,"endTime":1195,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=1056&ask_summarization=1"},{"index":11,"title":"Tek Dereceli Düğümler","list":{"type":"unordered","items":["Tek sayıda derecesi olan düğüm sayısı çift olmalıdır.","Tek dereceli düğüm en az bir olabilir ve bir düğümün tek dereceye sahip olması durumunda, onu dengeleyen başka bir tek dereceye sahip düğüm de olmalıdır.","Çift sayıda tek dereceye sahip düğüm olabilir, tek sayıda tek dereceye sahip düğüm olamaz."]},"beginTime":1195,"endTime":1263,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=1195&ask_summarization=1"},{"index":12,"title":"Yürüyüş ve Yollar","list":{"type":"unordered","items":["Walk (yürüyüş), kenar ve düğümlerin tekrar olabileceği bir yol olarak tanımlanır.","Path, tekrar olmayan bir yürüyüş olarak tanımlanır; aynı düğümden geçmek mümkündür ancak aynı kenardan geçmek yasaktır.","Kapalı yürüyüş (closed walk), başlangıç ve bitiş noktaları aynı olan bir yürüyüştir."]},"beginTime":1263,"endTime":1471,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=1263&ask_summarization=1"},{"index":13,"title":"Özel Graf Türleri","list":{"type":"unordered","items":["Boş graf veya nul graf, hiç kenarı olmayan graf olarak tanımlanır.","Tamamen boş graf, hem kenarlar hem de düğümler kümesi boş olan graf olarak tanımlanır.","Ağaç, cycle (döngü) içermeyen bir graf olarak tanımlanır, yani başlangıç noktasına dönen bir yol bulunmaz."]},"beginTime":1471,"endTime":1519,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=1471&ask_summarization=1"},{"index":14,"title":"Ağaçlar ve Özel Ağaç Türleri","list":{"type":"unordered","items":["Ağaç, iki düğümü bağlayan tek bir yol olan ve kopuk olmayan bir grafik türüdür.","Özel ağaçlara \"yıldız ağacı\" (star tree) ve \"yol ağacı\" (path tree) gibi isimler verilir.","Bilgisayar bilimlerinde ağaçlar genellikle \"directed acyclic graph\" (DAG) olarak tanımlanır, ancak bazı kaynaklarda directed olma şartı zorunlu değildir."]},"beginTime":1523,"endTime":1650,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=1523&ask_summarization=1"},{"index":15,"title":"Düzenli Grafikler","list":{"type":"unordered","items":["Düzenli (regular) grafik, bağlı ve tüm düğümlerinin derecesi aynı olan grafiklerdir.","Regular cycle, bağlı ve tüm düğümlerin derecesi iki olan grafiklerdir."]},"beginTime":1650,"endTime":1704,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=1650&ask_summarization=1"},{"index":16,"title":"İki Parçalı 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graftır."]},"beginTime":2059,"endTime":2260,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=2059&ask_summarization=1"},{"index":21,"title":"İzomorfizm Kavramı","list":{"type":"unordered","items":["İzomorfizm, birebir (one-to-one) ve örtün (onto) olan bir fonksiyonu gerektiren, iki graf arasında komşulukları koruyan bir eşleme ilişkisidir.","İzomorfik graflar arasında toplam kenar sayısı, toplam düğüm sayısı ve düğüm dereceleri aynıdır.","İzomorfik graflar, çizimlerinde düğümlerin yerlerini değiştirerek birbirine dönüştürülebilir ve bu kavram veri güvenliğinde de kullanılmaktadır."]},"beginTime":2260,"endTime":2445,"href":"/video/preview/10575151389641245791?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=2260&ask_summarization=1"},{"index":22,"title":"Grafların Farklı 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I'll be with you with an 8th-grade Turkish explanation of tables, graphs, and visual interpretation. My dear students, in today's lesson, we'll cover the topics of tables, graphs, and...","preview":{"posterSrc":"//avatars.mds.yandex.net/get-vthumb/3164020/01ccbe58afa664489d3ee663707868d2/564x318_1"},"target":"_self","position":"16","reqid":"1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL","summary":{"isFull":true,"fullTextUrl":"/video/result?ask_summarization=1&numdoc=1&noreask=1&nomisspell=1&parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=videoid:5721104362756129862","teaser":[{"list":{"type":"unordered","items":["Bu video, Eyüp Hoca tarafından sunulan 8. sınıf matematik dersinin konu anlatımıdır. Hoca, tablo, grafik ve görsel yorumlama konusunu detaylı bir şekilde anlatmaktadır.","Video, üç ana başlık altında yapılandırılmıştır: tablo okuma, tablo yorumlama ve tablo inceleme; görsel yorumlama; kroki okuma. Her bir konu için örnekler verilerek, tablo ve grafiklerden hangi bilgilerin çıkarılabileceği, hangi bilgilerin çıkarılamayacağı açıklanmaktadır. Ayrıca görsel yorumlama ve kroki okuma konularında da örnekler sunulmaktadır. Video, bir etkinlik çalışması ve soru çözüm videosu ile devam edecektir."]},"endTime":437,"title":"8. Sınıf Tablo, Grafik ve Görsel Yorumlama Konu Anlatımı","beginTime":0}],"fullResult":[{"index":0,"title":"Giriş ve Konu Tanıtımı","list":{"type":"unordered","items":["Eyüp hocanın 8. sınıf konu anlatımı, soru çözümü etkinlik videolarına kaldığı yerden devam ediyor.","Bu derste 8. sınıf için tablo, grafik ve görsel yorumlama konu anlatımı yapılacak.","Konu anlatımının ücretsiz PDF dosyası videonun açıklamalar kısmında mevcuttur."]},"beginTime":1,"endTime":55,"href":"/video/preview/5721104362756129862?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=1&ask_summarization=1"},{"index":1,"title":"Tablo Okuma","list":{"type":"unordered","items":["Tablolar, bilgileri daha kolay ifade etmek ve daha anlaşılır olması için kullanılır.","Tablolarda ifade edilen rakamlar sayısal çokluğu ifade eder ve tabloda verilen rakamların tam olarak neyi ifade ettiğini iyi görmemiz gerekir.","Tabloyu yorumlarken bilgileri kullanarak çıkarımda bulunabiliriz, ancak verilen bilgilerin dışında bir çıkarım yapmamak şartıyla."]},"beginTime":55,"endTime":91,"href":"/video/preview/5721104362756129862?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=55&ask_summarization=1"},{"index":2,"title":"Tablo Örneği ve Çıkarımlar","list":{"type":"unordered","items":["Sınıf başkanlığı seçiminde aday olan beş öğrencinin aldığı oylar tablo şeklinde verilmiş.","Tablodan sınıfta en fazla oyu Aysel'in, en az oyu Sevil'in aldığını, toplam oy sayısını ve kız öğrencilerden en çok oyu Aysen'in aldığını bulabiliriz.","Tablodan Sevil'e kimlerin oy verdiğini, sınıftaki kızların hangi adayı desteklediğini, erkeklerin kızlardan kaç fazla olduğunu veya öğrencilerin hangi sınıfta okuduğunu bilemeyiz."]},"beginTime":91,"endTime":207,"href":"/video/preview/5721104362756129862?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=91&ask_summarization=1"},{"index":3,"title":"Grafik Okuma","list":{"type":"unordered","items":["Grafiklerde şekiller ve işaretler hangi sayıya denk geldiğine bakılır.","Sütun grafikleri bilgileri kolay anlamamızı sağlar.","Grafiklere bakarak ulaşabileceğimiz bilgiler olduğu gibi ulaşamayacağımız bilgiler de olabilir."]},"beginTime":207,"endTime":229,"href":"/video/preview/5721104362756129862?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=207&ask_summarization=1"},{"index":4,"title":"Grafik Örneği ve Çıkarımlar","list":{"type":"unordered","items":["Beşinci sınıfta okuyan Eymen'in bir haftada çözdüğü soruları gösteren bir grafik verilmiş.","Grafikten Eymen'in haftada en çok sosyal bilgiler dersinden soru çözdüğünü ve bir haftada toplam kaç soru çözdüğünü bulabiliriz.","Grafikten Eymen'in en başarılı olduğu dersi, en sevdiği dersi veya ilk hangi dersten soru çözmeye başladığını bilemeyiz."]},"beginTime":229,"endTime":284,"href":"/video/preview/5721104362756129862?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=229&ask_summarization=1"},{"index":5,"title":"Görsel Okuma","list":{"type":"unordered","items":["Görsel okuma yazılı metinlerin dışında kalan resim, fotoğraf, sembol, şekil, işaret, harita ve karikatür gibi görsellerin ifade ettiği bilgileri veya ipuçlarını yakalamaktır.","Görselleri yorumlayarak bu ipuçlarını kolaylıkla yakalayabiliriz.","Görselden işçilerin birlikte çalıştığını, çalışma alanının bir inşaat olduğunu ve işçilerin bedensel güç gerektiren bir iş yaptığını yorumlayabiliriz, ancak işçilerin yaptıkları işi çok sevdiğini yorumlayamayız."]},"beginTime":284,"endTime":349,"href":"/video/preview/5721104362756129862?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=284&ask_summarization=1"},{"index":6,"title":"Kroki Okuma","list":{"type":"unordered","items":["Kroki, bir yerin ölçeksiz kabataslak halde kuşbakışı olarak çizilmesiyle oluşan gelişigüzel plandır.","Krokiler bir bölgenin ya da bir mekanın daha kolay bulunması için çizilir.","Verilen krokiye göre eczanenin batısında ve doğusunda park, kuzeyinde binalar ve park, batısında okul olduğunu kolaylıkla bulabiliriz."]},"beginTime":349,"endTime":433,"href":"/video/preview/5721104362756129862?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=349&ask_summarization=1"}],"linkTemplate":"/video/preview/5721104362756129862?parent-reqid=1769825361854080-13662353633503657866-balancer-l7leveler-kubr-yp-klg-5-BAL&text=Graph+The+General+-+Topics&t=%%timestamp%%&ask_summarization=1"},"isAdultDoc":false,"relatedParams":{"text":"8TH grade turkish / table, graph and visual interpretation topic explanation","related_orig_text":"Graph The General - 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