У нас вы можете посмотреть бесплатно Apollonius and polarity | Universal Hyperbolic Geometry 1 | NJ Wildberger или скачать в максимальном доступном качестве, видео которое было загружено на ютуб. Для загрузки выберите вариант из формы ниже:
Если кнопки скачивания не
загрузились
НАЖМИТЕ ЗДЕСЬ или обновите страницу
Если возникают проблемы со скачиванием видео, пожалуйста напишите в поддержку по адресу внизу
страницы.
Спасибо за использование сервиса ClipSaver.ru
This is the start of a new course on hyperbolic geometry that features a revolutionary simplifed approach to the subject, framing it in terms of classical projective geometry and the study of a distinguished circle. This subject will be called Universal Hyperbolic Geometry, as it extends the subject to arbitrary fields, as well as to the outside of the light cone/null circle. We begin by going back to Apollonius of Perga (in present day Turkey, not Italy!) and his understanding of the crucial role of polarity in studying conics, in particular the circle. Given a fixed circle, to each point in the plane we associate a line called the polar, and conversely to a line we associated a point called its pole. This duality is all important for hyperbolic geometry CONTENT SUMMARY: conics @00:00 the circle @5:00 Thales thm @05:20 Greek m'ment @06:20 polarity, pole of A and polar of a @09:06 def' of polarity (projective def') @14:40 Polar independence Theorem @19:13 projective def' of polarity @23:34 polar of a point inside the circle @25:10 3-way symetry @26:40 hands_on experience @27:52 pole, polar starting with four points on circle @29:12 Quadrangle and quadralateral @29:26 Polar duality thm @31:30 The distinguished circle @37:40 Pole of a line thm @38:00 (THANKS to EmptySpaceEnterprise) ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at / njwildberger Your support would be much appreciated. Here are the Insights into Mathematics Playlists: • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист Here are the Wild Egg Maths Playlists (some available only to Members!) • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист • Плейлист ************************