Quadrance and spread | Universal Hyperbolic Geometry 21 | NJ Wildberger скачать в хорошем качестве

Quadrance and spread | Universal Hyperbolic Geometry 21 | NJ Wildberger

This is the first video in the second part of this series on Universal Hyperbolic Geometry (UHG), introducing algebraic definitions of the main metrical concepts: quadrance between points and spread between lines. We first review the basics of Rational Trigonometry (RT) in the Euclidean affine setting, motivating the move to the hyperbolic projective setting. The five main laws of RT are laid out and compared with the four main laws of UHG. Video Contents: 00:00 Metrical notions (over rational numbers!); measurements 03:40 Affine geometry/Projective geometry compared 07:50 Preliminary: Rational Trigonometry in Euclidean Geometry; WildTrig series mentioned 13:31 Further development in the Euclidean affine case; Main laws of Rational Trigonometry; 1st and 2nd most important results in mathematics @16:37 ; the most powerful law among the 5 @18:30 20:02 Trigonometry in Universal Hyperbolic Geometry; In principle one could start the series here; the main definitions 25:45 Main laws of Hyperbolic trigonometry; njwildberger opinion @30:08 31:53 Exercises 21-(1:5) 33:19 Exercises 21-(6:9); right triangle, dual laws; closing motivational remarks @34:28 (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   ************************