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!) ************ Research Gate page: https://www.researchgate.net/profile/... Blog: http://njwildberger.com/ Online courses at openlearning.com (currently Algebraic Calculus One): https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! Patreon:   / njwildberger   Your support would be much appreciated. Wild Egg Maths YT channel: https://www.youtube.com/channel/UCriF... Insights into Mathematics Playlists:    • The Algebra of Boole, Logic and Circuit An...   (31 videos)    • Box Arithmetic: a new framework for Mathem...   (18 videos)    • Hypergroups and Diffusion Symmetry: an int...   (6 videos)    • Rational Trigonometry for maths, physics a...   (4 videos)    • Sociology and Pure Maths   (44 videos)    • Old Babylonian mathematics and Plimpton 322   (8 videos)    • Math Foundations   (226 videos)    • Math Seminars N J Wildberger   (26 videos)    • Math History (ancient to modern)   (45 videos)    • Geometric Linear Algebra   (43 videos)    • Algebraic Topology   (40 videos)    • Universal Hyperbolic Geometry   (55 videos)    • Differential Geometry   (34 videos)    • Elementary Probability and Statistics   (8 videos)    • Math Terminology for Incoming Uni Students   (9 videos)    • Famous Math Problems   ( 46 videos)    • Elementary Mathematics Explained (K-6)   (40 videos)    • Ancient Mathematics and insights of Howard...   (7 videos)    • Wild West Banking: A mathematician goes We...   (7 videos)    • Playing Go: the ancient oriental board game   (19 videos)    • Maths and Music   (21 videos)    • Year 9 Mathematics (review fractions, deci...   (10 videos)    • Wild Trig: An introduction to Rational Tri...   (94 videos) Wild Egg Maths Playlists:    • Intro to Algebraic Calculus with Box Arith...   (4 videos)    • Classical to Quantum (for Members)   (64 videos)    • Solving Polynomial Equations and the Geode...   (45 videos)    • De Casteljau Bezier curves and associated ...   (20 videos)    • Exploring q-series (for Members)   (8 videos)    • Six: A mathematical exploration   (9 videos)    • Algebraic Calculus One: a new foundation f...   (52 videos)    • Advice to prospective research mathematici...   (9 videos)