双曲几何(universal hyperbolic geometry)学习笔记 更新中

Link: https://www.youtube.com/playlist?list=PL6ACFCC19EA82CA71

List

  1. Intro
  2. Apollonius and polarity

Introduction

  • Distance and Angle not good for understanding hyperbolic geometry
  • new story: Apollonius.. conics… polarity… Minkowski… rational trigonometry
  • Quadrance+Spread.png
  • hyperbolic triangle geometry becomes a new vibrant subject

Apollonius and polarity

  • connection/duality between point and line
  • a is the pole of A
  • A is the polar of a
Perp.png
  • polar independence theorem : the polar A does not depend on the choice of lines thru a
  • polar duality theorem : if a lies on b perp, then b lies on a perp, vice versa
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