Universal Hyperbolic Geometry A (1-32) by Norman J Wildberger

source: njwildberger     2017年2月1日
Hyperbolic geometry, in this new series, is made simpler, more logical, more general and... more beautiful! The new approach will be called `Universal Hyperbolic Geometry', since it extends the subject in a number of directions. It works over general fields, it extends beyond the usual disk in the Beltrami Klein model, and it unifies hyperbolic and elliptic (and other) geometries.

23:13 0: Introduction
40:38 1: Apollonius and polarity
38:22 2: Apollonius and harmonic conjugates
21:38 3: Pappus' theorem and the cross ratio
37:14 4: First steps in hyperbolic geometry
35:54 5: The circle and Cartesian coordinates
50:38 6: Duality, quadrance and spread in Cartesian coordinates
37:40 7a: The circle and projective homogeneous coordinates
24:17 7b: The circle and projective homogeneous coordinates (cont.)
44:32 8: Computations with homogeneous coordinates
33:11 9: Duality and perpendicularity
44:06 10: Orthocenters exist!
37:28 11: Theorems using perpendicularity
36:20 12: Null points and null lines
26:31 13: Apollonius and polarity revisited
31:23 14: Reflections in hyperbolic geometry
50:29 15: Reflections and projective linear algebra
36:41 16: Midpoints and bisectors
34:09 17: Medians, midlines, centroids and circumcenters
29:35 18: Parallels and the double triangle
42:27 19: The J function, sl(2) and the Jacobi identity
38:44 20: Pure and applied geometry--understanding the continuum
35:54 21: Quadrance and spread
36:14 22: Pythagoras' theorem in Universal Hyperbolic Geometry
39:11 23: The Triple quad formula in Universal Hyperbolic Geometry
34:34 24: Visualizing quadrance with circles
25:22 25: Geometer's Sketchpad and circles in Universal Hyperbolic Geometry
20:20 26: Trigonometric laws in hyperbolic geometry using Geometer's Sketchpad
24:21 27: The Spread law in Universal Hyperbolic Geometry
35:26 28: The Cross law in Universal Hyperbolic Geometry
42:35 29: Thales' theorem, right triangles and Napier's rules
32:46 30: Isosceles triangles in hyperbolic geometry
42:05 31: Menelaus, Ceva and the Laws of proportion
35:47 32: Trigonometric dual laws and the Parallax formula