    1. Parallel Lines Push the infinite into the finite 2. Triangle Move it to infinity 3. Triangle and Inscribed Angle (07/06/25) Not constant, Absolute unit length (1) 4. Model Make a disk model, Open and closed 5. Disk and Hyperboloid Interchangeable relations 6. Equivalent Deformation, Comparison with Elliptic Geometry (1) (07/04/14) Locus of vertex of a triangle 7. Parallel Angle What is it? 8. Lobachevsky's Postulate (07/07/19) How was it found? Can we draw infinity? 9. Distance and Angle, Hyperbolic Trigonomery (07/06/22) Dependent relations, Absolute unit length (2) 10. Equidistant Lines (1) How does it look?  Parallel curves 11. Ultraparallel Lines Common perpendicular 12. Tiling (tessellation) (07/05/01) Reflection, Ideal triangle 13. Parallel Translation (1) Get locus by reflection 14. Circle Cutting hemisphere 15. Move Circle Toward infinity 16. Extending Disk Model (07/07/02) To get real hyperbolic plane 17. Horocycle (1) Hemisphere, Translation, Equidistant lines (2) 18. Pseudo-sphere (1) Is hyperbolic surface realized? 19. Upper Half-plane (1) Relation with Poincare's disk, Digitized model 20. Horocycle (2) Poincare's disk, Upper Half-plane (2) 21. Metric, Break Pythagorean Theorem (07/06/13) Riemann, Mercator, Pseudo-sphere (2) 22. Mutual Relations among Models Ray and chain 5 models 23. Curvature (1) Osculating circle, Curvature of pseudosphere (1) 24. Curvature (2) What happens if curvature changes? 25. Gauss-Bonnet Theorem Curvature of pseudosphere (2) 26. Touchable Model (07/06/20) Paper craft of true hyperbolic plane 27. H(+) Plane and Euclidean Plane Visual comparison under unchanged length 28. Analytic Curve Lambert's quardrangle 29. Hyperbolic Function Source, Hyperbolic angle, Definition of logarithm 30. Inversion and Infinity (under construction) What is the end of hyperbola? 31. Upper Half-plane (4) (under construction) Can we come to Eucledean plane without jump? 32. Right Angled Polygon (07/03/29) Infinite polygon 33. Dodecahedron 3-D tiling 34. Ideal Tetrahedron 3-D tiling 35. Projective Geometry (1) Camera shot, Mobius strip 36. Mobius Strip (1) If twisted? 37. Mobius Strip (2) 38. Projective Geometry (2) Quadratic curve 39. Crosscap (1) Can Mobius strip be covered with a disk? 40. Crosscap (2) Mobius strip and a disk as projective planes 41. Crosscap (3) (06/06/08) Correspondence between Cross-cap and Mobius strip 42. Klein Bottle & Projective plane (06/06/27) We cut and see their true colors. 43. Paper craft (06/08/13) Cross-cap and twist 44. Projective Geometry (3) Cross ratio (1), the Origin of model, Make Klein's disk 45. Projective Geometry (4) Real and Imaginary sphere, Hyperboloid 46. Projective/Mobius Trans (under construction) How do they change? 47. Projective Geometry (5) (under construction) Principle of continuity, Erlangen Programme, Cross ratio (2) 48. Conclusion for Part 2 (under construction) 49. Figure-8 knot (1) (under construction) topology 50. Figure-8 knot (2) (under construction) Ultra sphere 51. Figure-8 knot (3) (under construction) Formula of complement 52. Figure-8 knot (4) (under construction) tetrahedron 53. Figure-8 knot (5) (under construction) Hyperbolization (Gometrization) 54. Figure-8 knot (6) (under construction) Where has the knot gone? 55. Figure-8 knot (7) (under construction) horosphere 56. Summary (under construction)

Ending Notes
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