In this video lecture, Prof. N.J. Wildberger provides a few thoughts on how to learn mathematics, that should also be relevant for this course in Rational Trigonometry and Geometry. The basic idea: 'Mathematics is a landscape'. So learning mathematics is not that different from becoming knowledgable about an unfamiliar city or terrain. This is a short break from our usual thread of rational trigonometry.

This video is part of the WildTrig series, which introduces Rational Trigonometry and applies it to many different aspects of geometry.

1. An Invitation to Geometry: The WildTrig Series
2. Why Trig is Hard
3. Quadrance via Pythagoras and Archimedes
4. Spread, Angles and Astronomy
5. Five Main Laws of Rational Trigonometry
6. Applications of Rational Trigonometry
7. Heron's Formula Viewed Rationally
8. Solving Triangles With Rational Trigonometry
9. Centers of Triangles With Rational Trigonometry
10. The Laws of Proportion for a Triangle
11. The Laws of Proportion for a Triangle
12. Geometry of Circles with Rational Trigonometry
13. Applications of Rational Trig to Surveying
14. Cartesian Coordinates and Geometry
15. Why Spreads are Better than Angles
16. Rational Parameters for Circles
17. Complex Numbers and Rotations
18. Rational Trigonometry Quiz 1
19. Rational Trigonometry: Solutions to Quiz 1
20. Medians, Altitudes and Vertex Bisectors
21. Trigonometry With Finite Fields (I)
22. Trigonometry with Finite Fields (II)
23. Trigonometry with Finite Fields (III)
24. Highlights From Triangle Geometry (I)
25. Highlights From Triangle Geometry (II)
26. Spread Polynomials
27. Pentagons and Five-fold Symmetry
28. Applications of Rational Trig to Surveying (II)
29. Stewart's Theorem
30. What Size Ladder Fits Around a Corner?
31. Trisecting Angles and Hadley's Theorem
32. Polar Coordinates and Rational Trigonometry
33. Introduction to Projective Geometry
34. Projective Geometry and Perspective
35. Projective Geometry and Homogeneous Coordinates
36. Lines and Planes in Projective Geometry
37. Affine Geometry and Barycentric Coordinates
38. Affine Geometry and Vectors
39. The Cross Ratio
40. More About the Cross Ratio
41. Harmonic Ranges and Pencils
42. The Fundamental Theorem of Projective Geometry
43. Conics via Projective Geometry
44. An Algebraic Framework for Rational Trigonometry (Part I)
45. An Algebraic Framework for Rational Trigonometry (Part II)
46. How to Learn Mathematics
47. Einstein's Special Relativity: An Introduction
48. Red Geometry (Part I)
49. Red Geometry (Part II)
50. Red Geometry (Part III)
51. Circles in Red Geometry
52. Green Geometry (Part I)
53. Green Geometry (Part II)
54. Pythagorean Triples
55. An Introduction to Chromogeometry
56. Chromogeometry and Euler Lines
57. Chromogeometry and the Omega Triangle
58. Chromogeometry and Nine-point Circles
59. Proofs in Chromogeometry
60. Triangle Spread Rules
61. Triangle Spread Rules in Action
62. Acute and Obtuse Triangles
63. Proofs of the Triangle Spread Rules
64. Rational Trigonometry Quiz #2
65. Hints for Solutions to Quiz #2
66. The 6-7-8 Triangle
67. Barycentric Coordinates and the 6-7-8 Triangle
68. Squares in a Pentagon
69. Trisecting a Right Triangle
70. Euler's Four Point Relation
71. What is Geometry Really About?
72. Determinants in Geometry (Part I)
73. Determinants in Geometry (Part II)

In this course, Prof. N.J. Wildberger gives 72 video lectures on Rational Trigonometry.

This video series on Rational Trigonometry (RT) and related geometry presents a much needed alternative to the traditional tedious and painful subject of trigonometry, which alienates millions of students each year from mathematics. By dispensing with transcendental notions, circular functions and square roots, this new theory gives simpler, faster and more accurate ways to solve a wide variety of engineering, surveying, physics and geometry problems, essentially only with high school algebra (that's right, calculators or trig tables are not required). RT is also a much more satisfying and logical way to introduce young people to the beauty and elegance of geometry, and teaches them that mathematics should, first and foremost, always make sense. Prepare to depart on a modern adventure, in the spirit of the ancient Greeks! Assoc Prof N J Wildberger is the author of the first book on this subject, 'Divine Proportions: Rational Trigonometry to Universal Geometry'. He is also and innovative and highly regarded teacher in the School of Mathematics and Statistics at UNSW.