# Rational Trigonometry

### Course Description

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.

Prof. N.J. Wildberger Lecture 37: Affine Geometry and Vectors.
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### Video Lectures & Study Materials

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