### Lecture Description

In this video lecture, Prof. N.J. Wildberger talks about the cross ratio.

The cross ratio is the most important invariant in projective geometry, and plays a key role in hyperbolic geometry. We introduce it here using vectors, that is in the framework of affine geometry.

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

### Course Index

- An Invitation to Geometry: The WildTrig Series
- Why Trig is Hard
- Quadrance via Pythagoras and Archimedes
- Spread, Angles and Astronomy
- Five Main Laws of Rational Trigonometry
- Applications of Rational Trigonometry
- Heron's Formula Viewed Rationally
- Solving Triangles With Rational Trigonometry
- Centers of Triangles With Rational Trigonometry
- The Laws of Proportion for a Triangle
- The Laws of Proportion for a Triangle
- Geometry of Circles with Rational Trigonometry
- Applications of Rational Trig to Surveying
- Cartesian Coordinates and Geometry
- Why Spreads are Better than Angles
- Rational Parameters for Circles
- Complex Numbers and Rotations
- Rational Trigonometry Quiz 1
- Rational Trigonometry: Solutions to Quiz 1
- Medians, Altitudes and Vertex Bisectors
- Trigonometry With Finite Fields (I)
- Trigonometry with Finite Fields (II)
- Trigonometry with Finite Fields (III)
- Highlights From Triangle Geometry (I)
- Highlights From Triangle Geometry (II)
- Spread Polynomials
- Pentagons and Five-fold Symmetry
- Applications of Rational Trig to Surveying (II)
- Stewart's Theorem
- What Size Ladder Fits Around a Corner?
- Trisecting Angles and Hadley's Theorem
- Polar Coordinates and Rational Trigonometry
- Introduction to Projective Geometry
- Projective Geometry and Perspective
- Projective Geometry and Homogeneous Coordinates
- Lines and Planes in Projective Geometry
- Affine Geometry and Barycentric Coordinates
- Affine Geometry and Vectors
- The Cross Ratio
- More About the Cross Ratio
- Harmonic Ranges and Pencils
- The Fundamental Theorem of Projective Geometry
- Conics via Projective Geometry
- An Algebraic Framework for Rational Trigonometry (Part I)
- An Algebraic Framework for Rational Trigonometry (Part II)
- How to Learn Mathematics
- Einstein's Special Relativity: An Introduction
- Red Geometry (Part I)
- Red Geometry (Part II)
- Red Geometry (Part III)
- Circles in Red Geometry
- Green Geometry (Part I)
- Green Geometry (Part II)
- Pythagorean Triples
- An Introduction to Chromogeometry
- Chromogeometry and Euler Lines
- Chromogeometry and the Omega Triangle
- Chromogeometry and Nine-point Circles
- Proofs in Chromogeometry
- Triangle Spread Rules
- Triangle Spread Rules in Action
- Acute and Obtuse Triangles
- Proofs of the Triangle Spread Rules
- Rational Trigonometry Quiz #2
- Hints for Solutions to Quiz #2
- The 6-7-8 Triangle
- Barycentric Coordinates and the 6-7-8 Triangle
- Squares in a Pentagon
- Trisecting a Right Triangle
- Euler's Four Point Relation
- What is Geometry Really About?
- Determinants in Geometry (Part I)
- Determinants in Geometry (Part II)

### 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.