WT53: An introduction to chromogeometry

Chromogeometry is a new three-fold symmetry in planar geometry, that brings together the usual Euclidean geometry (here called `blue') with two relativistic geometries (called `red' and `green'). There are two basic principles: that the three geometries are essentially alike, and that they all fit together to form a harmonious whole.

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

Category:

Science & Technology

Tags:

• Geometry
• chromogeometry
• rational
• trigonometry
• relativistic
• Euclidean
• Wildberger
• blue
• red
• green

[dhirsbrunner2]

Are these quadratic forms translationally and rotationally invariant metrics on RxR, depending on how rotation is defined?

[njwildberger]

Yes that's right. Each quadratic form is translationally invariant. The usual form of rotation belongs to blue geometry, but there are also red and green versions (the physicists call them `Lorentz boosts' and we will later see that the red and green geometries are invariant under respectively red and green rotations.

[ZackMeyer1]

An article about chromogeometry says that it is based on Einstein's Theory of Relativity which is currently under question due to neutrinos being recorded at a speed faster than the speed of light. So, this could all be a load of nonsense.

[kevinsherwinguitar]

You said that "if you stick with angles, chromogeometry is almost invisible." Why does spread so inherently lend itself to chromogeometry?

Thanks,

Kevin

[Toxie207]

Interesting but really unnecessary to speak out all the expressions.