WT54: Chromogeometry and Euler lines

Chromogeometry allows many features of Euclidean geometry to be widely generalized and enriched. Here we look at the classical Euler line of a triangle, passing through the orthocenter, centroid and circumcenter also from two relativistic geometries. Then we combine all three pictures to produce the remarkable Omega triangle.

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
• Wildberger
• chromogeometry
• Omega
• triangle
• Euler
• line
• orthocenter
• centroid
• circumcenter

[njwildberger]

Hi Danodet, It is a nice question. I don't know the answer, but my guess is that there will be red and green analogs. The Descartes circle theorem interests me since it relates to the Triple quad formula (somewhat mysteriously), and also to an extension of that called the Quadruple quad formula, which I write down in WT69: What is geometry really about?

Please investigate if you like, and let us know!

[water0heaven]

Magnificent! 賞心悅目

[IIbikerII]

wow lol thats crazy, thatnk for the vid

[danodet]

Is there a red and a green version of the Descartes' Circle Theorem?