WT49: Circles in red geometry

A circle in red geometry looks like a rectangular hyperbola with asymptotes parallel to the lines of slope one and minus one. But in the red setting, such a `red' circle still satisfies many of the properties that we are used to for a circle. So this video shares some of the theorems of WildTrig 10, but in a completely different context.

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
• rational
• trigonometry
• circles
• relativistic
• red
• Thales
• subtended
• spread
• hyperbola
• rectangular
• Wildberger

[bt401010]

Another nice video. Thx.

Am I right in thinking that your method is a way to analogise/synonymise the various conic sections?

*If this is the case, what would be the effect of generalising the circle to that of an ellipse?

[njwildberger]

Thanks. I am not quite sure about your question. One possible direction is that what we did for the red circles (ie certain rectangular hyperbolas) can also be generalized to other conics by considering yet more general quadratic forms. However in each case the corresponding geometry is different. I will be discussing this more advanced subject later on.

[benthurston27]

At first I was thinking the drawback of basing geometry on arithmetic and algebra was because Euclidean geometry is decidable whereas when you add arithmetic by Godel's theorem there are certain undecidable statements that arise. I think maybe it would be interesting if all the strange quantum phenomena boil down to the fact that in the real world some statements can't be proven to be true or false.

[dhanedhar]

where can these geometry be used

[otherchaz]

So when the apple falls in WT45, that event is a circle?