Pythagoras meets Jordan

Geometry Level 4

True or False?

If $C$ is any Jordan curve and $P$ is any point on $C$ , then there exist points $Q,R$ on $C$ such that the triangle $PQR$ has a right angle at $P$ .

False An open problem True

1 solution

Otto Bretscher
Dec 2, 2018

As a simple counterexample, consider an equilateral triangle $C$ , and make $P$ one of its vertices. Thus the statement is $\boxed{\text{False}}$ .

Why should I consider an equilateral triangle? I can simply pick three points on the Jordan curve and arrange any right triangle with the right angle at the point P.

Oleg Yovanovich

Oleg Yovanovich - 2 years, 4 months ago

My point is that you cannot always do that. I'm using an equilateral triangle as a counterexample.

Otto Bretscher - 2 years, 4 months ago

Pythagoras meets Jordan

1 solution

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