Home » Subject » Topology
Importance: Medium ✭✭
Author(s): Toeplitz
Subject: Topology
Keywords: simple closed curve
square
Recomm. for undergrads: no
Posted by: dlh12
on: April 10th, 2008
Conjecture   Does every Jordan curve have 4 points on it which form the vertices of a square?

A Jordan curve is a continuous function $ f $ from the closed interval $ [0,1] $ to the plane $ \mathbb{R}^{2} $ with the properties that $ f $ is injective on the half-open interval $ [0,1) $ (i.e., $ f $ is simple) and $ f(0)=f(1) $ (i.e., $ f $ is closed).

Bibliography

[M] Meyerson, M.D., Equilateral triangles and continuous curves, Fund. Math. 110, (1980), 1--9.


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