A Special Hexagon with Two-Fold Symmetry Must Have an Inscribed Square Satisfying the Toeplitz Conjecture

Authors: Prashanth R. Rao

In this paper, we generate a special hexagon with two-fold symmetry by diagonally juxtaposing two squares of different dimensions so that they share exactly one common vertex and their adjacent sides are perpendicular to one another. We connect in specific pairs, the vertices adjacent to common vertex of both squares to generate a hexagon that is symmetrical about a line connecting the unconnected vertices. We show that this special hexagon must have one square whose points lie on its sides. With suitable modifications, it may be possible to use this technique to prove the Toeplitz conjecture for a simple closed curve generated by connecting the same six vertices of this special hexagon.

Comments: 3 Pages.

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Submission history

[v1] 2017-09-10 05:11:19

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