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arXiv · 1503.00566

$N$-Division Points of Hypocycloids

Nitya Mani·Simon Rubinstein-Salzedo
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Abstract

We show that the $n$-division points of all rational hypocycloids are constructible with an unmarked straightedge and compass for all integers $n$, given a pre-drawn hypocycloid. We also consider the question of constructibility of $n$-division points of hypocycloids without a pre-drawn hypocycloid in the case of a tricuspoid, concluding that only the $1$, $2$, $3$, and $6$-division points of a tricuspoid are constructible in this manner.

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Nitya Mani, Simon Rubinstein-Salzedo. 2015-02-27. $N$-Division Points of Hypocycloids. https://arxiv.org/abs/1503.00566

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