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N-Division Points of Hypocycloids

N-Division Points of Hypocycloids 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Arnold Mathematical Journal Springer Journals

N-Division Points of Hypocycloids

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References (6)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Institute for Mathematical Sciences (IMS), Stony Brook University, NY
Subject
Mathematics; Mathematics, general
ISSN
2199-6792
eISSN
2199-6806
DOI
10.1007/s40598-015-0034-2
Publisher site
See Article on Publisher Site

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.

Journal

Arnold Mathematical Journal – Springer Journals

Published: Jan 4, 2016

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