An Inverse Method of the Natural Setting for Integer, Half-integer and Rational "Perfect" Hypocycloids

Zarema Seidametova, Valerii Temnenko

2020

Abstract

The paper describes a family of remarkable curves (integer and half-integer hypocycloids and rational perfect hypocycloids) given in an inverse-natural form using a simple trigonometric relation s=s(χ), where s is the arc coordinate and χ is the angle defining the direction of the tangent. In the paper we presented all perfect hypocycloids with the number of cusps ν≤10. From designing the hypocycloid using inverse natural setting easy to determine the number of cusps and find the values of the λm parameter, corresponding to perfect hypocycloids.

Paper Citation

in Harvard Style

Seidametova Z. and Temnenko V. (2020). An Inverse Method of the Natural Setting for Integer, Half-integer and Rational "Perfect" Hypocycloids. In Proceedings of the 1st Symposium on Advances in Educational Technology - Volume 2: AET, ISBN 978-989-758-558-6, pages 584-589. DOI: 10.5220/0011009700003364

in Bibtex Style

@conference{aet20,
author={Zarema Seidametova and Valerii Temnenko},
title={An Inverse Method of the Natural Setting for Integer, Half-integer and Rational "Perfect" Hypocycloids},
booktitle={Proceedings of the 1st Symposium on Advances in Educational Technology - Volume 2: AET,},
year={2020},
pages={584-589},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0011009700003364},
isbn={978-989-758-558-6},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 1st Symposium on Advances in Educational Technology - Volume 2: AET,
TI - An Inverse Method of the Natural Setting for Integer, Half-integer and Rational "Perfect" Hypocycloids
SN - 978-989-758-558-6
AU - Seidametova Z.
AU - Temnenko V.
PY - 2020
SP - 584
EP - 589
DO - 10.5220/0011009700003364