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

Zarema Seidametova, Valerii Temnenko

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.

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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