ON THE OUTLINES OF PLANE CURVES OF THE FORM $(ax)^{\alpha}+(by)^{\alpha}=r^{\alpha}$ WITH $\alpha>0$
Print ISSN: 2319-1023 | Online ISSN: 2582-5461 | Total Downloads : 99
DOI:
Author :
Norihiro Someyama (Shin-yo-ji Buddhist Temple, 5-44-4 Minamisenju, Arakawa-ku, Tokyo 116-0003 JAPAN)
Abstract
We consider plane curves of the form $(ax)^{\alpha}+(by)^{\alpha}=r^{\alpha}$ defined on the first quadrant of $\mathbb R^2$, where $\alpha>0$ and $a,b,r>0$. We summarize the outlines of them by using elementary differential calculus. We will in this note understand that they are classified into three types of curves, convex, straight and concave, depending on $\alpha$.
Keywords and Phrases
Plane curve, implicit function, orthogonal representation, polar representation, differential calculus, area, integral.
A.M.S. subject classification
14H50, 26B10.
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