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hypocycloid

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hypocycloid
hypocycloid Geom. (hɪpəʊ-, haɪpəʊˈsaɪklɔɪd) [f. hypo- 2 + cycloid. Cf. F. hypocycloïde.] A curve traced by a point in the circumference of a circle which rolls round the interior circumference of another circle (cf. epicycloid).1843 [see hypotrochoid]. 1854 Moseley Astron. lxi. (ed. 4) 183 This curv... Oxford English Dictionary
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Hypocycloid
The area enclosed by a hypocycloid is given by: The arc length of a hypocycloid is given by: Examples The hypocycloid is a special kind of hypotrochoid The pedal of a hypocycloid with pole at the center of the hypocycloid is a rose curve. The isoptic of a hypocycloid is a hypocycloid. wikipedia.org
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Hypotrochoid
Special cases include the hypocycloid with and the ellipse with and . The eccentricity of the ellipse is becoming 1 when (see Tusi couple). correlations See also Cycloid Cyclogon Epicycloid Rosetta (orbit) Apsidal precession Spirograph References External links Flash Animation of Hypocycloid wikipedia.org
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Another method of finding area of hypocycloids I was finding the are the of hypocycloids. Then it struck me that apart from integration, there could be another method of finding the area of the hypocycloid with differ...
I think you assume that hypocycloids consist of circle arcs, but this is not the case: Consider e.g. the Astroid: ![]( It is an algebraic curve of degree 6, defined by $$ (x^2+y^2-a^2)^3+27a^2x^2y^2=0 $$ which is nowhere close to circle. To come back to your example: The Deltoid is defined by this e...
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Calculate the length of the portion of the hypocycloid $x^{\frac{2}{3}}+y^{\frac{2}{3}}=1$ Calculate the length of the portion of the hypocycloid $x^{\frac{2}{3}}+y^{\frac{2}{3}}=1$ in the first quadrant from the poin...
Formula for arc length is $$L=\int_{\frac18}^1\sqrt{1+\left(y'\right)^2}dx$$ It is easy to find the derivative: $$y'=-\frac{\sqrt{1-x^{\frac23}}}{x^\frac13}$$ The length is now: $$\begin{align}L&=\int_{\frac18}^1\sqrt{1+\left(-\frac{\sqrt{1-x^{\frac23}}}{x^\frac13}\right)^2}dx\\\&=\int_{\frac18}^1x^...
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Cyclocycloid
And r can be positive or negative depending on whether it is of an Epicycloid or Hypocycloid variety. See also Centered trochoid Cycloid Epicycloid Hypocycloid Spirograph External links Plane curves wikipedia.org
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Plotting an animated hypocycloid I want to animate a Hypocycloid using computer code. So far i have drawn the circles here. I have found this definition on wikipedia and I want to animate the image that is on the rig...
You misunderstand the meaning of $x(\theta)$. The parentheses do not indicate multiplication; they instead indicate that $x$ is a **function** of the parameter $\theta$. To plot this curve for a given $R$, $r$, and $k$, all you need to do is plug in various values of $\theta$ into each equation on t...
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Epitrochoid
See also Cycloid Cyclogon Epicycloid Hypocycloid Hypotrochoid Spirograph List of periodic functions Rosetta (orbit) Apsidal precession References wikipedia.org
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Superellipse
See also Astroid, the superellipse with n =  and a = b, is a hypocycloid with four cusps. Deltoid curve, the hypocycloid of three cusps. wikipedia.org
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English to Chinese Dictionary - Meaning of Hypocycloid in Chinese is ...
Hypocycloid: Chinese Meaning: 摆线, 内摆线 a line generated by a point on a circle that rolls around inside another circle / A curve traced by a point in the circumference of a circle which rolls on the concave side in the fixed circle.
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astroid
astroid, a. and n. (ˈæstrɔɪd) [f. Gr. ἀστροειδής star-like, f. ἀστήρ star: see -oid.] A. adj. Star-shaped, star-like (cf. asteroid a.).1909 in Webster. B. n. Geom. A hypocycloid with four cusps.1897 H. Lamb Infinit. Calculus ix. §138 The ‘four-cusped hypocycloid’..is sometimes called the ‘astroid’. Oxford English Dictionary
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Deltoid
to: The deltoid muscle, a muscle in the shoulder Kite (geometry), also known as a deltoid, a type of quadrilateral A deltoid curve, a three-cusped hypocycloid wikipedia.org
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内旋轮线
外部链接 Flash Animation of Hypocycloid（内旋轮线的Flash动画，英文） 曲线 de:Zykloide#Epi- und Hypozykloide ja:トロコイド#内トロコイド wikipedia.org
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عجلي تحتي
على دويري تحتي عندما R = 2r نحصل على قطع ناقص انظر أيضًا عجلي فوقي عجلي دويري دويري تحتي دويري فوقي المراجع وصلات خارجية Flash Animation of Hypocycloid wikipedia.org
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hixuco/VanvaSpiralScreensaver - GitHub
A screensaver of Hypocycloid, i call it Vanva screensaver - GitHub - hixuco/VanvaSpiralScreensaver: A screensaver of Hypocycloid, i call it Vanva screensaver
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