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epicycloid

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epicycloid
epicycloid (ɛpɪˈsaɪklɔɪd) [f. epicycle + -oid.] A curve generated by a point in the circumference of a moveable circle, which revolves on that of a fixed circle; in accurate phraseology the term is now limited to the case in which the moveable circle rolls on the exterior of the other (formerly exte... Oxford English Dictionary
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Epitrochoid
Special cases include the limaçon with and the epicycloid with . The classic Spirograph toy traces out epitrochoid and hypotrochoid curves. See also Cycloid Cyclogon Epicycloid Hypocycloid Hypotrochoid Spirograph List of periodic functions Rosetta (orbit) Apsidal precession References wikipedia.org
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epitrochoid
epitrochoid Math. (ɛpɪˈtrɒkɔɪd) [f. Gr. ἐπί upon + τροχός wheel + -oid; after analogy of epicycloid.] The curve described by a point rigidly connected with the centre of a circle which rolls on the outside of another circle. Cf. epicycloid.1843 Penny Cycl. XXV. 284/2. 1879 Thomson & Tait Nat. Phil. ... Oxford English Dictionary
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Hypocycloid
Thanks to this result, one can use the fact that SU(k) fits inside SU(k+1) as a subgroup to prove that an epicycloid with k cusps moves snugly inside one See also Roulette (curve) Special cases: Tusi couple, Astroid, Deltoid List of periodic functions Cyclogon Epicycloid Hypotrochoid Epitrochoid wikipedia.org
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Epicycloid: How do I get the characteristic equation given a picture and specific points I am simulating a process and the resulting line has the shape of an epicyloid. the epicycloid- like shape of the line For my n...
You are talking about prolate epicycloid.
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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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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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Hypotrochoid
Hypotrochoids describe the support of the eigenvalues of some random matrices with cyclic correlations See also Cycloid Cyclogon Epicycloid Rosetta wikipedia.org
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epicycloidal
epicycloidal, a. (ˌɛpɪsaɪˈklɔɪdəl) [f. prec. + -al1.] Of the form or nature of an epicycloid.1812 Woodhouse Astron. xvi. 172 The true pole..will describe an epicycloidal curve. 1837 Whewell Hist. Induct. Sc. iii. iv. §3 I. 205 The epicycloidal form of her orbit. 1884 F. J. Britten Watch & Clockm. 29... Oxford English Dictionary
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Trochoid
The special cases of the epicycloid and hypocycloid, generated by tracing the locus of a point on the perimeter of a circle of radius while it is rolled wikipedia.org
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Arc length of epicycloid when small radius goes to 0 So I've been working out on epicycloids and I got the arc length formula, let's say for a lap around the big circumference. Big radius is $R$ and small radius going...
At the same time, we can look at the area enclosed, which I believe to be $A=\pi m(m-b)$, we see that area of the epicycloid approaches that of the circle
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دويري فوقي
الدويريّ الفوقي أو الدحروج الفوقي (Epicycloid) هو منحنى ترسمه نقطة من محيط دائرة متحرّكة تتدحرج دون انزلاق على دائرة ثابتة. wikipedia.org
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Determining coefficients of a parametrization of an epicycloid given a predefined arc length. I am trying to determine the coefficient q in the parametrization of a epicycloid which gives me the arc length of 4.25. Th...
If you actually evaluate the function you're trying to mess with, suing something like this: x = -8:.01:8; s = numel(x); y = zeros(s, 1); for i = 1:s y(i) = fun2(x(i)); end plot(x, y); then your resulting plot looks like this: ![enter image description here]( That plot pretty much tells you why you ...
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Von Neumann's elephant
See also Epicycloid Curve fitting References External links "Fitting an Elephant" at the Wolfram Demonstrations Project site Curves Recreational wikipedia.org
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摆线
更进一步，如果我们让圆也沿着一个圆滚动而不是直线的话，我们会得到外摆线（epicycloid，沿着圆的外部运动，定点在圆的边缘），内摆线（hypocycloid，沿着圆内部滚动，定点在圆的边缘）以及外旋轮线（epitrochoid）和内旋轮线（hypotrochoid，定点可以在圆内的任一点包括边界。 wikipedia.org
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