In geometry, an epicycloid (also called hypercycloid) is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called...
7 KB (964 words) - 07:02, 30 May 2024
the epitrochoid.) Special cases include the limaçon with R = r and the epicycloid with d = r. The classic Spirograph toy traces out epitrochoid and hypotrochoid...
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x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} . The special cases of the epicycloid and hypocycloid, generated by tracing the locus of a point on the perimeter...
6 KB (1,028 words) - 23:51, 5 April 2024
reducing friction and wear). Their gear tooth profile is based on the epicycloid and hypocycloid curves, which are the curves generated by a circle rolling...
7 KB (897 words) - 21:25, 8 May 2024
nephros) 'kidney-shaped') is a specific plane curve. It is a type of epicycloid in which the smaller circle's radius differs from the larger one by a...
14 KB (2,934 words) - 20:07, 11 July 2023
fixed, then a point on the pitch circle of the planet gear traces an epicycloid curve. An epicyclic gear train can be assembled so the planet gear rolls...
36 KB (5,301 words) - 09:59, 10 July 2024
making it an example of a hedgehog. Cardioid – an epicycloid with one cusp Nephroid – an epicycloid with two cusps Deltoid – a hypocycloid with three...
8 KB (1,157 words) - 22:57, 29 January 2024
geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes...
8 KB (826 words) - 07:31, 24 May 2024
it is of an epicycloid or hypocycloid variety. The classic Spirograph toy traces out these curves. Centered trochoid Cycloid Epicycloid Hypocycloid Spirograph...
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around a fixed circle of the same radius. It can also be defined as an epicycloid having a single cusp. It is also a type of sinusoidal spiral, and an inverse...
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eigenvalues of some random matrices with cyclic correlations. Cycloid Cyclogon Epicycloid Rosetta (orbit) Apsidal precession Spirograph J. Dennis Lawrence (1972)...
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Construction of a two-lobed cycloidal rotor. The red curve is an epicycloid and the blue curve is a hypocycloid. The smaller generating circles (red and...
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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 with k+1 cusps. The evolute of a...
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which a circle rolls on the inside of another circle instead of a line. Epicycloid: variant of a cycloid in which a circle rolls on the outside of another...
26 KB (3,771 words) - 22:19, 30 June 2024
sections Squircle Trifolium Curve Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rose...
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geometry. Dürer's geometric constructions include helices, conchoids and epicycloids. He also draws on Apollonius, and Johannes Werner's Libellus super viginti...
72 KB (8,319 words) - 20:01, 21 August 2024
Squircle Three-leaved clover Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Hypotrochoid Lissajous curve Poinsot's...
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positive integer, the central region in each of these sets is always an epicycloid of ( d − 1 ) {\displaystyle (d-1)} cusps. A similar development with negative...
57 KB (7,526 words) - 02:19, 18 August 2024
needed] Quintic of l'Hospital Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rational...
47 KB (3,580 words) - 17:01, 29 June 2024
{sgn} } is the sign function. K means Elliptic integral K(m) Epitrochoid Epicycloid (special case of the epitrochoid) Limaçon (special case of the epitrochoid)...
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and this value serves as a parameter for the movement of the "trunk". Epicycloid Curve fitting Dyson, Freeman (January 22, 2004). "A meeting with Enrico...
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been described. The best-known of these is the cardioid, which is an epicycloid with one cusp; though as the cardioid lacks the point, it may be seen...
28 KB (3,161 words) - 04:15, 13 August 2024
cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema, epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid...
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(circular arc with constant tooth depth), Klingelnberg Cyclo-Palloid (Epicycloid with constant tooth depth) or Klingelnberg Palloid. The tooth faces in...
83 KB (11,268 words) - 00:35, 21 August 2024
ellipses, which removed the need for Copernicus' epicycles as well. Analemma Epicycloid Occam's razor Overfitting Scientific method Harper, Douglas. "epicycle"...
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treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708. His works on conic sections and epicycloids were based...
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cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema, epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid...
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z is at a vertex it traces an epicyclogon or a hypocyclogon. Cycloid Epicycloid Hypocycloid Tom M. Apostol, Mamikon Mnatsakanian (2012). New Horizons...
5 KB (394 words) - 19:08, 11 September 2023
π r 2 {\displaystyle A=(k+1)(k+2)\pi r^{2}} where A is the area of an epicycloid with the smaller circle of radius r and the larger circle of radius kr...
37 KB (7,868 words) - 14:06, 26 August 2024
these associated curves of the parabola, the logarithmic spiral and epicycloids around 1692. The lemniscate of Bernoulli was first conceived by Jacob...
19 KB (2,181 words) - 02:51, 20 June 2024