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...

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...

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...

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...

making it an example of a hedgehog. Cardioid – an epicycloid with one cusp Nephroid – an epicycloid with two cusps Deltoid – a hypocycloid with three...

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...

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...

sections Squircle Trifolium Curve Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rose...

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...

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...

geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes...

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...

{sgn} } is the sign function. K means Elliptic integral K(m) Epitrochoid Epicycloid (special case of the epitrochoid) Limaçon (special case of the epitrochoid)...

eigenvalues of some random matrices with cyclic correlations. Cycloid Cyclogon Epicycloid Rosetta (orbit) Apsidal precession Spirograph J. Dennis Lawrence (1972)...

geometry. Dürer's geometric constructions include helices, conchoids and epicycloids. He also draws on Apollonius, and Johannes Werner's Libellus super viginti...

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...

it is of an epicycloid or hypocycloid variety. The classic Spirograph toy traces out these curves. Centered trochoid Cycloid Epicycloid Hypocycloid Spirograph...

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...

Squircle Three-leaved clover Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Hypotrochoid Lissajous curve Poinsot's...

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...

needed] Quintic of l'Hospital Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rational...

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...

cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema, epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid...

treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708. His works on conic sections and epicycloids were based...

(circular arc with constant tooth depth), Klingelnberg Cyclo-Palloid (Epicycloid with constant tooth depth) or Klingelnberg Palloid. The tooth faces in...

z is at a vertex it traces an epicyclogon or a hypocyclogon. Cycloid Epicycloid Hypocycloid Tom M. Apostol, Mamikon Mnatsakanian (2012). New Horizons...

ellipses, which removed the need for Copernicus' epicycles as well. Analemma Epicycloid Occam's razor Overfitting Scientific method Harper, Douglas. "epicycle"...

polygon Tangential quadrilateral Roulettes Centered trochoid Epitrochoid Epicycloid Cardioid Nephroid Deferent and epicycle Hypotrochoid Hypocycloid Astroid...

cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema, epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid...

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...