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Plane curve traced by a point on a circle rolled around another circle
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
Epicycloid
Toothed gear based on epicycloids and hypocycloids
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
Cycloid_gear
Three-shaft planetary gearset
fixed, then a point on the pitch circle of the planet gear traces an epicycloid curve. An epicyclic gear train can be assembled so that the planet gear
Epicyclic_gearing
Plane curve formed by rolling a circle on the outside of another
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
Epitrochoid
Type of plane curve
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
Cardioid
Plane curve; an epicycloid with radii differing by 1/2
νεφρός (nephrós) 'kidney') 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
Nephroid
Curve traced by a circle rolling along a line
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
Trochoid
Symbol representing the heart
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
Heart_symbol
Curve traced by a point on a circle rolling within another circle
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
Hypocycloid
Curve traced by a point on a rolling circle
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
Cycloid
Fractal named after mathematician Benoit Mandelbrot
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
Mandelbrot_set
Mathematical curves generated by rolling other curves together
curves, a roulette is a kind of kinematic curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes
Roulette_(curve)
Curve generated by rolling a circle inside another circle with 4x or (4/3)x the radius
of a hedgehog. Cardioid – an epicycloid with one cusp Deltoid – a hypocycloid with three cusps Nephroid – an epicycloid with two cusps Spirograph Stoner–Wohlfarth
Astroid
it is of an epicycloid or hypocycloid variety. The classic Spirograph toy traces out these curves. Centered trochoid Cycloid Epicycloid Hypocycloid Spirograph
Cyclocycloid
German artist and theorist (1471–1528)
geometry. Dürer's geometric constructions include helices, conchoids and epicycloids. He also draws on Apollonius, and Johannes Werner's Libellus super viginti
Albrecht_Dürer
Curve traced by a point outside a circle rolling within another circle
eigenvalues of some random matrices with cyclic correlations. Cycloid Cyclogon Epicycloid Rosetta (orbit) Apsidal precession Spirograph J. Dennis Lawrence (1972)
Hypotrochoid
Positive-displacement lobe pump
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
Roots_blower
sections Squircle Trifolium curve Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rose
Gallery_of_curves
REACTION, L'HOSPITAL QUINTIC Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Lissajous curve Poinsot's spirals Rational
List_of_mathematical_shapes
Rotating circular machine part with teeth that mesh with another toothed part
(circular arc with constant tooth depth), Klingelnberg Cyclo-Palloid (Epicycloid with constant tooth depth) or Klingelnberg Palloid. The tooth faces in
Gear
Squircle Three-leaved clover Astroid Atriphtaloid Nephroid Quadrifolium Epicycloid Epispiral Epitrochoid Hypocycloid Hypotrochoid Lissajous curve Poinsot's
List_of_curves
{sgn} } is the sign function. K means Elliptic integral K(m) Epitrochoid Epicycloid (special case of the epitrochoid) Limaçon (special case of the epitrochoid)
List_of_periodic_functions
Problem in recreational mathematics
non-linearities) are inevitably too broad to be of any practical use. Epicycloid Curve fitting Dyson, Freeman (January 22, 2004). "A meeting with Enrico
Von_Neumann's_elephant
Swiss mathematician (1655–1705)
these associated curves of the parabola, the logarithmic spiral and epicycloids around 1692. The lemniscate of Bernoulli was first conceived by Jacob
Jacob_Bernoulli
All Latin and Greek roots beginning with G
cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema, epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid
List of Greek and Latin roots in English/A–G
List_of_Greek_and_Latin_roots_in_English/A–G
Uses of the constant
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
List_of_formulae_involving_π
Curve traced by a vertex of a polygon as it rolls
z is at a vertex it traces an epicyclogon or a hypocyclogon. Cycloid Epicycloid Hypocycloid Tom M. Apostol, Mamikon Mnatsakanian (2012). New Horizons
Cyclogon
Epitrochoid – Plane curve formed by rolling a circle on the outside of another Epicycloid – Plane curve traced by a point on a circle rolled around another circle
List_of_circle_topics
Planetary motions in archaic models of the Solar System
ellipses, which removed the need for Copernicus' epicycles as well. Analemma Epicycloid Occam's razor Overfitting Scientific method Harper, Douglas. "epicycle"
Deferent_and_epicycle
Guidance of sperm
path, followed by a period of straight swimming, leading to the observed epicycloid-like movements directed towards the chemoattractant source. The particular
Sperm_chemotaxis
French painter and architect (1640–1718)
treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708. His works on conic sections and epicycloids were based
Philippe_de_La_Hire
All Latin and Greek roots beginning with C
cyclone, cyclops, cyclosis, cyclotomic, dicyclic, eccyclema, epicycle, epicycloid, hemicycle, hemicyclium, heterocyclic, homocyclic, hypercycle, hypocycloid
List of Greek and Latin roots in English/C
List_of_Greek_and_Latin_roots_in_English/C
French mathematician
series. In 1706, he wrote a work on roulettes, particularly spherical epicycloids. In 1729 and 1731, he published memoirs on Newton's essay on curves of
François_Nicole
formal purity of genres, and concentration of meaning. Hauser uses an epicycloid to express the effect of modernist patterns on postmodern patterns. Postmodern
Michael_Hauser
Biological process
path, followed by a period of straight swimming, leading to the observed epicycloid-like movements directed towards the chemoattractant source. The molecular
Sperm_guidance
EPICYCLOID
EPICYCLOID
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Boy/Male
English American Shakespearean
Ford near a slope. From an Old English surname and place name, used commonly as a first name...
Girl/Female
American, Australian, Gaelic, German, Irish
Leader; Superiority; Of a Ruling Family Superiority; Descendant of Fallamhan; In Charge; Descended from a Ruler
Girl/Female
French, German
Of the Dark Hair; Dark Warrior
Girl/Female
American, Australian, Basque, British, Chinese, Christian, Czechoslovakian, Danish, Dutch, English, Finnish, French, German, Hungarian, Italian, Japanese, Latin, Norse, Romanian, Scandinavian, Slovenia, Swedish, Swiss, Teutonic
Ever-powerful; Honorable Ruler; Ruler Forever; Alone
Boy/Male
Indian
Decisive
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Blue
Girl/Female
Arabic, Muslim
Beautiful Butterfly
Girl/Female
Indian, Telugu
Royal
Girl/Female
Indian
Sunbeam, Gentle, Brilliant, Radiant
Boy/Male
Shakespearean
Much Ado About Nothing' A Headborough.
EPICYCLOID
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EPICYCLOID
n.
A kind of curve. See Epicycloid, any Trochoid.
n.
A curve, traced by a point in the radius, or radius produced, of a circle which rolls upon the concave side of a fixed circle. See Hypocycloid, Epicycloid, and Trochoid.
a.
Pertaining to the epicycloid, or having its properties.
n.
A curve traced by a point in the circumference of a circle which rolls on the concave side in the fixed circle. Cf. Epicycloid, and Trochoid.
n.
A curve traced by a point in the circumference of a circle which rolls on the convex side of a fixed circle.
n.
The curve described by any point in a wheel rolling on a line; a cycloid; a roulette; in general, the curve described by any point fixedly connected with a moving curve while the moving curve rolls without slipping on a second fixed curve, the curves all being in one plane. Cycloids, epicycloids, hypocycloids, cardioids, etc., are all trochoids.