# Category: Roulettes (curve)

Cissoid of Diocles
In geometry, the cissoid of Diocles (from Ancient Greek κισσοειδής (kissoeidēs) 'ivy-shaped'; named for Diocles) is a cubic plane curve notable for the property that it can be used to construct two me
Cyclogon
In geometry, a cyclogon is the curve traced by a vertex of a polygon that rolls without slipping along a straight line. There are no restrictions on the nature of the polygon. It can be a regular poly
Limaçon
In geometry, a limaçon or limacon /ˈlɪməsɒn/, also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls
Epicycloid
In geometry, an epicycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle—called an epicycle—which rolls without slipping around a fixed circle. It is
Hypotrochoid
In geometry, a hypotrochoid is a roulette traced by a point attached to a circle of radius r rolling around the inside of a fixed circle of radius R, where the point is a distance d from the center of
Roulette (curve)
In the differential geometry of curves, a roulette is a kind of curve, generalizing cycloids, epicycloids, hypocycloids, trochoids, epitrochoids, hypotrochoids, and involutes.
Astroid
In mathematics, an astroid is a particular type of roulette curve: a hypocycloid with four cusps. Specifically, it is the locus of a point on a circle as it rolls inside a fixed circle with four times
Epitrochoid
In geometry, an epitrochoid (/ɛpɪˈtrɒkɔɪd/ or /ɛpɪˈtroʊkɔɪd/) is a roulette traced by a point attached to a circle of radius r rolling around the outside of a fixed circle of radius R, where the point
Involute
In mathematics, an involute (also known as an evolvent) is a particular type of curve that is dependent on another shape or curve. An involute of a curve is the locus of a point on a piece of taut str
Hypocycloid
In geometry, a hypocycloid is a special plane curve generated by the trace of a fixed point on a small circle that rolls within a larger circle. As the radius of the larger circle is increased, the hy
Tusi couple
The Tusi couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of
Nephroid
In geometry, a nephroid (from Ancient Greek ὁ νεφρός (ho 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 by
Cycloid
In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve
Centered trochoid
In geometry, a centered trochoid is the roulette formed by a circle rolling along another circle. That is, it is the path traced by a point attached to a circle as the circle rolls without slipping al
Catenary
In physics and geometry, a catenary (US: /ˈkætənɛri/, UK: /kəˈtiːnəri/) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform
Cycloid gear
The cycloidal gear profile is a form of toothed gear used in mechanical clocks, rather than the involute gear form used for most other gears. The gear tooth profile is based on the epicycloid and hypo
Trochoid
In geometry, a trochoid (from Greek trochos 'wheel') is a roulette curve formed by a circle rolling along a line. It is the curve traced out by a point fixed to a circle (where the point may be on, in
Deltoid curve
In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps. In other words, it is the roulette created by a point on the circumference of a circle
Cardioid
In geometry, a cardioid (from Greek καρδιά (kardiá) 'heart') is a plane curve traced by a point on the perimeter of a circle that is rolling around a fixed circle of the same radius. It can also be de