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Cardioid, the Glossary

In geometry, a cardioid 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.^[1]

41 relations: Acoustics, Alexander Bogomolny, Apple, Cartesian coordinate system, Caustic (mathematics), Caustic (optics), Chord (geometry), Cissoid of Diocles, Complex analysis, Complex plane, Cusp (singularity), Deltoid curve, Direction finding, Envelope (mathematics), Epicycloid, Evolute, Geometry, Giovanni Salvemini, Image (mathematics), Inverse curve, Lemniscate of Bernoulli, Limaçon, List of trigonometric identities, Loop antenna, Luigi Cremona, Mandelbrot set, Microphone, Nephroid, Orthogonal trajectory, Parabola, Parametric equation, Partial derivative, Pedal curve, Pencil (geometry), Plane curve, Polar coordinate system, Radius of curvature, Sinusoidal spiral, Space cardioid, Wittgenstein's rod, Yagi–Uda antenna.
Quartic curves
Roulettes (curve)

Acoustics

Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound.

See Cardioid and Acoustics

Alexander Bogomolny

Alexander Bogomolny (January 4, 1948 July 7, 2018) was a Soviet-born Israeli-American mathematician.

See Cardioid and Alexander Bogomolny

Apple

An apple is a round, edible fruit produced by an apple tree (''Malus spp.'', among them the domestic or orchard apple; Malus domestica).

See Cardioid and Apple

In geometry, a Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system.

See Cardioid and Cartesian coordinate system

Caustic (mathematics)

In differential geometry, a caustic is the envelope of rays either reflected or refracted by a manifold.

See Cardioid and Caustic (mathematics)

Caustic (optics)

In optics, a caustic or caustic network is the envelope of light rays which have been reflected or refracted by a curved surface or object, or the projection of that envelope of rays on another surface.

See Cardioid and Caustic (optics)

Chord (geometry)

A chord (from the Latin chorda, meaning "bowstring") of a circle is a straight line segment whose endpoints both lie on a circular arc.

See Cardioid and Chord (geometry)

Cissoid of Diocles

In geometry, the cissoid of Diocles (named for Diocles) is a cubic plane curve notable for the property that it can be used to construct two mean proportionals to a given ratio. Cardioid and cissoid of Diocles are roulettes (curve).

See Cardioid and Cissoid of Diocles

Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

See Cardioid and Complex analysis

Complex plane

In mathematics, the complex plane is the plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, called the imaginary axis, is formed by the imaginary numbers.

See Cardioid and Complex plane

Cusp (singularity)

In mathematics, a cusp, sometimes called spinode in old texts, is a point on a curve where a moving point must reverse direction.

See Cardioid and Cusp (singularity)

Deltoid curve

In geometry, a deltoid curve, also known as a tricuspoid curve or Steiner curve, is a hypocycloid of three cusps. Cardioid and deltoid curve are Quartic curves and roulettes (curve).

See Cardioid and Deltoid curve

Direction finding

Direction finding (DF), or radio direction finding (RDF), is the use of radio waves to determine the direction to a radio source.

See Cardioid and Direction finding

Envelope (mathematics)

In geometry, an envelope of a planar family of curves is a curve that is tangent to each member of the family at some point, and these points of tangency together form the whole envelope.

See Cardioid and Envelope (mathematics)

Epicycloid

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 an epicycle—which rolls without slipping around a fixed circle. Cardioid and epicycloid are roulettes (curve).

See Cardioid and Epicycloid

Evolute

In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature.

See Cardioid and Evolute

Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

See Cardioid and Geometry

Giovanni Salvemini

Giovanni Francesco Mauro Melchiorre Salvemini di Castiglione FRS (15 January 1708 in Castiglione del Valdarno – 11 October 1791 in Berlin) was an Italian mathematician and astronomer.

See Cardioid and Giovanni Salvemini

Image (mathematics)

In mathematics, for a function f: X \to Y, the image of an input value x is the single output value produced by f when passed x. The preimage of an output value y is the set of input values that produce y. More generally, evaluating f at each element of a given subset A of its domain X produces a set, called the "image of A under (or through) f".

See Cardioid and Image (mathematics)

Inverse curve

In inversive geometry, an inverse curve of a given curve is the result of applying an inverse operation to.

See Cardioid and Inverse curve

Lemniscate of Bernoulli

In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points and, known as foci, at distance from each other as the locus of points so that. Cardioid and lemniscate of Bernoulli are Quartic curves.

See Cardioid and Lemniscate of Bernoulli

Limaçon

In geometry, a limaçon or limacon, 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 around the outside of a circle of equal radius. Cardioid and limaçon are Quartic curves and roulettes (curve).

See Cardioid and Limaçon

List of trigonometric identities

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.

See Cardioid and List of trigonometric identities

Loop antenna

A loop antenna is a radio antenna consisting of a loop or coil of wire, tubing, or other electrical conductor, that for transmitting is usually fed by a balanced power source or for receiving feeds a balanced load.

See Cardioid and Loop antenna

Luigi Cremona

Antonio Luigi Gaudenzio Giuseppe Cremona (7 December 1830 – 10 June 1903) was an Italian mathematician.

See Cardioid and Luigi Cremona

Mandelbrot set

The Mandelbrot set is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified.

See Cardioid and Mandelbrot set

Microphone

A microphone, colloquially called a mic, or mike, is a transducer that converts sound into an electrical signal.

See Cardioid and Microphone

Nephroid

In geometry, a nephroid is a specific plane curve. Cardioid and nephroid are roulettes (curve).

See Cardioid and Nephroid

Orthogonal trajectory

In mathematics, an orthogonal trajectory is a curve which intersects any curve of a given pencil of (planar) curves orthogonally.

See Cardioid and Orthogonal trajectory

Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

See Cardioid and Parabola

Parametric equation

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

See Cardioid and Parametric equation

Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

See Cardioid and Partial derivative

Pedal curve

In mathematics, a pedal curve of a given curve results from the orthogonal projection of a fixed point on the tangent lines of this curve.

See Cardioid and Pedal curve

Pencil (geometry)

In geometry, a pencil is a family of geometric objects with a common property, for example the set of lines that pass through a given point in a plane, or the set of circles that pass through two given points in a plane.

See Cardioid and Pencil (geometry)

Plane curve

In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane.

See Cardioid and Plane curve

Polar coordinate system

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

See Cardioid and Polar coordinate system

Radius of curvature

In differential geometry, the radius of curvature,, is the reciprocal of the curvature.

See Cardioid and Radius of curvature

Sinusoidal spiral

In algebraic geometry, the sinusoidal spirals are a family of curves defined by the equation in polar coordinates where is a nonzero constant and is a rational number other than 0.

See Cardioid and Sinusoidal spiral

Space cardioid

The space cardioid is a 3-dimensional curve derived from the cardioid.

See Cardioid and Space cardioid

Wittgenstein's rod

Wittgenstein's rod is a problem in geometry discussed by 20th-century philosopher Ludwig Wittgenstein.

See Cardioid and Wittgenstein's rod

Yagi–Uda antenna

A Yagi–Uda antenna, or simply Yagi antenna, is a directional antenna consisting of two or more parallel resonant antenna elements in an end-fire array; these elements are most often metal rods (or discs) acting as half-wave dipoles.

See Cardioid and Yagi–Uda antenna

References

[1] https://en.wikipedia.org/wiki/Cardioid

Also known as Cardiod, Cardioid article proofs, Cardioid proofs, Cardioid/Proofs, Cardioids, Cardoid, Cartoid function.

Cardioid, the Glossary

Table of Contents

See also

Quartic curves

Roulettes (curve)

References