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Trilinear coordinates

Index Trilinear coordinates

In geometry, the trilinear coordinates x:y:z of a point relative to a given triangle describe the relative directed distances from the three sidelines of the triangle. [1]

27 relations: Altitude (triangle), Barycentric coordinate system, Cartesian coordinate system, Centroid, Circumconic and inconic, Circumscribed circle, Collinearity, Concurrent lines, Conic section, Cornell University, De Longchamps point, Determinant, Distance, Euclidean vector, Extended side, Feuerbach point, Geometry, Homogeneous coordinates, Incenter, Incircle and excircles of a triangle, Inscribed figure, Nine-point center, Symmedian, Ternary plot, Triangle, Trigonometric functions, Vertex (geometry).

Altitude (triangle)

In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).

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Barycentric coordinate system

In geometry, the barycentric coordinate system is a coordinate system in which the location of a point of a simplex (a triangle, tetrahedron, etc.) is specified as the center of mass, or barycenter, of usually unequal masses placed at its vertices.

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Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

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Centroid

In mathematics and physics, the centroid or geometric center of a plane figure is the arithmetic mean position of all the points in the shape.

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Circumconic and inconic

In triangle geometry, a circumconic is a conic section that passes through the three vertices of a triangle, and an inconic is a conic section inscribed in the sides, possibly extended, of a triangle.

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Circumscribed circle

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

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Collinearity

In geometry, collinearity of a set of points is the property of their lying on a single line.

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Concurrent lines

In geometry, three or more lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point.

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Conic section

In mathematics, a conic section (or simply conic) is a curve obtained as the intersection of the surface of a cone with a plane.

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Cornell University

Cornell University is a private and statutory Ivy League research university located in Ithaca, New York.

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De Longchamps point

In geometry, the de Longchamps point of a triangle is a triangle center named after French mathematician Gaston Albert Gohierre de Longchamps.

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Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

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Distance

Distance is a numerical measurement of how far apart objects are.

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Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

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Extended side

In plane geometry, an extended side or sideline of a polygon is the line that contains one side of the polygon.

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Feuerbach point

In the geometry of triangles, the incircle and nine-point circle of a triangle are internally tangent to each other at the Feuerbach point of the triangle.

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Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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Homogeneous coordinates

In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.

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Incenter

In geometry, the incenter of a triangle is a triangle center, a point defined for any triangle in a way that is independent of the triangle's placement or scale.

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Incircle and excircles of a triangle

In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.

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Inscribed figure

An inscribed triangle of a circle In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid.

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Nine-point center

In geometry, the nine-point center is a triangle center, a point defined from a given triangle in a way that does not depend on the placement or scale of the triangle.

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Symmedian

In geometry, symmedians are three particular geometrical lines associated with every triangle.

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Ternary plot

A ternary plot, ternary graph, triangle plot, simplex plot, Gibbs triangle or de Finetti diagram is a barycentric plot on three variables which sum to a constant.

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Triangle

A triangle is a polygon with three edges and three vertices.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Vertex (geometry)

In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet.

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Redirects here:

Trilinear coordinate, Trilinears.

References

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

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