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Angular defect

Index Angular defect

In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the Euclidean plane would. [1]

30 relations: Alexandrov's uniqueness theorem, Angle, Cube, Dihedral angle, Dodecahedron, Elongated square pyramid, Euler characteristic, Face (geometry), Gauss–Bonnet theorem, Gaussian curvature, Geometry, Great stellated dodecahedron, Homeomorphism, Hyperbolic triangle, Icosahedron, Internal and external angles, Maxima and minima, Octahedron, Pentagon, Platonic solid, Polyhedron, René Descartes, Saddle point, Small stellated dodecahedron, Spherical trigonometry, Square pyramid, Tetrahedron, Toroidal polyhedron, Turn (geometry), Two-dimensional space.

Alexandrov's uniqueness theorem

The Alexandrov uniqueness theorem is a rigidity theorem in mathematics, describing three-dimensional convex polyhedra in terms of the distances between points on their surfaces.

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Angle

In plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

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Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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Dihedral angle

A dihedral angle is the angle between two intersecting planes.

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Dodecahedron

In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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Elongated square pyramid

In geometry, the elongated square pyramid is one of the Johnson solids (J8).

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Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

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Face (geometry)

In solid geometry, a face is a flat (planar) surface that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by flat faces is a polyhedron.

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Gauss–Bonnet theorem

The Gauss–Bonnet theorem or Gauss–Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic).

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Gaussian curvature

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point: For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere.

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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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Great stellated dodecahedron

In geometry, the great stellated dodecahedron is a Kepler-Poinsot polyhedron, with Schläfli symbol.

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Homeomorphism

In the mathematical field of topology, a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function.

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Hyperbolic triangle

In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane.

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Icosahedron

In geometry, an icosahedron is a polyhedron with 20 faces.

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Internal and external angles

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint.

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Maxima and minima

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).

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Octahedron

In geometry, an octahedron (plural: octahedra) is a polyhedron with eight faces, twelve edges, and six vertices.

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Pentagon

In geometry, a pentagon (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

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Polyhedron

In geometry, a polyhedron (plural polyhedra or polyhedrons) is a solid in three dimensions with flat polygonal faces, straight edges and sharp corners or vertices.

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René Descartes

René Descartes (Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist.

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Saddle point

In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes.

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Small stellated dodecahedron

In geometry, the small stellated dodecahedron is a Kepler-Poinsot polyhedron, named by Arthur Cayley, and with Schläfli symbol.

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Spherical trigonometry

Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons (especially spherical triangles) defined by a number of intersecting great circles on the sphere.

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Square pyramid

In geometry, a square pyramid is a pyramid having a square base.

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Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

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Toroidal polyhedron

In geometry, a toroidal polyhedron is a polyhedron which is also a toroid (a g-holed torus), having a topological genus of 1 or greater.

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Turn (geometry)

A turn is a unit of plane angle measurement equal to 2pi radians, 360 degrees or 400 gradians.

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Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

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Redirects here:

Angle defect, Angular deficiency, Angular deficit, Defect (geometry), Descartes' theorem on total angular defect.

References

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

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