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The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

The point F at which the incircle and nine-point circle are tangent. It has triangle center function alpha=1-cos(B-C) (1) and is Kimberling center X_(11). If F is the ...

The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...

A figurate number which is the sum of two consecutive pyramidal numbers, O_n=P_(n-1)+P_n=1/3n(2n^2+1). (1) The first few are 1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891, ...

A spherical ring is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring. Let the sphere have radius R and ...

The tensor product of two vector spaces V and W, denoted V tensor W and also called the tensor direct product, is a way of creating a new vector space analogous to ...

The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of two ovals. They were first studied by Descartes ...

The circle H which touches the incircles I, I_A, I_B, and I_C of a circular triangle ABC and its associated triangles. It is either externally tangent to I and internally ...

The Maclaurin trisectrix is a curve first studied by Colin Maclaurin in 1742. It was studied to provide a solution to one of the geometric problems of antiquity, in ...

A natural equation is an equation which specifies a curve independent of any choice of coordinates or parameterization. The study of natural equations began with the ...