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Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

A magic tesseract is a four-dimensional generalization of the two-dimensional magic square and the three-dimensional magic cube. A magic tesseract has magic constant ...

The triangle DeltaM_AM_BM_C formed by joining the midpoints of the sides of a triangle DeltaABC. The medial triangle is sometimes also called the auxiliary triangle (Dixon ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...

An orthogonal coordinate system is a system of curvilinear coordinates in which each family of surfaces intersects the others at right angles. Orthogonal coordinates ...

The pedal of a curve C with respect to a point O is the locus of the foot of the perpendicular from O to the tangent to the curve. More precisely, given a curve C, the pedal ...

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. ...

How can n points be distributed on a unit sphere such that they maximize the minimum distance between any pair of points? This maximum distance is called the covering radius, ...

Let a spherical triangle be drawn on the surface of a sphere of radius R, centered at a point O=(0,0,0), with vertices A, B, and C. The vectors from the center of the sphere ...

A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...