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A pyramid is a polyhedron with one face (known as the "base") a polygon and all the other faces triangles meeting at a common polygon vertex (known as the "apex"). A right ...

Combinatorial geometry is a blending of principles from the areas of combinatorics and geometry. It deals with combinations and arrangements of geometric objects and with ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...

Let x and y be vectors. Then the triangle inequality is given by |x|-|y|<=|x+y|<=|x|+|y|. (1) Equivalently, for complex numbers z_1 and z_2, ...

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

A surface of revolution is a surface generated by rotating a two-dimensional curve about an axis. The resulting surface therefore always has azimuthal symmetry. Examples of ...

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a ...

The word "surface" is an important term in mathematics and is used in many ways. The most common and straightforward use of the word is to denote a two-dimensional ...

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q. Irrational numbers have decimal expansions that neither terminate nor ...