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Homogeneous barycentric coordinates are barycentric coordinates normalized such that they become the actual areas of the subtriangles. Barycentric coordinates normalized so ...

When two cycles have a transversal intersection X_1 intersection X_2=Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only ...

A right triangle with the two legs (and their corresponding angles) equal. An isosceles right triangle therefore has angles of 45 degrees, 45 degrees, and 90 degrees. For an ...

The Jackson-Slater identity is the q-series identity of Rogers-Ramanujan-type given by sum_(k=0)^(infty)(q^(2k^2))/((q)_(2k)) = ...

The jinc function is defined as jinc(x)=(J_1(x))/x, (1) where J_1(x) is a Bessel function of the first kind, and satisfies lim_(x->0)jinc(x)=1/2. The derivative of the jinc ...

Consider an n-digit number k. Square it and add the right n digits to the left n or n-1 digits. If the resultant sum is k, then k is called a Kaprekar number. For example, 9 ...

A planar convex quadrilateral consisting of two adjacent sides of length a and the other two sides of length b. The rhombus is a special case of the kite, and the lozenge is ...

A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...

The second-order ordinary differential equation y^('')+g(y)y^('2)+f(x)y^'=0 (1) is called Liouville's equation (Goldstein and Braun 1973; Zwillinger 1997, p. 124), as are the ...

The log sine function, also called the logsine function, is defined by S_n=int_0^pi[ln(sinx)]^ndx. (1) The first few cases are given by S_1 = -piln2 (2) S_2 = ...