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A triangle DeltaA^'B^'C^' is said to be inscribed in a triangle DeltaABC if A^' lies on BC, B^' lies on CA, and C^' lies on AB (Kimberling 1998, p. 184). Examples include the ...

Lines that intersect in a point are called intersecting lines. Lines that do not intersect are called parallel lines in the plane, and either parallel or skew lines in ...

Q_n^((alpha,beta))(x)=2^(-n-1)(x-1)^(-alpha)(x+1)^(-beta) ×int_(-1)^1(1-t)^(n+alpha)(1+t)^(n+beta)(x-t)^(-n-1)dt. In the exceptional case n=0, alpha+beta+1=0, a nonconstant ...

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.

The Lambert cylindrical equal-area projection is a cylindrical equal-area projection with standard parallel phi_s=0 degrees.

Let alpha(x) be a monotone increasing function and define an interval I=(x_1,x_2). Then define the nonnegative function U(I)=alpha(x_2)-alpha(x_1). The Lebesgue integral with ...

Any complex measure lambda decomposes into an absolutely continuous measure lambda_a and a singular measure lambda_c, with respect to some positive measure mu. This is the ...

A function giving the distribution of the interpoint distances of a curve. It is defined by p(r)=1/Nsum_(ij)delta_(r_(ij)=r).

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

The least number of crossings that occur in any projection of a link. In general, it is difficult to find the crossing number of a given link. Knots and links are generally ...