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Given an obtuse triangle, the polar circle has center at the orthocenter H. Call H_i the feet. Then the square of the radius r is given by r^2 = HA^_·HH_A^_ (1) = HB^_·HH_B^_ ...

A polar zonohedron is a convex zonohedron derived from the star which joins opposite vertices of any right n-gonal prism (for n even) or antiprism (for n odd). The faces of ...

A class of map projections in which the parallels are represented by a system of non-concentric circular arcs with centers lying on the straight line representing the central ...

The (signed) area of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) is A=1/2(|x_1 x_2; y_1 y_2|+|x_2 x_3; y_2 y_3|+...+|x_n x_1; y_n y_1|), ...

The length of the polygonal spiral is found by noting that the ratio of inradius to circumradius of a regular polygon of n sides is r/R=(cot(pi/n))/(csc(pi/n))=cos(pi/n). (1) ...

For a polynomial P=sum_(k=0)^na_kz^k, (1) several classes of norms are commonly defined. The l_p-norm is defined as ||P||_p=(sum_(k=0)^n|a_k|^p)^(1/p) (2) for p>=1, giving ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...

The mean of a distribution with probability density function P(x) is the first raw moment mu_1^', defined by mu=<x>, (1) where <f> is the expectation value. For a continuous ...

Consider solutions to the equation x^y=y^x. (1) Real solutions are given by x=y for x,y>0, together with the solution of (lny)/y=(lnx)/x, (2) which is given by ...

Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through ...