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Draw the perpendicular line from the intersection of the two small semicircles in the arbelos. The two circles C_1 and C_2 tangent to this line, the large semicircle, and ...

In general, the catacaustics of the astroid are complicated curves. For an astroid with parametric equations x = cos^3t (1) y = sin^3t, (2) the catacaustic for a radiant ...

Let the characteristic polynomial of an n×n complex matrix A be written in the form P(lambda) = |lambdaI-A| (1) = ...

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

The boustrophedon ("ox-plowing") transform b of a sequence a is given by b_n = sum_(k=0)^(n)(n; k)a_kE_(n-k) (1) a_n = sum_(k=0)^(n)(-1)^(n-k)(n; k)b_kE_(n-k) (2) for n>=0, ...

The system of ordinary differential equations u^' = A+u^2v-(B+1)u (1) v^' = Bu-u^2v (2) (Hairer et al. 1987, p. 112; Zwillinger 1997, p. 136). The so-called full Brusselator ...

A sum of the digits in a given transmission modulo some number. The simplest form of checksum is a parity bit appended on to 7-bit numbers (e.g., ASCII characters) such that ...

A set of functions {f_1(n,x),f_2(n,x)} is termed a complete biorthogonal system in the closed interval R if, they are biorthogonal, i.e., int_Rf_1(m,x)f_1(n,x)dx = ...

A measure nu of a strange attractor which allows the presence of chaos to be distinguished from random noise. It is related to the capacity dimension D and information ...

The radial curve of the deltoid x = 1/3a[2cost+cos(2t)] (1) y = 1/3a[2sint-sin(2t)] (2) with pedal point (x_0,y_0) is x_p = 1/6[3x+cost+3xcost-cos(2t)-3ysint] (3) y_p = ...