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Let a space curve have line elements ds_N, ds_T, and ds_B along the normal, tangent, and binormal vectors respectively, then ds_N^2=ds_T^2+ds_B^2, (1) where ds_N^2 = ...

Given a parabola with parametric equations x = at^2 (1) y = at, (2) the evolute is given by x_e = 1/2a(1+6t^2) (3) y_e = -4at^3. (4) Eliminating x and y gives the implicit ...

A pair of dice which have the same odds for throwing every number as a normal pair of 6-sided dice. They are the only such alternate arrangement if face values are required ...

A formula of first-order logic is said to be in Skolemized form (sometimes also called Skolem standard form or universal form) if it is of the form forall x_1... forall x_nM, ...

Solution of a system of second-order homogeneous ordinary differential equations with constant coefficients of the form (d^2x)/(dt^2)+bx=0, where b is a positive definite ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

The map projection having transformation equations x = (lambda-lambda_0)cosphi_s (1) y = sinphisecphi_s (2) for the normal aspect, where lambda is the longitude, lambda_0 is ...

The graph strong product, also known as the graph AND product or graph normal product, is a graph product variously denoted G□AdjustmentBox[x, BoxMargins -> {{-0.65, ...

Probability and Statistics

Go is played on a 19×19 grid, with pieces being placed at the intersections of grid lines, rather than in the middle of them. Go boards have a number of peculiarities, ...