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The parallel curves of a circle with radius a with offset k are given by the parametric equations x_p(t) = (a+k)cost (1) y_p(t) = (a+k)sint (2) and are therefore themselves ...

A formal argument in logic in which it is stated that (1) P=>Q and R=>S (where => means "implies"), and (2) either P or R is true, from which two statements it follows that ...

The surface given by the parametric equations x = e^(bv)cosv+e^(av)cosucosv (1) y = e^(bv)sinv+e^(av)cosusinv (2) z = e^(av)sinu. (3) For a=b=1, the coefficients of the first ...

The cotangent function cotz is the function defined by cotz = 1/(tanz) (1) = (i(e^(iz)+e^(-iz)))/(e^(iz)-e^(-iz)) (2) = (i(e^(2iz)+1))/(e^(2iz)-1), (3) where tanz is the ...

A formal argument in logic in which it is stated that 1. P=>Q and R=>S (where => means "implies"), and 2. Either not-Q or not-S is true, from which two statements it follows ...

The Doppler spiral is the curve obtained from an Archimedes' spiral which is translated horizontally with speed k. It has parametric equations x(t) = a(tcost+kt) (1) y(t) = ...

The simplest algebraic language, denoted D. If X is the alphabet {x,x^_}, then D is the set of words u of X which satisfy 1. |u|_x=|u|_(x^_), where |u|_x is the numbers of ...

The involute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_i = ...

Let A and B be two classes of positive integers. Let A(n) be the number of integers in A which are less than or equal to n, and let B(n) be the number of integers in B which ...

A figurate number which is equal to the cubic number n^3. The first few are 1, 8, 27, 64, ... (OEIS A000578).