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The radial curve of the cycloid with parametric equations x = a(t-sint) (1) y = a(1-cost) (2) is the circle x_r = x_0+2asint (3) y_r = -2a+y_0+2acost. (4)

The evolute of the epicycloid x = (a+b)cost-bcos[((a+b)/b)t] (1) y = (a+b)sint-bsin[((a+b)/b)t] (2) is another epicycloid given by x = a/(a+2b){(a+b)cost+bcos[((a+b)/b)t]} ...

A map projection in which the distances between one or two points and every other point on the map differ from the corresponding distances on the sphere by only a constant ...

The amazing identity for all theta, where Gamma(z) is the gamma function. Equating coefficients of theta^0, theta^4, and theta^8 gives some amazing identities for the ...

For a semicubical parabola with parametric equations x = t^2 (1) y = at^3, (2) the involute is given by x_i = (t^2)/3-8/(27a^2) (3) y_i = -(4t)/(9a), (4) which is half a ...

The radial curve of the tractrix x = a(t-tanht) (1) y = asecht (2) with radiant point (x_0,y_0) is the kappa curve x_r = x_0+atanht (3) y_r = y_0+asinhttanht. (4)

A Carmichael number is an odd composite number n which satisfies Fermat's little theorem a^(n-1)-1=0 (mod n) (1) for every choice of a satisfying (a,n)=1 (i.e., a and n are ...

The Labs septic is a septic surface having 99 ordinary double points, which is the maximum number known for any septic surface.

A Maurer rose is a plot of a "walk" along an n- (or 2n-) leafed rose curve in steps of a fixed number d degrees, including all cosets.

An algebraic extension K over a field F is a purely inseparable extension if the algebraic number minimal polynomial of any element has only one root, possibly with ...