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A roll of eight on a pair of six-sided dice in the game of craps. The probability of rolling "eighter from Decatur" is 5/36, or 13.888...%.

An Eisenstein series with half-period ratio tau and index r is defined by G_r(tau)=sum^'_(m=-infty)^inftysum^'_(n=-infty)^infty1/((m+ntau)^r), (1) where the sum sum^(') ...

A perspective collineation in which the center and axis are incident.

Given positive numbers s_a, s_b, and s_c, the Elkies point is the unique point Y in the interior of a triangle DeltaABC such that the respective inradii r_a, r_b, r_c of the ...

The intersection of an ellipse centered at the origin and semiaxes of lengths a and b oriented along the Cartesian axes with a line passing through the origin and point ...

For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

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

The parallel curves for (outward) offset k of an ellipse with semi-axis lengths a and b are given by x_p = (a+(bk)/(sqrt(a^2sin^2t+b^2cos^2t)))cost (1) y_p = ...

An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

Given a Jacobi amplitude phi in an elliptic integral, the argument u is defined by the relation phi=am(u,k). It is related to the elliptic integral of the first kind F(u,k) ...