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A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

The hypothesis that an integer n is prime iff it satisfies the condition that 2^n-2 is divisible by n. Dickson (2005, p. 91) stated that Leibniz believe to have proved that ...

Construct a square equal in area to a circle using only a straightedge and compass. This was one of the three geometric problems of antiquity, and was perhaps first attempted ...

A column-convex polyomino is a self-avoiding convex polyomino such that the intersection of any vertical line with the polyomino has at most two connected components. ...

The theory of classifying problems based on how difficult they are to solve. A problem is assigned to the P-problem (polynomial-time) class if the number of steps needed to ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...

For vectors u=(u_x,u_y,u_z) and v=(v_x,v_y,v_z) in R^3, the cross product in is defined by uxv = x^^(u_yv_z-u_zv_y)-y^^(u_xv_z-u_zv_x)+z^^(u_xv_y-u_yv_x) (1) = ...

Cube duplication, also called the Delian problem, is one of the geometric problems of antiquity which asks, given the length of an edge of a cube, that a second cube be ...

Curves which, when rotated in a square, make contact with all four sides. Such curves are sometimes also known as rollers. The "width" of a closed convex curve is defined as ...

Let the divisor function d(n) be the number of divisors of n (including n itself). For a prime p, d(p)=2. In general, sum_(k=1)^nd(k)=nlnn+(2gamma-1)n+O(n^theta), where gamma ...