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A hexagon (not necessarily regular) on whose polygon vertices a circle may be circumscribed. Let sigma_i=Pi_i(a_1^2,a_2^2,a_3^2,a_4^2,a_5^2,a_6^2) (1) denote the ith-order ...

Any continuous function G:B^n->B^n has a fixed point, where B^n={x in R^n:x_1^2+...+x_n^2<=1} is the unit n-ball.

For any M, there exists a t^' such that the sequence n^2+t^', where n=1, 2, ... contains at least M primes.

Let f be a contraction mapping from a closed subset F of a Banach space E into F. Then there exists a unique z in F such that f(z)=z.

If a minimal surface is given by the equation z=f(x,y) and f has continuous first and second partial derivatives for all real x and y, then f is a plane.

Two unit-speed plane curves which have the same curvature differ only by a Euclidean motion.

Let K be a finite complex, let h:|K|->|K| be a continuous map. If Lambda(h)!=0, then h has a fixed point.

Let f:D(z_0,r)\{z_0}->C be analytic and bounded on a punctured open disk D(z_0,r), then lim_(z->z_0)f(z) exists, and the function defined by f^~:D(z_0,r)->C f^~(z)={f(z) for ...

In 1638, Fermat proposed that every positive integer is a sum of at most three triangular numbers, four square numbers, five pentagonal numbers, and n n-polygonal numbers. ...

A simple graph is a line graph of some simple graph iff if does not contain any of the above nine graphs, known in this work as Beineke graphs, as a forbidden induced ...