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If a circular pizza is divided into 8, 12, 16, ... slices by making cuts at equal angles from an arbitrary point, then the sums of the areas of alternate slices are equal. ...

The principal theorem of axonometry, first published without proof by Pohlke in 1860. It states that three segments of arbitrary length a^'x^', a^'y^', and a^'z^' which are ...

If P be a point in the plane of an equilateral triangle DeltaABC, then the lengths of line segments AP, BP, and CP correspond the sides of a triangle, which is degenerate ...

A result in control theory. Define H(psi,x,u)=(psi,f(x,u))=sum_(a=0)^npsi_af^a(x,u). Then in order for a control u(t) and a trajectory x(t) to be optimal, it is necessary ...

The number of digits used to perform a given computation. The concepts of accuracy and precision are both closely related and often confused. While the accuracy of a number x ...

Given a subset S subset R^n and a real function f which is Gâteaux differentiable at a point x in S, f is said to be pseudoconvex at x if del f(x)·(y-x)>=0,y in ...

The rectifiable sets include the image of any Lipschitz function f from planar domains into R^3. The full set is obtained by allowing arbitrary measurable subsets of ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon. If each point of intersection is associated with a node and diagonals are split ar each ...

A subset M subset R^n is called a regular surface if for each point p in M, there exists a neighborhood V of p in R^n and a map x:U->R^n of an open set U subset R^2 onto V ...

Let K subset= C be compact, let f be analytic on a neighborhood of K, and let P subset= C^*\K contain at least one point from each connected component of C^*\K. Then for any ...