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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. ...

There are two different definitions of the polar angle. In the plane, the polar angle theta is the counterclockwise angle from the x-axis at which a point in the xy-plane ...

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 ...

A topology on a set X whose open sets are the unions of open balls B(X_0,r)={x in x|g(x_0,x)<r}, where g is a pseudometric on X, x_0 is any point of X, and r>0. There is a ...

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 z_0 be a point in a simply connected region R!=C, where C is the complex plane. Then there is a unique analytic function w=f(z) mapping R one-to-one onto the disk |w|<1 ...

The period for a quasiperiodic trajectory to pass through the same point in a surface of section. If the rotation number is irrational, the trajectory will densely fill out a ...