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The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then [(z-x),x^',x^('')]=0, where ...

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. ...

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 ...

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 ...

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 ...

A tetractys, also called a tetraktys or decad, is an arrangement of 10 points in the form of a triangle with 1 point in the first row, two in the second, three in the third, ...

A sequence of numbers V={nu_n} is said to be weakly complete if every positive integer n beyond a certain point N is the sum of some subsequence of V (Honsberger 1985). ...