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A number of attractive 7-compounds of the regular dodecahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

The parallel curves for (outward) offset k of an ellipse with semi-axis lengths a and b are given by x_p = (a+(bk)/(sqrt(a^2sin^2t+b^2cos^2t)))cost (1) y_p = ...

A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

The radical circle of the excircles has center at the Spieker center X_(10) and radius R_E=1/2sqrt((a^2b+ab^2+a^2c+abc+b^2c+ac^2+bc^2)/(a+b+c)). Its circle function is ...

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.

The Frobenius equation is the Diophantine equation a_1x_1+a_2x_2+...+a_nx_n=b, where the a_i are positive integers, b is an integer, and the solutions x_i are nonnegative ...

A finite extension K=Q(z)(w) of the field Q(z) of rational functions in the indeterminate z, i.e., w is a root of a polynomial a_0+a_1alpha+a_2alpha^2+...+a_nalpha^n, where ...

A set S is said to be GCD-closed if GCD(x_i,x_j) in S for 1<=i,j<=n.

A global extremum, also known as an absolute extremum, is a global minimum or global maximum. It is impossible to construct an algorithm that will find a global extremum for ...

A global maximum, also known as an absolute maximum, the largest overall value of a set, function, etc., over its entire range. It is impossible to construct an algorithm ...