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An isosceles triangle is a triangle with (at least) two equal sides. In the figure above, the two equal sides have length b and the remaining side has length a. This property ...

A spherical ring is a sphere with a cylindrical hole cut so that the centers of the cylinder and sphere coincide, also called a napkin ring. Let the sphere have radius R and ...

A regular continued fraction is a simple continued fraction x = b_0+1/(b_1+1/(b_2+1/(b_3+...))) (1) = K_(k=1)^(infty)1/(b_k) (2) = [b_0;b_1,b_2,...], (3) where b_0 is an ...

The (lower) domination number gamma(G) of a graph G is the minimum size of a dominating set of vertices in G, i.e., the size of a minimum dominating set. This is equivalent ...

For a fractal process with values y(t-Deltat) and y(t+Deltat), the correlation between these two values is given by the Brown function r=2^(2H-1)-1, also known as the ...

A set within which the values of a function lie (as opposed to the range, which is the set of values that the function actually takes).

An equation of the form f(x)=b (mod m), (1) where the values of 0<=x<m for which the equation holds are sought. Such an equation may have none, one, or many solutions. There ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

The upper and lower hinges are descriptive statistics of a set of N data values, where N is of the form N=4n+5 with n=0, 1, 2, .... The hinges are obtained by ordering the ...

Let f(x) be a finite and measurable function in (-infty,infty), and let epsilon be freely chosen. Then there is a function g(x) such that 1. g(x) is continuous in ...