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The study of the probabilities involved in geometric problems, e.g., the distributions of length, area, volume, etc. for geometric objects under stated conditions. The ...

The hyperbolic cosine is defined as coshz=1/2(e^z+e^(-z)). (1) The notation chx is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). This function describes the ...

By way of analogy with the usual tangent tanz=(sinz)/(cosz), (1) the hyperbolic tangent is defined as tanhz = (sinhz)/(coshz) (2) = (e^z-e^(-z))/(e^z+e^(-z)) (3) = ...

Landau's problems are the four "unattackable" problems mentioned by Landau in the 1912 Fifth Congress of Mathematicians in Cambridge, namely: 1. The Goldbach conjecture, 2. ...

An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

Dickson states "In a letter to Tanner [L'intermediaire des math., 2, 1895, 317] Lucas stated that Mersenne (1644, 1647) implied that a necessary and sufficient condition that ...

Hardy and Littlewood (1914) proved that the sequence {frac(x^n)}, where frac(x) is the fractional part, is equidistributed for almost all real numbers x>1 (i.e., the ...

An extended rooted binary tree satisfying the following conditions: 1. Every node has two children, each colored either red or black. 2. Every tree leaf node is colored ...

Taking a connected graph or network with a high graph diameter and adding a very small number of edges randomly, the diameter tends to drop drastically. This is known as the ...

Sphere tetrahedron picking is the selection of quadruples of of points corresponding to vertices of a tetrahedron with vertices on the surface of a sphere. n random ...