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Square triangle picking is the selection of triples of points (corresponding to endpoints of a triangle) randomly placed inside a square. n random triangles can be picked in ...

The numbers three and four appear prominently in the game of baseball. There are three strikes for an out, three outs per half-inning (i.e., teams switch after three outs, ...

A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a,b and hypotenuse c. By the Pythagorean theorem, this is ...

A (0,2)-graph is a connected graph such that any two vertices have 0 or 2 common neighbors. (0,2)-graphs are regular, and the numbers of (0,2)-graphs with vertex degree 0, 1, ...

An antiprism graph is a graph corresponding to the skeleton of an antiprism. Antiprism graphs are therefore polyhedral and planar. The n-antiprism graph has 2n vertices and ...

Ball triangle picking is the selection of triples of points (corresponding to vertices of a general triangle) randomly placed inside a ball. n random triangles can be picked ...

A caterpillar graph, caterpillar tree, or simply "caterpillar," is a tree in which every graph vertex is on a central stalk or only one graph edge away from the stalk (in ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

The deltoidal icositetrahedral graph is Archimedean dual graph which is the skeleton of the deltoidal icositetrahedron. It is implemented in the Wolfram Language as ...

The Dirichlet beta function is defined by the sum beta(x) = sum_(n=0)^(infty)(-1)^n(2n+1)^(-x) (1) = 2^(-x)Phi(-1,x,1/2), (2) where Phi(z,s,a) is the Lerch transcendent. The ...