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The Harborth graph is the smallest known 4-regular matchstick graph. It is therefore both planar and unit-distance. It has 104 edges and 52 vertices. This graph was named ...

A general prism is a polyhedron possessing two congruent polygonal faces and with all remaining faces parallelograms (Kern and Bland 1948, p. 28; left figure). A right prism ...

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 ...

Pick three points P=(x_1,y_1), Q=(x_2,y_2), and R=(x_3,y_3) distributed independently and uniformly in a unit disk K (i.e., in the interior of the unit circle). Then the ...

A generalized mobile automaton is a generalization of the mobile automaton in which the automaton may have more than one active cell. Generalized mobile automata allow for ...

There are several definitions of the strength of a graph. Harary and Palmer (1959) and Harary and Palmer (1973, p. 66) define the strength of a tree as the maximum number of ...

The incidence matrix of a graph gives the (0,1)-matrix which has a row for each vertex and column for each edge, and (v,e)=1 iff vertex v is incident upon edge e (Skiena ...

An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A ...

A formula relating the number of polyhedron vertices V, faces F, and polyhedron edges E of a simply connected (i.e., genus 0) polyhedron (or polygon). It was discovered ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...