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A weakly binary tree is a planted tree in which all nonroot graph vertices are adjacent to at most three graph vertices. Let g(z)=sum_(i=0)^inftyg_iz^i, (1) be the generating ...

Bézout's theorem for curves states that, in general, two algebraic curves of degrees m and n intersect in m·n points and cannot meet in more than m·n points unless they have ...

"The" continuity axiom is an additional Axiom which must be added to those of Euclid's Elements in order to guarantee that two equal circles of radius r intersect each other ...

A grammar defining formal language L is a quadruple (N,T,R,S), where N is a finite set of nonterminals, T is a finite set of terminal symbols, R is a finite set of ...

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the ...

The radical circle of the McCay circles has center (1) which is not a Kimberling center, and radius (2) where (3) Its circle function is (4) where (5) which is also does not ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

The second Fermat point X^' or F_2 (also known as the second isogonic center) can be constructed by drawing equilateral triangles on the inside of a given triangle and ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...

A labeled binary tree containing the labels 1 to n with root 1, branches leading to nodes labeled 2 and 3, branches from these leading to 4, 5 and 6, 7, respectively, and so ...