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"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 ...

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 ...

The word configuration is sometimes used to describe a finite collection of points p=(p_1,...,p_n), p_i in R^d, where R^d is a Euclidean space. The term "configuration" also ...

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 ...

Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...

A topological space, also called an abstract topological space, is a set X together with a collection of open subsets T that satisfies the four conditions: 1. The empty set ...

Let G be a simple connected graph, and take 0<=i<=d(G), where d(G) is the graph diameter. Then G has global parameters c_i (respectively a_i, b_i) if the number of vertices ...

Let X be a set and S a collection of subsets of X. A subset A subset X is shattered by S if each subset B subset A of A can be expressed as the intersection of A with a ...