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A connection game is a board game in which players compete to develop or complete a type of topological connection with their pieces. This could involve forming a path ...

A number which can be represented by a finite number of additions, subtractions, multiplications, divisions, and finite square root extractions of integers. Such numbers ...

"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 15_3 configuration of 15 lines and 15 points, with three lines through three points, three points on every line, and containing no triangles. It is illustrated above in two ...

The Danzer configuration is a 35_4 self-dual configuration of 35 lines and 35 points in which 4 points lie on each line and 4 lines pass through each point. The Levi graph of ...

A subspace A of X is called a deformation retract of X if there is a homotopy F:X×I->X (called a retract) such that for all x in X and a in A, 1. F(x,0)=x, 2. F(x,1) in A, ...

An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

A generalization of Turán's theorem to non-complete graphs.

A Euclidean number is a number which can be obtained by repeatedly solving the quadratic equation. Euclidean numbers, together with the rational numbers, can be constructed ...

A differential of the form df=P(x,y)dx+Q(x,y)dy (1) is exact (also called a total differential) if intdf is path-independent. This will be true if ...