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The connected sum M_1#M_2 of n-manifolds M_1 and M_2 is formed by deleting the interiors of n-balls B_i^n in M_i^n and attaching the resulting punctured manifolds M_i-B^._i ...

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

A constructive proof is a proof that directly provides a specific example, or which gives an algorithm for producing an example. Constructive proofs are also called ...

"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 general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological ...

The term "continuum" has (at least) two distinct technical meanings in mathematics. The first is a compact connected metric space (Kuratowski 1968; Lewis 1983, pp. 361-394; ...

An integral obtained by contour integration. The particular path in the complex plane used to compute the integral is called a contour. As a result of a truly amazing ...

The contrapedal curve, also called a normal pedal curve, is defined analogously to a usual pedal curve with "tangent" replaced by "normal." In particular, the contrapedal ...

A sequence is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, a sequence S_n converges to the limit S lim_(n->infty)S_n=S if, ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...