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A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...

Simpson's rule is a Newton-Cotes formula for approximating the integral of a function f using quadratic polynomials (i.e., parabolic arcs instead of the straight line ...

Given a triangle with one vertex at the origin and the others at positions v_1 and v_2, one might think that a random point inside the triangle would be given by ...

If M^3 is a closed oriented connected 3-manifold such that every simple closed curve in M lies interior to a ball in M, then M is homeomorphic with the hypersphere, S^3.

A relation between compact boundaryless manifolds (also called closed manifolds). Two closed manifolds are bordant iff their disjoint union is the boundary of a compact ...

While some authors define "circumference" as distance around an arbitrary closed object (sometimes restricted to a closed curved object), in the work, the term "perimeter" is ...

A subset of a topological space is called clopen if it is both closed and open.

The quartic surface resembling a squashed round cushion on a barroom stool and given by the equation z^2x^2-z^4-2zx^2+2z^3+x^2-z^2 -(x^2-z)^2-y^4-2x^2y^2-y^2z^2+2y^2z+y^2=0.

The double sphere is the degenerate quartic surface (x^2+y^2+z^2-r^2)^2=0 obtained by squaring the left-hand side of the equation of a usual sphere x^2+y^2+z^2-r^2=0.

A closed ideal I in a C^*-algebra A is called essential if I has nonzero intersection with every other nonzero closed ideal A or, equivalently, if aI={0} implies a=0 for all ...