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Let K_1^n and K_2^n be disjoint bicollared knots in R^(n+1) or S^(n+1) and let U denote the open region between them. Then the closure of U is a closed annulus S^n×[0,1]. ...

The augmented truncated dodecahedron is Johnson solid J_(68) constructed by affixing a pentagonal cupola to one of the decagonal faces of a truncated dodecahedron such that ...

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.

A quartic curve that resembles the symbol for the zodiacal sign Capricorn given by the implicit equation a^2x^2(x^2+y^2)-b(ay-x^2-y^2)^2=0, where a>0, b>a^2. The curve ...

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

The inverse curve of the cochleoid r=(sintheta)/theta (1) with inversion center at the origin and inversion radius k is the quadratrix of Hippias. x = ktcottheta (2) y = kt. ...

A complex rotation is a map of the form z|->ze^(itheta), where theta is a real number, which corresponds to counterclockwise rotation by theta radians about the origin of ...

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A intersection B))/(P(B)), (1) which can be proven directly using a ...

int_0^inftye^(-omegaT)cos(omegat)domega=T/(t^2+T^2), which can be computed using integration by parts.

The limit points of a set P, denoted P^'.