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An algebraic variety over a field K that becomes isomorphic to a projective space.

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 ...

For the cardioid given parametrically as x = a(1+cost)cost (1) y = a(1+cost)sint, (2) the involute is given by x_i = 2a+3acostheta(1-costheta) (3) y_i = ...

The conjecture proposed by Catalan in 1888 and extended by E. Dickson that each aliquot sequence ends in a prime, a perfect number, or a set of sociable numbers. The ...

A sum of the digits in a given transmission modulo some number. The simplest form of checksum is a parity bit appended on to 7-bit numbers (e.g., ASCII characters) such that ...

Given two closed curves, the circuminscribed curve is simultaneously inscribed in the outer one and circumscribed on the inner one.

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

Code 912 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...