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Four circles may be drawn through an arbitrary point P on a torus. The first two circles are obvious: one is in the plane of the torus and the second perpendicular to it. The ...

The term "wedge" has a number of different meanings in mathematics. It is sometimes used as another name for the caret symbol. The term also refers to the notation ( ^ ) used ...

Let (K,L) be a pair consisting of finite, connected CW-complexes where L is a subcomplex of K. Define the associated chain complex C(K,L) group-wise for each p by setting ...

A famous perceptual illusion in which the brain switches between seeing a young girl and an old woman (or "wife" and "mother in law"). An anonymous German postcard from 1888 ...

Analysis

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

The first of the Hardy-Littlewood conjectures. The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, ...

Given a Hilbert space H, a *-subalgebra A of B(H) is said to be a von Neumann algebra in H provided that A is equal to its bicommutant A^('') (Dixmier 1981). Here, B(H) ...

666 is the occult "number of the beast," also called the "sign of the devil" (Wang 1994), associated in the Bible with the Antichrist. It has figured in many numerological ...

The first Brocard point is the interior point Omega (also denoted tau_1 or Z_1) of a triangle DeltaABC with points labeled in counterclockwise order for which the angles ...