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Given a principal bundle pi:A->M, with fiber a Lie group G and base manifold M, and a group representation of G, say phi:G×V->V, then the associated vector bundle is ...

The binary logarithm log_2x is the logarithm to base 2. The notation lgx is sometimes used to denote this function in number theoretic literature. However, because Russian ...

The number of binary bits necessary to represent a number, given explicitly by BL(n) = 1+|_lgn_| (1) = [lg(n+1)], (2) where [x] is the ceiling function, |_x_| is the floor ...

Calabi's triangle is the unique triangle other that the equilateral triangle for which the largest inscribed square can be inscribed in three different ways (Calabi 1997). ...

A Cartesian product of any finite or infinite set I of copies of Z_2, equipped with the product topology derived from the discrete topology of Z_2. It is denoted Z_2^I. The ...

If r is the inradius of a circle inscribed in a right triangle with sides a and b and hypotenuse c, then r=1/2(a+b-c). (1) A Sangaku problem dated 1803 from the Gumma ...

The word "degree" has many meanings in mathematics. The most common meaning is the unit of angle measure defined such that an entire rotation is 360 degrees. This unit harks ...

A set A in a first-countable space is dense in B if B=A union L, where L is the set of limit points of A. For example, the rational numbers are dense in the reals. In ...

An elongated square pyramid is a solid formed by attaching a square pyramid atop a square prism. Such a solid might also be termed an obelisk (although that term is also used ...

Define an emirpimes ("semiprime" spelled backwards) as a semiprime whose (base 10) reversal is a different semiprime. The first such number is 15, because 15 reversed is 51 ...