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The Heaviside step function is a mathematical function denoted H(x), or sometimes theta(x) or u(x) (Abramowitz and Stegun 1972, p. 1020), and also known as the "unit step ...

Keller conjectured that tiling an n-dimensional space with n-dimensional hypercubes of equal size yields an arrangement in which at least two hypercubes have an entire ...

The Klein bottle crossing number of a graph G is the minimum number of crossings possible when embedding G on a Klein bottle (cf. Garnder 1986, pp. 137-138). While the ...

Kobon Fujimura asked for the largest number N(n) of nonoverlapping triangles that can be constructed using n lines (Gardner 1983, p. 170). A Kobon triangle is therefore ...

Let z be defined as a function of w in terms of a parameter alpha by z=w+alphaphi(z). (1) Then Lagrange's inversion theorem, also called a Lagrange expansion, states that any ...

A normalized form of the cumulative normal distribution function giving the probability that a variate assumes a value in the range [0,x], ...

If all the diagonals--including those obtained by "wrapping around" the edges--of a magic square sum to the same magic constant, the square is said to be a panmagic square ...

An ambiguous figure in which the brain switches between seeing a rabbit and a duck. The duck-rabbit was "originally noted" by American psychologist Joseph Jastrow (Jastrow ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

A Smith number is a composite number the sum of whose digits is the sum of the digits of its prime factors (excluding 1). (The primes are excluded since they trivially ...