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Given a Pythagorean triple (a,b,c), the fractions a/b and b/a are called Pythagorean fractions. Diophantus showed that the Pythagorean fractions consist precisely of ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...

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 ...

The Cauchy distribution, also called the Lorentzian distribution or Lorentz distribution, is a continuous distribution describing resonance behavior. It also describes the ...

An algebraic surface with affine equation P_d(x_1,x_2)+T_d(x_3)=0, (1) where T_d(x) is a Chebyshev polynomial of the first kind and P_d(x_1,x_2) is a polynomial defined by ...

Cluster analysis is a technique used for classification of data in which data elements are partitioned into groups called clusters that represent collections of data elements ...

In voting theory, a Condorcet candidate is a candidate who always wins in a 2-person election but loses in larger election. For example, consider the 6-tuples of 6-sided die ...

The "contiguous USA graph" is the graph whose vertices represent the contiguous 48 states of the United States plus the District of Columbia (DC) and whose edges connect ...

The number of digits D in an integer n is the number of numbers in some base (usually 10) required to represent it. The numbers 1 to 9 are therefore single digits, while the ...

Let four lines in a plane represent four roads in general position, and let one traveler T_i be walking along each road at a constant (but not necessarily equal to any other ...