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A game in which no draw is possible. Steinhaus (1999, p. 16) stated that all categorical games are unfair, but this is incorrect. For example, the game "Odds or Evens" pits ...

The word "median" has several different meanings in mathematics all related to the "middle" of mathematical objects. The statistical median is an order statistic that gives ...

An extremal graph in which the forced triangles are all the same color. Call R the number of red monochromatic forced triangles and B the number of blue monochromatic forced ...

Divide a set of data into two groups (high and low) of equal size at the statistical median if there is an even number of data points, or two groups consisting of points on ...

A circle having a given number of lattice points on its circumference. The Schinzel circle having n lattice points is given by the equation {(x-1/2)^2+y^2=1/45^(k-1) for n=2k ...

Given relatively prime integers p and q (i.e., (p,q)=1), the Dedekind sum is defined by s(p,q)=sum_(i=1)^q((i/q))(((pi)/q)), (1) where ((x))={x-|_x_|-1/2 x not in Z; 0 x in ...

The symbol used by engineers and some physicists to denote i, the imaginary number sqrt(-1). j is probably preferred over i because the symbol i (or I) is commonly used to ...

A complex number z may be represented as z=x+iy=|z|e^(itheta), (1) where |z| is a positive real number called the complex modulus of z, and theta (sometimes also denoted phi) ...

Catalan (1876, 1891) noted that the sequence of Mersenne numbers 2^2-1=3, 2^3-1=7, and 2^7-1=127, and (OEIS A007013) were all prime (Dickson 2005, p. 22). Therefore, the ...

A repunit is a number consisting of copies of the single digit 1. The term "repunit" was coined by Beiler (1966), who also gave the first tabulation of known factors. In ...