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A unit-distance graph is a distance graph having an embedding in the Euclidean plane (unit-distance embedding) in which vertices are distinct points and all edges are of ...

A Hadamard matrix is a type of square (-1,1)-matrix invented by Sylvester (1867) under the name of anallagmatic pavement, 26 years before Hadamard (1893) considered them. In ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

Two fractions are said to be adjacent if their difference has a unit numerator. For example, 1/3 and 1/4 are adjacent since 1/3-1/4=1/12, but 1/2 and 1/5 are not since ...

The set A^2 of all ordered pairs of complex numbers.

Arnauld's paradox states that if negative numbers exist, then (-1)/1 must equal 1/(-1), which asserts that the ratio of a smaller to a larger quantity equals the ratio of the ...

The sequence whose definition is: "t is the first, fourth, eleventh, ... letter of this sentence." The first few values are 1, 4, 11, 16, 24, 29, 33, 35, 39, ... (OEIS ...

The field of complex numbers, denoted C.

Two complex numbers z=x+iy and z^'=x^'+iy^' are added together componentwise, z+z^'=(x+x^')+i(y+y^'). In component form, (x,y)+(x^',y^')=(x+x^',y+y^') (Krantz 1999, p. 1).

The division of two complex numbers can be accomplished by multiplying the numerator and denominator by the complex conjugate of the denominator, for example, with z_1=a+bi ...