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The number two (2) is the second positive integer and the first prime number. It is even, and is the only even prime (the primes other than 2 are called the odd primes). The ...

An affine variety V is an algebraic variety contained in affine space. For example, {(x,y,z):x^2+y^2-z^2=0} (1) is the cone, and {(x,y,z):x^2+y^2-z^2=0,ax+by+cz=0} (2) is a ...

An alternating permutation is an arrangement of the elements c_1, ..., c_n such that no element c_i has a magnitude between c_(i-1) and c_(i+1) is called an alternating (or ...

An antimagic square is an n×n array of integers from 1 to n^2 such that each row, column, and main diagonal produces a different sum such that these sums form a sequence of ...

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

An official chessboard is an 8×8 board containing squares alternating in color between olive green and buff (where "buff" is a color variously defined as a moderate orange ...

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

There are no fewer than three distinct notions of curve throughout mathematics. In topology, a curve is a one-dimensional continuum (Charatonik and Prajs 2001). In algebraic ...

The number N_d^((b))(n) of digits d in the base-b representation of a number n is called the b-ary digit count for d. The digit count is implemented in the Wolfram Language ...

The classic treatise in geometry written by Euclid and used as a textbook for more than 1000 years in western Europe. An Arabic version The Elements appears at the end of the ...