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The summatory function Phi(n) of the totient function phi(n) is defined by Phi(n) = sum_(k=1)^(n)phi(k) (1) = sum_(m=1)^(n)msum_(d|m)(mu(d))/d (2) = ...

A permutation group in which the permutations are limited to transpositions.

A word derived from the Latin roots tri- (three) and via (ways, roads), therefore a crossing of three roads. In medieval universities, the trivium consisted of the three ...

The catacaustic of the Tschirnhausen cubic with parametric representation x = 3(t^2-3) (1) y = t(t^2-3) (2) with radiant point at (-8,0) is the semicubical parabola with ...

The ultraradical symbol is a notation thet can be used to express solutions not obtainable by finite root extraction. The solution to the irreducible quintic equation x^5+x=a ...

Possessing a single unique mode. The term unimodal distribution, which refers to a distribution having a single local maximum is a slight corruption of this definition.

A "visual representation" number which is a sum of some simple function of its digits. For example, 1233 = 12^2+33^2 (1) 2661653 = 1653^2-266^2 (2) 221859 = 22^3+18^3+59^3 ...

The substitution of x=w-p/(3w) (1) into the standard form cubic equation x^3+px=q. (2) The result reduces the cubic to the equation w^3-(p^3)/(27w^3)-q=0, (3) which is easily ...

A horizontal line placed above multiple quantities to indicate that they form a unit. It is most commonly used to denote 1. A radical (sqrt(12345)), 2. Repeating decimals ...

Wilker's inequalities state that 2+(16)/(pi^4)x^3tanx<(sin^2x)/(x^2)+(tanx)/x<2+2/(45)x^3tanx for 0<x<pi/2, where the constants 2/45 and 16/pi^4 are the best possible ...