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The mean triangle area of a triangle picked inside a regular n-gon of unit area is A^__n=(9cos^2omega+52cosomega+44)/(36n^2sin^2omega), (1) where omega=2pi/n (Alikoski 1939; ...

In general, polynomial equations higher than fourth degree are incapable of algebraic solution in terms of a finite number of additions, subtractions, multiplications, ...

A root of a polynomial P(z) is a number z_i such that P(z_i)=0. The fundamental theorem of algebra states that a polynomial P(z) of degree n has n roots, some of which may be ...

Let n be a positive nonsquare integer. Then Artin conjectured that the set S(n) of all primes for which n is a primitive root is infinite. Under the assumption of the ...

Let K be a number field with r_1 real embeddings and 2r_2 imaginary embeddings and let r=r_1+r_2-1. Then the multiplicative group of units U_K of K has the form ...

A rooted tree is a tree in which a special ("labeled") node is singled out. This node is called the "root" or (less commonly) "eve" of the tree. Rooted trees are equivalent ...

A line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a ...

Multiply all the digits of a number n by each other, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative ...

Given a field F and an extension field K superset= F, an element alpha in K is called algebraic over F if it is a root of some nonzero polynomial with coefficients in F. ...

The radical circle of the mixtilinear incircles has a center with trilinear center function alpha_(999)=cosA-2, (1) which is Kimberling center X_(999). It has radius (2) ...