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In a 1631 edition of Academiae Algebrae, J. Faulhaber published the general formula for the power sum of the first n positive integers, sum_(k=1)^(n)k^p = H_(n,-p) (1) = ...

The integral 1/(2pi(n+1))int_(-pi)^pif(x){(sin[1/2(n+1)x])/(sin(1/2x))}^2dx which gives the nth Cesàro mean of the Fourier series of f(x).

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

Values one step outside the hinges are called inner fences, and values two steps outside the hinges are called outer fences. Tukey calls values outside the outer fences far ...

A partial order defined by (i-1, i), (i+1, i) for odd i.

A plane curve of the form y=x^n. For n>0, the curve is a generalized parabola; for n<0 it is a generalized hyperbola.

The Diophantine equation x^n+y^n=z^n. The assertion that this equation has no nontrivial solutions for n>2 has a long and fascinating history and is known as Fermat's last ...

The W-polynomials obtained by setting p(x)=3x and q(x)=-2 in the Lucas polynomial sequence. The first few Fermat polynomials are F_1(x) = 1 (1) F_2(x) = 3x (2) F_3(x) = ...

In a given acute triangle DeltaABC, locate a point whose distances from A, B, and C have the smallest possible sum. The solution is the point from which each side subtends an ...

Ferrari's identity is the algebraic identity