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Gabriel's horn, also called Torricelli's trumpet, is the surface of revolution of the function y=1/x about the x-axis for x>=1. It is therefore given by parametric equations ...

Clausen's integral, sometimes called the log sine integral (Borwein and Bailey 2003, p. 88) is the n=2 case of the S_2 Clausen function Cl_2(theta) = ...

Let a convex polygon be inscribed in a circle and divided into triangles from diagonals from one polygon vertex. The sum of the radii of the circles inscribed in these ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...

An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers. In the season 7, ...

The function Pi_(a,b)(x)=H(x-a)-H(x-b) which is equal to 1 for a<=x<=b and 0 otherwise. Here H(x) is the Heaviside step function. The special case Pi_(-1/2,1/2)(x) gives the ...

x^(2n)+1=[x^2-2xcos(pi/(2n))+1] ×[x^2-2xcos((3pi)/(2n))+1]×...× ×[x^2-2xcos(((2n-1)pi)/(2n))+1].

Given a vector bundle pi:E->M, its dual bundle is a vector bundle pi^*:E^*->M. The fiber bundle of E^* over a point p in M is the dual vector space to the fiber of E.

Let Pi(x) be the rectangle function, then the Fourier transform is F_x[Pi(x)](k)=sinc(pik), where sinc(x) is the sinc function.

Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...