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Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to another in the least time. The term ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

A ternary diagram is a triangular diagram which displays the proportion of three variables that sum to a constant and which does so using barycentric coordinates. The ...

A circle that in internally tangent to two sides of a triangle and to the circumcircle is called a mixtilinear incircle. There are three mixtilinear incircles, one ...

The Abel prize is a new mathematics prize of the Norwegian Academy of Science and Letters, dedicated to the memory of Niels Henrik Abel (1802-1829) on the occasion of the ...

Given a differential operator D on the space of differential forms, an eigenform is a form alpha such that Dalpha=lambdaalpha (1) for some constant lambda. For example, on ...

A curvature of a submanifold of a manifold which depends on its particular embedding. Examples of extrinsic curvature include the curvature and torsion of curves in ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

Let the elliptic modulus k satisfy 0<k^2<1, and the Jacobi amplitude be given by phi=amu with -pi/2<phi<pi/2. The incomplete elliptic integral of the first kind is then ...