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j_n(z)=(z^n)/(2^(n+1)n!)int_0^picos(zcostheta)sin^(2n+1)thetadtheta, where j_n(z) is a spherical Bessel function of the first kind.

Square line picking is the selection of pairs of points (corresponding to endpoints of a line segment) randomly placed inside a square. n random line segments can be picked ...

A quantity which transforms like a tensor except for a scalar factor of a Jacobian.

257 is a Fermat prime, and the 257-gon is therefore a constructible polygon using compass and straightedge, as proved by Gauss. An illustration of the 257-gon is not included ...

Place two solid spheres of radius 1/2 inside a hollow sphere of radius 1 so that the two smaller spheres touch each other at the center of the large sphere and are tangent to ...

A 3-cusped hypocycloid, also called a tricuspoid. The deltoid was first considered by Euler in 1745 in connection with an optical problem. It was also investigated by Steiner ...

Find the plane lamina of least area A which is capable of covering any plane figure of unit generalized diameter. A unit circle is too small, but a hexagon circumscribed on ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

Find the minimum size square capable of bounding n equal squares arranged in any configuration. The first few cases are illustrated above (Friedman). The only packings which ...

The angular twist theta of a shaft with given cross section is given by theta=(TL)/(KG) (1) (Roark 1954, p. 174), where T is the twisting moment (commonly measured in units ...