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The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...

Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

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 ...

The Buffon-Laplace needle problem asks to find the probability P(l,a,b) that a needle of length l will land on at least one line, given a floor with a grid of equally spaced ...

It is always possible to "fairly" divide a cake among n people using only vertical cuts. Furthermore, it is possible to cut and divide a cake such that each person believes ...

Cartesian coordinates are rectilinear two- or three-dimensional coordinates (and therefore a special case of curvilinear coordinates) which are also called rectangular ...

The nth central trinomial coefficient is defined as the coefficient of x^n in the expansion of (1+x+x^2)^n. It is therefore the middle column of the trinomial triangle, i.e., ...

A class of complete orientable minimal surfaces of R^3 derived from Enneper's minimal surface. They are named for the mathematicians who found the first two examples in 1982. ...

Continuum percolation can be thought of as a continuous, uncountable version of percolation theory-a theory which, in its most studied form, takes place on a discrete, ...

A convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities mx<=b, where m is a real s×3 matrix and b is a real s-vector. ...