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Given an n-ball B^n of radius R, find the distribution of the lengths s of the lines determined by two points chosen at random within the ball. The probability distribution ...

A barrel solid of revolution composed of parallel circular top and bottom with a common axis and a side formed by a smooth curve symmetrical about the midplane. The term also ...

Given two normal subgroups G_1 and G_2 of a group, and two normal subgroups H_1 and H_2 of G_1 and G_2 respectively, H_1(G_1 intersection H_2) is normal in H_1(G_1 ...

A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). For a right circular cone, let s be the slant height and R_1 ...

The cross polytope beta_n is the regular polytope in n dimensions corresponding to the convex hull of the points formed by permuting the coordinates (+/-1, 0, 0, ..., 0). A ...

Dots and boxes is a two-person game based on a rectangular lattice of points. Each player, in turn, draws a horizontal or vertical line connecting two adjacent points. ...

An inellipse inconic that is an ellipse. The locus of the centers of the ellipses inscribed in a triangle is the interior of the medial triangle. Newton gave the solution to ...

An interval is a connected portion of the real line. If the endpoints a and b are finite and are included, the interval is called closed and is denoted [a,b]. If the ...

The Paris-Harrington theorem is a strengthening of the finite Ramsey's theorem by requiring that the homogeneous set be large enough so that cardH>=minH. Clearly, the ...

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid. For a right pyramidal frustum, let s be the slant height, h the ...