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Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

A figurate number Te_n of the form Te_n = sum_(k=1)^(n)T_k (1) = 1/6n(n+1)(n+2) (2) = (n+2; 3), (3) where T_k is the kth triangular number and (n; m) is a binomial ...

The mean tetrahedron volume of a tetrahedron with vertices chosen at random inside another tetrahedron of unit volume is given by V^_ = (13)/(720)-(pi^2)/(15015) (1) = ...

Every semisimple Lie algebra g is classified by its Dynkin diagram. A Dynkin diagram is a graph with a few different kinds of possible edges. The connected components of the ...

A property of X is said to hold almost everywhere if the set of points in X where this property fails is contained in a set that has measure zero.

An object is amphichiral (also called reflexible) if it is superposable with its mirror image (i.e., its image in a plane mirror).

The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry ...

1. A fixed polyomino. 2. The set of points obtained by taking the centers of a fixed polyomino.

The radial curve of the astroid x = acos^3t (1) y = asin^3t (2) is the quadrifolium x_r = x_0+12acostsin^2t (3) y_r = y_0+12acos^2tsint. (4)

The set of points in the space of system variables such that initial conditions chosen in this set dynamically evolve to a particular attractor.