Search Results for ""

On July 10, 2003, Eric Weisstein computed the numbers of n×n (0,1)-matrices all of whose eigenvalues are real and positive, obtaining counts for n=1, 2, ... of 1, 3, 25, 543, ...

The conjecture that, for any triangle, 8omega^3<ABC (1) where A, B, and C are the vertex angles of the triangle and omega is the Brocard angle. The Abi-Khuzam inequality ...

The square of the area of the base (i.e., the face opposite the right trihedron) of a trirectangular tetrahedron is equal to the sum of the squares of the areas of its other ...

D_q=1/(1-q)lim_(epsilon->0)(lnI(q,epsilon))/(ln(1/epsilon),) (1) where I(q,epsilon)=sum_(i=1)^Nmu_i^q, (2) epsilon is the box size, and mu_i is the natural measure. The ...

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

Van der Corput sequences are a means of generating sequences of points that are maximally self-avoiding (a.k.a. quasirandom sequences). In the one-dimensional case, the ...

An xyz embedding, also called an "xyz drawing," is a three-dimensional embedding such that every axis-parallel line contains either zero or two vertices. Such an embedding is ...

Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...

Let V(r) be the volume of a ball of radius r in a complete n-dimensional Riemannian manifold with Ricci curvature tensor >=(n-1)kappa. Then V(r)<=V_kappa(r), where V_kappa is ...

If f has no spectrum in [-lambda,lambda], then ||f||_infty<=pi/(2lambda)||f^'||_infty (1) (Bohr 1935). A related inequality states that if A_k is the class of functions such ...