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Given triangle DeltaA_1A_2A_3, let the point of intersection of A_2Omega and A_3Omega^' be B_1, where Omega and Omega^' are the Brocard points, and similarly define B_2 and ...

The subset B of the Euclidean plane formed by the union of the interval [0,1] of the x-axis and all line segments of unit length passing through the origin which form an ...

Let f:M|->N be a map between two compact, connected, oriented n-dimensional manifolds without boundary. Then f induces a homomorphism f_* from the homology groups H_n(M) to ...

A bubble is a minimal-energy surface of the type that is formed by soap film. The simplest bubble is a single sphere, illustrated above (courtesy of J. M. Sullivan). More ...

Bürmann's theorem deals with the expansion of functions in powers of another function. Let phi(z) be a function of z which is analytic in a closed region S, of which a is an ...

If the section function of a centered convex body in n-dimensional Euclidean space (n>=3) is smaller than that of another such body, is its volume also smaller? The solution ...

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 ...

Given a chord PQ of a circle, draw any other two chords AB and CD passing through its midpoint. Call the points where AD and BC meet PQ X and Y. Then M is also the midpoint ...

A binary unit of information equal to 8 bits. Unfortunately, the storage of binary numbers in computers is not entirely standardized. Because computers store information in ...

A C-matrix is a symmetric (C^(T)=C) or antisymmetric (C^(T)=-C) C_n (-1,0,1)-matrix with diagonal elements 0 and others +/-1 that satisfies CC^(T)=(n-1)I, (1) where I is the ...