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The triangular orthobicupola is Johnson solid J_(27), consisting of eight equilateral triangles and six squares. If a triangular orthobicupola is oriented with triangles on ...

There are at least two results known as "the area principle." The geometric area principle states that (|A_1P|)/(|A_2P|)=(|A_1BC|)/(|A_2BC|). (1) This can also be written in ...

The p-layer of H, L_(p^')(H) is the unique minimal normal subgroup of H which maps onto E(H/O_(p^')(H)).

An antimagic square is an n×n array of integers from 1 to n^2 such that each row, column, and main diagonal produces a different sum such that these sums form a sequence of ...

There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo ...

An illusion is an object or drawing which appears to have properties which are physically impossible, deceptive, or counterintuitive. Kitaoka maintains a web page of ...

The Jacobi polynomials, also known as hypergeometric polynomials, occur in the study of rotation groups and in the solution to the equations of motion of the symmetric top. ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method (MINRES) and ...