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Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

A perfect magic cube is a magic cube for which the rows, columns, pillars, space diagonals, and diagonals of each n×n orthogonal slice sum to the same number (i.e., the magic ...

The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

When two cycles have a transversal intersection X_1 intersection X_2=Y on a smooth manifold M, then Y is a cycle. Moreover, the homology class that Y represents depends only ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♭. Then A is a right Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

A left Hilbert Algebra A whose involution is an antilinear isometry is called a unimodular Hilbert algebra. The involution is usually denoted xi|->xi^*.

Transitivity is a result of the symmetry in the group. A group G is called transitive if its group action (understood to be a subgroup of a permutation group on a set Omega) ...

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...