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Given a matrix A, a Jordan basis satisfies Ab_(i,1)=lambda_ib_(i,1) and Ab_(i,j)=lambda_ib_(i,j)+b_(i,j-1), and provides the means by which any complex matrix A can be ...

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.

The identity (xy)x^2=x(yx^2) satisfied by elements x and y in a Jordan algebra.

For 0<=x<=pi/2, 2/pix<=sinx<=x.

The throwing and catching of multiple objects such that at least one is always in the air. Some aspects of juggling turn out to be quite mathematical. The best examples are ...

A point of discontinuity, also called a leap.

A geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...

A bistable eight-sided polyhedron discovered by Wunderlich and Schwabe (1986).

An optical illusion, illustrated above, in which the eye perceives a white upright equilateral triangle where none is actually drawn.

D_(KY)=j+(sigma_1+...+sigma_j)/(|sigma_(j+1)|), (1) where sigma_1<=sigma_n are Lyapunov characteristic exponents and j is the largest integer for which ...