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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).

The Kampyle of Eudoxus is a curve studied by Eudoxus in relation to the classical problem of cube duplication. It is given by the polar equation r=asec^2theta, (1) and the ...

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 ...

A generalization of the Runge-Kutta method for solution of ordinary differential equations, also called Rosenbrock methods.

The system of partial differential equations f_x = 2fgc(x-t) (1) g_t = 2fgc(x-t). (2)

Let D be a domain in R^n for n>=3. Then the transformation v(x_1^',...,x_n^')=(a/(r^'))^(n-2)u((a^2x_1^')/(r^('2)),...,(a^2x_n^')/(r^('2))) onto a domain D^', where ...