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Consider the plane quartic curve X defined by x^3y+y^3z+z^3x=0, where homogeneous coordinates have been used here so that z can be considered a parameter (the plot above ...

A three-dimensional shadow of a four-dimensional Klein bottle.

A three-dimensional shadow of a four-dimensional Klein bottle.

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...

The system of partial differential equations del ^2s-(|a|^2+1)s = 0 (1) del ^2a-del (del ·a)-s^2a = a. (2)

f(z)=k/((cz+d)^r)f((az+b)/(cz+d)) where I[z]>0.

An algebraic surface of degree 12. Examples of dodecic surfaces include the figure-eight parametrization of the Klein bottle and Sarti dodecic.

A one-sided surface reminiscent of the Möbius strip, attributed to Gourmalin (Bouvier and George 1979, p. 477; Boas 1995). This surface is topologically equivalent to a Klein ...

The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

Let a closed surface have genus g. Then the polyhedral formula generalizes to the Poincaré formula chi(g)=V-E+F, (1) where chi(g)=2-2g (2) is the Euler characteristic, ...