The HyperSphere, from an Artistic point of View

The mathematical objects that live on the sphere in four dimensional space -- the hypersphere -- are both beautiful and interesting. The four dimensional sphere is a unique object, with properties both similar to and surprisingly different from those of our ordinary sphere. Similarly to the case in three dimensions, there is a family of Platonic and Archimedean solids that can be viewed on the four dimensional sphere. These shapes can be seen to have a structure that is comfortingly analogous to that of the Platonic solids we know and love. However, there are some properties of the four dimensional sphere that are startlingly different. In contrast to the ordinary sphere, it is possible to "comb the hair" on the four dimensional sphere. That is to say, there is a continous one-dimensional flow that maps this space to itself. This is a deep property that gives this space important and unique physical characteristics. This flow is made up of a family of circles, each of which link every other one exactly once. Images which show off this property can be strikingly beautiful. These images can also be used to explain important ideas in physics and mathematics, but this essay concentrates on their aesthetic appeal and possibilities.

:Link:
_________________

Aquarchy Rules. Liquidate the Reds

ANCAPS Forum, Ancapolis, Aqua-Terra Atlantis Division.

_________________

Aquarchy Rules. Liquidate the Reds

ANCAPS Forum, Ancapolis, Aqua-Terra Atlantis Division.