posted on Aug, 30 2005 @ 03:34 PM
The following is compliments of World Book Encyclopedia Online:
Topology, «tuh POL uh jee», is a branch of mathematics that explores certain properties of geometrical figures. The properties are those that do
not change when the figures are deformed by bending, stretching, or molding. Topology makes no distinction between a sphere and a cube because these
figures can be molded into one another. Topology makes a distinction between a sphere and a torus (a doughnut-shaped figure) because a sphere cannot
be deformed into a torus without being torn. Topology is called rubber-sheet geometry because its figures can be deformed.
Unlike high school geometry, topology ignores straightness, parallelism, and distance because deformation can alter them. Instead, topology studies
such problems as the number of intersections made by a curve with itself, whether a surface is closed or has boundaries, and whether or not a surface
Topology makes up theorems and tries to prove them. The four-color theorem applies to maps. It states that four colors are sufficient to color any map
so that, in any group of adjacent countries, each country is a different color. The American mathematician Kenneth Appel and the German-born
mathematician Wolfgang Haken proved the theorem in 1976.
Then I recommend you check out various websites that deal with something called Knot Theory. Now, you may think Knots are boring, but if you're
curious about geometric shapes and their impact of reality, consider how the shape of something the size of Earth might have it's gravitational pull
affected because it's the shape of...oh, say...a Granny knot.
Consider this: Our own sun is a simple sphere. Yet, it has a whole multitude of Magnetic Polar Points whereas our Earth has two.
[edit on 30-8-2005 by Toelint]