the torus, page
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reply posted on 30-8-2005 @ 11:41 AM by Annacryst
harmonicresolution.com...

what i know about it so far ive learned from this site, so my understanding is most basic at that.


reply posted on 30-8-2005 @ 03:34 PM by Toelint
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 is connected.

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.
END

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.

Weird, eh?



[edit on 30-8-2005 by Toelint]
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