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Topology

Hyperbolic Space

Here are two computer-animated videos from Youtube that demonstrate some properties of knots, the relations between knots and space, and how we arrive at hyperbolic space. Easy to watch, and very informative.   Part Two:  

/ January 13, 2013

Poincaré Conjecture

This explanation is quoted from the  The Clay Mathematics Institute, Poincaré Conjecture. (solved by: Grigoriy Perelman, 2002-3) “If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving...

/ November 22, 2011

Knot theory

Knot theory is a very fast growing field of mathematics.  Knots are not natural phenomena, and there exists only a finite number of distinct knots in three-dimensional space. Knots define spaces, because we can think of a knot as a...

/ November 22, 2011

Klein Bottle

The Klein bottle is the next step up from a Moebius strip.  A Moebius Strip is a two-dimensional object in three-dimensional space, and a Klein Bottle is a one-dimensional object in three-dimensional space. Therefore, it has to intersect itself in...

/ November 21, 2011

Topology

Definition Topology is a mathematical sub-discipline that studies the properties of objects and spaces. Topology is the modern version of geometry; it was used first in 1847 by the German mathematician Johann Benedict Listing. The shapes of objects can change...

/ November 8, 2011