# Tagged: 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...

## Turning a Sphere inside-out

How do you turn a sphere inside out, without punching a hole into it? It is possible,as you can see in the transformations in this fascinating video:

## 0 to 6 dimensions and back – simple rotation.

This is a simple computer-simulated rotation from a point, which has 0 dimensions, to a line (1 dimension), a square (2), a cube (3), all the way up to 6...

## Tesseracts: from 3 to 4 Dimensions.

The short video clip below shows the 3D rotations of a 4D object. The deeper questions concern the nature of a “dimension”. How do we know what a dimension is, and if we live in a 3D universe, could we possible also exist in a higher-dimensional universe? it is best to start with simple examples in order to train the mind to think about these questions. The clip below shows a tesseract, which is the four-dimensional analog of a cube. (In geomery, it is called a regular octachoron or cubic prism.) The tesseract is to the cube as the cube is to the square.

## 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...

## 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...

## 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...

## 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...