Gluing a Torus

Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus.

Often the fundamental group of the glued object can be calculated from the pieces (here a rectangles) and the glue (here two intersecting circles). The mathematical tool to do this is called the Seifert-van Kampen Theorem.

This Video was produces for a topology seminar at the Leibniz Universitaet Hannover.

http://www-ifm.math.uni-hannover.de/~fugru/?topologie_teil1

Category:

Howto & Style

Tags:

• topology
• mathematics
• glueing
• glue
• torus
• seifert
• van
• kampen
• bothmer
• fugru
• cg

[MrDrpersonman]

I'm going to make doughnuts like this from now on... ^_^

[erischaot]

don't thumb down if you don't explain the rules. wir verwenden ein theoretisches Material, was sich nicht wirklich wie Papier verhaelt. Es ist eher wie Gummi, und dann geht es. Ausserdem kann es sich selbst durchdringen, das wird hier aber nicht gebraucht. Die Animations ist schoen, etwas Erlaeuterung (Audio zum Video) waere schoener :)

[rubiksboi]

... and this makes a torus? whats amazing about it...its just a way to make a torus :|

[Phanu9000]

I love seeing all the people who know nothing about math saying that this is fake or not possible. Cracks me up lol

[SilverDHedgehog2]

this was great, considering the rules are that the material used would be infinitely elastic, cannot crease or tear! and this works accordiing to those rules

[818doodooroo]

0:13 we see that the paper is forming a donut, that is not possible because the outer radius and inner radius of a donut is not the same..

[mediteight]

A truly unique insult :) - many thanks.

If you're trying to say that you think I'm wrong you need to use "you're" instead of "your". I've given you an example in the previous sentence in case you still don't understand. (Just think, the one with the apostrophe is short for "you are" and you'll never have to make the same mistake again...)

Could you use your imaginatively creative language to give me a clue as to what you think I'm wrong about?...

[morningrunner123]

you doughnut frigging patronising piece of shit. your wrong

[mediteight]

Amusing idea - what does it even mean for a computer animation to be "phony"? :) The simulation seems to be illustrating nicely a topological idea - not a direct model of how to make a torus out of some non-stretchable piece of paper. But even if it were, it is starting with a rectangle - so the two lengths are not the same at the start...

[ilterisderici]

this is wrong also. In middle you have a smaller (inner ) circle , and when top reaches bottom ( 18 sec ), you have the longest (outer ) circle. However, you start with the same LENGTH to make 2 different circles the circumference of which are different. That is where it FAILS. Think about it guys, outer circle and inner circles are made from same length of SURFACE. This is PHONY !