29 Dec '05 19:52

how is it possible to have a one-sided strip of paper? how about a one sided 3D object?

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under the sink29 Dec '05 21:111 editA Möbius ring actually has two sides because the paper has thickness.

Envision a flexible rectangular solid with dimensions of, say, 1 x 1 x 8. If you can join the two square ends together but incorporate a quarter twist in so doing, then you will have a 3D solid object with adjacent edges that are 90 degrees offset from each other and still only has one surface.- Joined
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30 Dec '05 14:331 edit

If you are looking for the 3D equivalent of the mobius strip, it is called a Klein Bottle. A true Klein bottle is actually 4 dimensional, but we (humans) make 3D projections of true Klein Bottles, and the inside does turn out to be the outside.*Originally posted by ketch90***how is it possible to have a one-sided strip of paper? how about a one sided 3D object?**- Joined
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Out of my mind31 Dec '05 07:56

Would you care to elaborate on that?*Originally posted by rheymans***If you are looking for the 3D equivalent of the mobius strip, it is called a Klein Bottle. A true Klein bottle is actually 4 dimensional, but we (humans) make 3D projections of true Klein Bottles, and the inside does turn out to be the outside.**

The mobius strip is still 2 dimensional btw...a cilindric shell is also 2 dimensional.

There is a formula so calculate the dimension of an object:

D = log(f)/log(2)

D is the dimension, f is the factor. The factor is how many times the object increases in size when the length/withs/depth/.. are doubled.

A cube thus has factor 8 and has dimension D=log(8)/log(2)=3

A mobius strip becomes 4 times as large and thus has dimension D=log(4)/log(2)=2

The Bottle has dimension 3.- Joined
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01 Jan '06 01:59

I am not familiar with the formula you have given for calculating dimensions. This link explains the Klein bottle better than I can.*Originally posted by TheMaster37***Would you care to elaborate on that?**

The mobius strip is still 2 dimensional btw...a cilindric shell is also 2 dimensional.

There is a formula so calculate the dimension of an object:

D = log(f)/log(2)

D is the dimension, f is the factor. The factor is how many times the object increases in size when the length/withs/depth/.. are doubled.

...[text shortened]... becomes 4 times as large and thus has dimension D=log(4)/log(2)=2

The Bottle has dimension 3.

http://www.kleinbottle.com/whats_a_klein_bottle.htm