29 Dec 05
1 edit
A 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.
30 Dec 05
1 edit
Originally posted by ketch90If 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.
how is it possible to have a one-sided strip of paper? how about a one sided 3D object?
31 Dec 05
Originally posted by rheymansWould you care to elaborate on that?
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.
01 Jan 06
Originally posted by TheMaster37I am not familiar with the formula you have given for calculating dimensions. This link explains the Klein bottle better than I can.
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