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.
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?
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.
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