Dimensional twists

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

Originally posted by ketch90
how about a one sided 3D object?

A solid sphere.

A one-sided strip of paper (Möbius ring) is a 3D object.

Originally posted by Mephisto2
A one-sided strip of paper (Möbius ring) is a 3D object.

Are you sure?

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.

is it possible to make a bottle one-sided?

Well there is the Klein bottle. Not exactly a bottle though...

Originally posted by Bowmann
Are you sure?

Approximatively. I assumed a "strip" to be of 2D nature (lenght, width and no/extremely small depth) and you need a 3d dimension to give it a twist to make a Möbius ring.

Si no e vero, e bien trovato.

no habla espanol

Originally posted by ketch90
is it possible to make a bottle one-sided?

is a doughnut one-sided?

Originally posted by The Plumber
is a doughnut one-sided?

Not Nessie celery.

Originally posted by ketch90
how is it possible to have a one-sided strip of paper? how about a one sided 3D object?

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 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.

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.

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 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.

I am not familiar with the formula you have given for calculating dimensions. This link explains the Klein bottle better than I can.

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