Following on from the "how many sides does a sphere have?" thread, I thought it might be interesting to see how people react when asked to describe Klein Bottles.

 

How many (a) sides, (b) surfaces, © edges, (d) contained volumes do they have?

a)1 b)1 c)0 d) 0

Maybe.

 

I remember hearing about those. Weird. I should show my math teacher when we're doing geometry.

Saw the movie about the building up of a Klein bottle.

a.1

b.1

c.0

d.?

And one more question, what is their use (if they have one)?

a. 1

b. 1

c. 0

d. not sure, maybe 0, but dont know for sure...

 

and repeating solaris, why are they special? is it because of the answer to the question sayo posted in his 1st post?

a)[MATH]\infty[/MATH]

b)1

c)0

d)1

1)?

2)1

3)0

4)1

 

Pretty much same as pulkit, though #1 is still questionable for much the same reasons as the circle with so questionable. If I had to guess, though, I'd say 1.

the volume or capacity is dependant on it`s size, with rotational manipulation to avoid air pockets, one could easily fill such a bottle with water to determine this

 

I`ll think about the other 3 later

Too much to think about, eh? YT?

 

[Edit]

 

This is way over the top of my head!

What are you saying YT? Which question were you trying to answer? I'm assuming #4, but that asks how many contained volumes there are, not how much the contained volume is. Can you explain?

Why isn't where the neck rejoins the body considered an edge?

but can be physically realized only in four dimensions, since it must pass through itself without the presence of a hole

 

I don't understand sides, corners, edges and contained volumes when it comes to 4D...

 

Nice shape though.

The answer is Inside and Outside

The answer is Inside and Outside

 

 

 

No, it's not. A klein bottle's inside and outside are the same side

https://en.wikipedia.org/wiki/Klein_bottle

Why isn't where the neck rejoins the body considered an edge?

 

The neck doesn't rejoin the body in a true Klein bottle. What you have seen is a three dimensional representation if a figure that only exists in four dimensions.