# Turning a sphere inside out (video)

• awvvu
In summary, the video is about a sphere that has a different euler characteristic depending on the color of the dome or bowl. It is an amazing video and has many real world applications.
awvvu
Some of you guys have probably seen this before, but I thought this was really interesting:

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HORRIBLE voice acting, but really cool stuff nonetheless.

This is for you smart math number theory working at NSA people.

That's pretty amazing. I wonder if it would be possible to work out how to do it for n dimensions 3=>. Those crazy pure maths cats.

I wonder if you could reduce the time by using extra dimensions. I wonder if you could prove that you can?

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Cyrus said:
This is for you smart math number theory working at NSA people.

what does this have to do with number theory

Dont people who do number theory crack codes at the NSA?

That's topology on steroids.

Hmph. It is utterly incomprehensible with the audio off.

DaveC426913 said:
Hmph. It is utterly incomprehensible with the audio off.

hahaha what do you expect?

I was expressing myself so much that things got worse somewhere along the microphone plugin

I seriously don't know what was-is going on

Believe it or not a sphere eversion video (the optiverse i think it was called) was actually one of the reasons I became interested in math in the first place.

I wonder what kind of real-world applications sphere-eversion has...

This would make a good action movie. The music is fitting. All it needs is maybe an antagonist (any ideas?) and some romance between the narrators and its good to go.

i was enjoying it, although getting impatient with the pacing, until the narrator said the euler characteristic of a sphere equals 1, instead of the correct number, 2.

but i was learning something.or maybe they were using a modification of the euler number, involving the coloring of the domes and bowls, to make it come out 1.

Well, is the 'sphere' part of this very useful in the real world as it has so many real world applications?----

Now, I can see why those being more pure mathematicians invented string theory and MWI, and have promoted it;-- and, why it hasn't been worked on experimentally in the labs.

(nice cgi animations, though, for the 'explanation')

I was just watching that the other day. It's a little slow at times, but not too bad overall.

mathwonk said:
i was enjoying it, although getting impatient with the pacing, until the narrator said the euler characteristic of a sphere equals 1, instead of the correct number, 2.
That wasn't the Euler number, was it?

Wow. Seeing it the first time is mind boggling. What makes it even more amazing is the fact that this was first worked out on paper.
Does anybody know if there's a formal way of "ruffling" the surface of the sphere? Are there any simpler ways of doing it?

ehrenfest said:
I wonder what kind of real-world applications sphere-eversion has...

Believe it or not leading string theorists believe our universe is a giant sphere and at the nodes of intersection between two parts of the sphere are black holes.

::/End Sarcasm::

Does it need an application?

That was so cool to watch. This was actually my first time of ever hearing about it, let alone watching it. I enjoyed it though, and learned some too :)

Heres my favorite version,

The Narrator doesn't talk to you like your watching Barney concurrently either.

So is the type of thing like Geometric Topology/Algebraic Geometry? I really want to learn more about it from a math standpoint. This is the video that got me interested in maths in the first place back when I was in Geometry in High School.

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wow, that's really cool

I like the video that Rocket put up better It has a bunch more pretty colors, too

## 1. How is it possible to turn a sphere inside out?

The process of turning a sphere inside out, also known as sphere eversion, involves continuously deforming the sphere without tearing or puncturing it. This can be achieved through a series of complex mathematical movements known as homotopy.

## 2. Who first discovered the concept of turning a sphere inside out?

The concept of sphere eversion was first discovered by mathematician Stephen Smale in 1958. He proved that it was possible to continuously deform a sphere into its inverse form without causing any singularities or discontinuities.

## 3. What practical applications does the concept of turning a sphere inside out have?

The concept of sphere eversion has no direct practical applications, but it has helped to advance our understanding of topology and geometry. It also serves as a fascinating mathematical puzzle and has been used in various art forms, such as animation and sculpture.

## 4. Is it possible to physically turn a sphere inside out?

While the concept of sphere eversion is possible mathematically, it is not physically possible to turn a sphere inside out without stretching or tearing it. This is due to the constraints of physical materials and the laws of physics.

## 5. Are there other shapes that can be turned inside out?

Yes, the concept of sphere eversion can be applied to other 3-dimensional shapes, such as cylinders and tori. However, the process becomes more complex and may involve higher dimensions. The general term for this concept is "manifold eversion".

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