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Klein Bottles. In 1882, Felix Klein imagined sewing two Möebius loops together to create a single-sided bottle with no boundary.

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Presentation on theme: "Klein Bottles. In 1882, Felix Klein imagined sewing two Möebius loops together to create a single-sided bottle with no boundary."— Presentation transcript:

1 Klein Bottles

2

3 In 1882, Felix Klein imagined sewing two Möebius loops together to create a single-sided bottle with no boundary. Its inside is its outside, so it contains itself.

4 Klein Steins?

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6 Why Is This Man Smiling?

7 What Is Mans Place In The Universe?

8 Ancient Man: The Earth is the center of the Universe. We know this because everything in the sky turns around the Earth. Its obvious man!!

9 Copernicus (15??): The Sun is the center of the Universe. I know this because the orbital calculations come out with less overall error this way. The orbits are perfect circles.

10 Kepler (16??): The Sun sits at one of the focal points of each planets elliptical orbit. I know this because I stole Tycho Brahes data and theres simply less error in the calculations if you assume elliptical orbits.

11 1700s to early 1900s: The Sun is just one of: TENS OF THOUSANDS TENS OF MILLIONS HUNDREDS OF MILLIONS HUNDREDS OF BILLIONS of other stars in the Universe.

12 1920-ish: Hey, those fuzzy spiral blobs in the sky are other galaxies! And the Milky Way is just one galaxy out of HUNDREDS OF BILLIONS of others!!

13 Does this mean we are on an insignificant planet orbiting an average star which is a member of an ordinary galaxy? Is there nothing special about us?

14 Edwin Hubble (19??): Hey – all those other galaxies are running away from us! Maybe were special after all?

15 Nope – it turns out that in an expanding universe, everyone sees it as if all the other stars are running away from them.

16 1950s: Hey – none of these galaxies seem like they have enough visible mass to explain their rotation speeds!

17 1970s: Hey – none of these galaxy clusters seem to have enough visible mass to explain the motions of the galaxies inside them!

18 1980s: No problem. That just means that theres more than meets the eye when it comes to Astronomy. Well just call that missing stuff dark matter, and try to look for different kinds of it.

19 1990s: Yknow what? Weve found lots and lots of dark matter, but it STILL doesnt add up to enough to explain anything. Its as if 70% to 90% of the Universes mass is hidden. Whats this mean?

20 The ultimate insult: We arent even made of the most common type of matter in the universe. What could be more humbling than that?

21 Well.... If the current thinking is correct, then we might be aware of only 3 of the 10 or 11 dimensions that exist.

22 Or, worse yet? We might be living in just one universe out of an infinite number of universes that were created all together in the 11- dimensional Big Bang that started everything.

23 Is all that really so bad though?


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