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johncarlosbaez's profile
John Carlos Baez
John Carlos Baez
John Carlos Baez
@johncarlosbaez

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John Carlos Baez

@johncarlosbaez

I do math, physics, network theory at U. C. Riverside and the Centre for Quantum Technologies in Singapore.

Riverside, CA
math.ucr.edu/home/baez/
Joined September 2016

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    John Carlos Baez‏ @johncarlosbaez 16 Nov 2019
    • Report Tweet

    In the world of geometry, the small stellated dodecahedron is a superstar! It's a star made of stars. It has 12 pentagrams as faces. But it's also the most symmetrical Riemann surface with 4 holes. Huh? Let me explain. (1/n)pic.twitter.com/ZnzN0qMEx3

    8:24 AM - 16 Nov 2019
    • 79 Retweets
    • 248 Likes
    • Lee C. tsar bimbo Adam Anderson Harphony TangerIIIne Jessica Flack Brayan Escobar Marcin Benke FlamingKetchup
    1 reply 79 retweets 248 likes
      1. New conversation
      2. John Carlos Baez‏ @johncarlosbaez 16 Nov 2019
        • Report Tweet

        You can think of each pentagram here as a pentagon that's been mapped into space in a very distorted way, with a "branch point of order 2" at its center. What does that mean? (2/n)pic.twitter.com/fbdVLn496o

        1 reply 1 retweet 24 likes
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      3. John Carlos Baez‏ @johncarlosbaez 16 Nov 2019
        • Report Tweet

        Stand at the center of a pentagon! Measure the angle you see between two corners that are connected by an edge. You get 2π/5. Now stand at the center of a pentagram. Measure the angle you see between two corners that are connected by an edge. You get 4π/5. Twice as big! (3/n)

        1 reply 2 retweets 24 likes
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      4. John Carlos Baez‏ @johncarlosbaez 16 Nov 2019
        • Report Tweet

        So, to map a pentagon into space in a way that makes it look like a pentagram, you need to wrap it twice around its central point. That's what a "branch point of order 2" is all about: https://en.wikipedia.org/wiki/Branch_point … (4/n)

        1 reply 2 retweets 23 likes
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      5. John Carlos Baez‏ @johncarlosbaez 16 Nov 2019
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        That's the cool way to think of this shape. It's a surface made of 12 pentagons, each wrapped twice around its center, 5 meeting at each sharp corner. If you use Euler's formula V - E + F = 2 - 2g to count its number of holes - its "genus" g - you'll see it has 4 holes. (5/n)pic.twitter.com/vb9ifpX78t

        1 reply 2 retweets 28 likes
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      6. John Carlos Baez‏ @johncarlosbaez 16 Nov 2019
        • Report Tweet

        It's actually a Riemann surface, the most symmetrical Riemann surface with 4 holes! We're seeing it as a branched cover of the sphere. But you can also build it by taking a tiling of the hyperbolic plane by pentagons, and modding out by a certain group action. (6/n)pic.twitter.com/4sZVtzP56s

        1 reply 4 retweets 43 likes
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      7. John Carlos Baez‏ @johncarlosbaez 16 Nov 2019
        • Report Tweet

        Most of this stuff - and more - was discovered by Felix Klein in 1877. You can read details in this blog post of mine: https://blogs.ams.org/visualinsight/2016/06/15/small-stellated-dodecahedron/ … (7/n, n = 7)pic.twitter.com/0p97aKGfa3

        3 replies 3 retweets 51 likes
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      8. End of conversation
      1. New conversation
      2. Toni‏ @pinkusman 16 Nov 2019
        • Report Tweet
        Replying to @pinkusman @johncarlosbaez

        Amazing. It should be like a football (soccer ball).

        0 replies 0 retweets 0 likes
      3. End of conversation

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