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fermatslibrary's profile
Fermat's Library
Fermat's Library
Fermat's Library
@fermatslibrary

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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

fermatslibrary.com
Joined September 2015

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    Fermat's Library‏ @fermatslibrary Jan 6
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    Here's cool instance of the Brouwer Fixed-Point Theorempic.twitter.com/zv5toM9tga

    5:48 AM - 6 Jan 2020
    • 307 Retweets
    • 1,816 Likes
    • Aad van Moorsel Frida Dayan oneninefive Peter Morgan TheMineTrooper ramsam Malik the Mad Farid Shahandeh rekotc
    23 replies 307 retweets 1,816 likes
      1. New conversation
      2. shreejit‏ @ShreejitJadhav Jan 6
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        Replying to @fermatslibrary

        1. If we start with two sheets of shape A, crumble first and place it on the second, the crumbled one's projection on the second is represented by B. So, we are essentially demanding a mapping of A onto B.pic.twitter.com/TxLqGtlJCt

        2 replies 0 retweets 32 likes
      3. shreejit‏ @ShreejitJadhav Jan 6
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        Replying to @ShreejitJadhav @fermatslibrary

        2. Now, because the area B of first (crumbled) sheet has been crumbled to a smaller area (say C) within area B of the second one, we can see that there is a recursive mapping that is self-inscribing.

        2 replies 0 retweets 21 likes
      4. 2 more replies
      1. New conversation
      2. Julian Luttrell‏ @JulianLuttrell Jan 6
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        Replying to @fermatslibrary

        My algebra lecturer told us: take a map that contains your location, crumple it up; drop it on the floor; one point in the crumpled blob now lies exactly over the real point is represents.

        3 replies 2 retweets 64 likes
      3. Julian Luttrell‏ @JulianLuttrell Jan 6
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        Replying to @JulianLuttrell @fermatslibrary

        *it

        0 replies 0 retweets 2 likes
      4. End of conversation
      1. Roger Sauer‏ @rsauer3473 Jan 6
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        Replying to @fermatslibrary

        This is not much different from the Brewer’s Fixed Pint Theorem in which a tippler might in the space of a fortnight find himself back in the same pub he’d been drinking earlier. #MathBooze

        0 replies 0 retweets 37 likes
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      1. New conversation
      2. The Target Demographic‏ @nuts_y_gum Jan 6
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        Replying to @fermatslibrary

        Is it guaranteed to be exactly one point?

        1 reply 0 retweets 2 likes
      3. Brahminical Patriarch‏ @grvbjh Jan 6
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        Replying to @nuts_y_gum @fermatslibrary

        Atleast one point.

        0 replies 0 retweets 21 likes
      4. End of conversation
      1. New conversation
      2. Gamma‏ @NotTheRealGamma Jan 6
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        Replying to @fermatslibrary

        Is this like the map thing? Where one place is accurately placed on it

        1 reply 0 retweets 4 likes
      3. bert boerland‏ @bertboerland Jan 6
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        Replying to @NotTheRealGamma @fermatslibrary

        see https://en.wikipedia.org/wiki/Brouwer_fixed-point_theorem … examples

        0 replies 0 retweets 4 likes
      4. End of conversation
      1. New conversation
      2. жиза в стіл‏ @3zub Jan 6
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        Replying to @fermatslibrary

        imo more mind-blowing case: Take an ordinary map of a country, and suppose that that map is laid out on a table inside that country. There will always be a "You are Here" point on the map which represents that same point in the country. (c) Wiki

        1 reply 1 retweet 8 likes
      3. Hari B‏ @8u1x0 Jan 6
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        Replying to @3zub @fermatslibrary

        Came here to say this

        0 replies 0 retweets 0 likes
      4. End of conversation

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