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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 11 Jan 2019
    • Report Tweet
    • Report NetzDG Violation

    The convergence of the following series is still an open problem in Mathematicspic.twitter.com/ARPFX6JNY7

    5:50 AM - 11 Jan 2019
    • 611 Retweets
    • 2,304 Likes
    • Esteban Castro V E Julia El Duderino abhishek nick Leakvoid Mahdi baghbani junitex
    57 replies 611 retweets 2,304 likes
      1. New conversation
      2. Leonardo Pacheco  🇧🇷‏ @lpacheco 11 Jan 2019
        • Report Tweet
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        Replying to @fermatslibrary

        I have a really clever solution to this problem but it doesn’t fit in a tweet.

        11 replies 15 retweets 316 likes
      3. Wisnu Aribowo‏ @waribowo_ 11 Jan 2019
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        Replying to @lpacheco

        pic.twitter.com/c55oRtnmGl

        1 reply 2 retweets 50 likes
      4. 1 more reply
      1. New conversation
      2. Wouter Vanhove‏ @woutervhove 11 Jan 2019
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        Replying to @fermatslibrary

        Converges to slightly more than 30?pic.twitter.com/HgiivStrdg

        3 replies 1 retweet 15 likes
      3. Alirez‏ @ialireza13 11 Jan 2019
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        Replying to @woutervhove @fermatslibrary

        I think everyone is looking for a rigorous analytical proof.

        1 reply 0 retweets 36 likes
      4. 4 more replies
      1. New conversation
      2. Apsara‏ @Apsaraism 11 Jan 2019
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        Replying to @fermatslibrary

        I think it depends on the rational approximations to Pi. Because it won't be convergent if the denominator part becomes 0 implying that the sin function gives 0. Why can't we just use a supercomputer and observe its behavior up to some gigantic range of values?

        3 replies 0 retweets 3 likes
      3. Gro-Tsen‏ @gro_tsen 11 Jan 2019
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        Replying to @Apsaraism @fermatslibrary

        As you guessed, convergence of this series is just a bizarre reformulation of a statement about how π can be approximated by rationals, namely that its "approximation exponent" is less than 5/2. But there is no doubt in anyone's mind that it's really 2, and series converges. …

        1 reply 1 retweet 8 likes
      4. 3 more replies
      1. Bill Davies‏ @BillJDavies 11 Jan 2019
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        Replying to @fermatslibrary

        Doesn't look like it'll converge. Small, though.pic.twitter.com/id0LNsjXMW

        0 replies 2 retweets 36 likes
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      1. New conversation
      2.  ♣§}{ØŤĄ ♣‏ @ShotaSdf 11 Jan 2019
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        Replying to @fermatslibrary

        Seems to converge to somewhere near 30.3145 but no idea whypic.twitter.com/W7siejlMWx

        3 replies 2 retweets 24 likes
      3. Brian Armstrong  💙 🦄 @ Flutter Institute‏ @killermonk 11 Jan 2019
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        Replying to @ShotaSdf @fermatslibrary

        But but ... Why not `sum += term;`? Why the extra characters!?!?!??

        3 replies 0 retweets 3 likes
      4. 2 more replies
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      2. DℝOℕ∈‏ @d_r_o_n_e 11 Jan 2019
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        Replying to @fermatslibrary

        It's called Flint Hills series. Alekseyev in 2011 has shown that the question of the convergence of the Flint Hill series is related to the irrationality measure of π

        1 reply 1 retweet 31 likes
      3. B1ff B1ff‏ @b1ffb1ff 11 Jan 2019
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        Replying to @d_r_o_n_e @fermatslibrary

        Don't confuse it with the Flint HillS series!

        0 replies 0 retweets 1 like
      4. End of conversation

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