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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 31 Aug 2018
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    This is called the staircase paradox, or why π ≠ 4 Can you explain what is wrong with this construction?pic.twitter.com/VLdeE7C70e

    5:50 AM - 31 Aug 2018
    • 447 Retweets
    • 1,649 Likes
    • Pythonic News 卐 Vikram Dutt Aidan Mohamad Adami musubimeriron Yosua Manurung Goras Agoras Nick
    88 replies 447 retweets 1,649 likes
      1. New conversation
      2. Tamás Görbe‏ @TamasGorbe 31 Aug 2018
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        Replying to @fermatslibrary

        Here's a similar fun fact: If you put N small circles along the diameter of a big circle, the total circumference of small circles equals that of the big one for any N, but the total area of small circles goes to zero as N→∞pic.twitter.com/JFpZ0kDizd

        3 replies 7 retweets 74 likes
      3. Ayush DEV‏ @d_anomalous 1 Sep 2018
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        Replying to @TamasGorbe

        pic.twitter.com/Tut8fss5hZ

        0 replies 0 retweets 21 likes
      4. End of conversation
      1. New conversation
      2. pawan krishna‏ @pawankrishna10 31 Aug 2018
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        Replying to @fermatslibrary

        The sum of the length of two perpendicular lines is always greater than the arc included between them...hence 4 > π

        2 replies 6 retweets 146 likes
      3. S & T‏ @_CuriousBit_ 31 Aug 2018
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        Replying to @pawankrishna10 @fermatslibrary

        Bravo!!

        0 replies 0 retweets 2 likes
      4. End of conversation
      1. New conversation
      2. Jason - Automaths  🍓‏ @paljasn 31 Aug 2018
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        Replying to @fermatslibrary

        This is wrong... In fact, Pi = 2 ! The dotted line has length 2, so for each color, the total length of the line is Pi... and the sequence of circles converges towards this dotted line, meaning Pi = 2pic.twitter.com/qgc35jLDuN

        1 reply 2 retweets 14 likes
      3. Fabie[N] Boyer‏ @Dw4rFNaheulbeuK 31 Aug 2018
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        Replying to @paljasn @fermatslibrary

        Bon OK on fait une moyenne à 3. D'ailleurs pi=3 à été établi par Bougre de Sagouin Jeanson (dans Timbré des annales du disque monde. <3 Terry Pratchett forever).

        0 replies 0 retweets 2 likes
      4. End of conversation
      1. Sassan Ordibehesht‏ @S_Ordibehesht 31 Aug 2018
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        Replying to @fermatslibrary

        How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension,* by Benoit #Mandelbrot (@sciencemagazine Vol. 156, Issue 3775, pp. 636-638, 1967): http://science.sciencemag.org/content/156/3775/636 … ____ *https://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf … (@Yale - free access)

        0 replies 2 retweets 13 likes
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      2. Robert Low‏ @RobJLow 31 Aug 2018
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        Replying to @fermatslibrary

        Length of curves is not continuous in the topology given by pointwise convergence.

        1 reply 0 retweets 11 likes
      3. Andrew Stacey‏ @mathforge 31 Aug 2018
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        Replying to @RobJLow @fermatslibrary

        This is why I don't like the in/exscribed polygon approximations of pi. Area is far better behaved than arc length.

        1 reply 0 retweets 4 likes
      4. 1 more reply
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      2.  🌊 Brendan Hoar  🌊‏ @BrendanHoar 31 Aug 2018
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        Replying to @fermatslibrary

        Fractals, man, fractals.

        1 reply 0 retweets 45 likes
      3. IE Media News‏ @IEMediaNews 31 Aug 2018
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        Replying to @BrendanHoar @fermatslibrary

        did someone just type fractals? Got 3 minutes and 15 seconds? 😀https://www.youtube.com/watch?v=bOLTCBTex-s …

        0 replies 0 retweets 1 like
      4. End of conversation

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