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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 23 Aug 2018
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    The Tautochrone curve has an interesting property: A bead placed anywhere will fall under the effect of gravity and reach the bottom of the curve at the same time.pic.twitter.com/TB3x3FEK1Z

    6:07 AM - 23 Aug 2018
    • 1,290 Retweets
    • 4,848 Likes
    • Tjennermark Matthew McCormick Joan-Llorenç 卐 Melody Woods Rhoden 🦖 Fondi Avvoltoio Decodifica Lara. 078 Dimitrios Kalemis
    41 replies 1,290 retweets 4,848 likes
      1. Blunt Dutchman‏ @werfb 23 Aug 2018
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        Replying to @fermatslibrary

        You can create a pendulum clock using the Tautochrone curve. That clock would always run at the same speed, no matter the size of the swing. It was invented by Christiaan Huygens in 1659. However, the added friction became a new problem.pic.twitter.com/qP6Ij8CDDu

        1 reply 9 retweets 30 likes
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      2. yass‏ @UchiwaItachi12 23 Aug 2018
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        Replying to @fermatslibrary

        Looks a lot like the brachistocrone

        1 reply 0 retweets 18 likes
      3. Karol Turbiarz‏ @KKZiomek0 23 Aug 2018
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        Replying to @UchiwaItachi12 @fermatslibrary

        Yep, in fact it is close to being a bracistochrone.pic.twitter.com/j9r2TuJHSu

        1 reply 0 retweets 26 likes
      4. End of conversation
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      2. Mr Kimchi‏ @MrKimchiBoy 23 Aug 2018
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        Replying to @fermatslibrary

        I wonder if the same curve is dependent on the strength of gravity. IE would the same curve behave the same on Mars, Jupiter, or 3753 Cruithne?

        2 replies 0 retweets 0 likes
      3. Maarten Mortier‏ @maartengm 23 Aug 2018
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        Replying to @MrKimchiBoy @fermatslibrary

        Yes, it would. Less gravity would just slow time. As long as you keep ignoring that the top of curve would have a different gravitational ‘constant’ than the bottom, it would work the same on any object.

        1 reply 0 retweets 6 likes
      4. End of conversation
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      2. 傲览千古‏ @lxg6226 23 Aug 2018
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        Replying to @fermatslibrary

        然而,作为科学家,必须要换位思考这么一个有趣的问题:如果不存在地球重力场,比如,在350公里高的国际空间站中,那么上述所有的结论,将成为一种谬论。对不对?

        2 replies 0 retweets 3 likes
      3. d4n1el‏ @d4n1elchen 23 Aug 2018
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        Replying to @lxg6226 @fermatslibrary

        怎麼會成為謬論

        1 reply 0 retweets 0 likes
      4. End of conversation
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      2. Toreole‏ @ToreoleM 23 Aug 2018
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        Replying to @fermatslibrary

        its basically a pendulum without a pendulum

        1 reply 0 retweets 4 likes
      3. ꜱᴡᴀᴘɴɪʟ ಠ_ಠ ʙʜᴀᴛɪᴀ‏ @synbiocs 23 Aug 2018
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        Replying to @ToreoleM @fermatslibrary

        It's actually not a pendulum; to think it is is to miss the Central point: it's a cycloid. Two identical penduli released from different points will definitely not arrive at the bottom at the same time!

        1 reply 0 retweets 0 likes
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      2. Frederik Vanhoutte‏ @wblut 23 Aug 2018
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        Only true for small oscillations though... The derivation of that relationship substitutes sin(x) for x to make it analytically solvable. A reasonable approach for small angles, but increasingly invalid for larger ones.

        0 replies 0 retweets 1 like
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