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Fermat's Library
Fermat's Library
Fermat's Library
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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 26 Aug 2018

    Aristotle's Wheel Paradox: This image seems to imply that the two circumferences of different sized circles are equal. Can you guess the fallacy?pic.twitter.com/QWfqbpfSyv

    6:15 am - 26 Aug 2018
    • 2,893 Retweets
    • 7,850 Likes
    • NIRAJ MISHRA mrss shourie Hilal Kaya ROHIT KUMAR FireStarters Podcast Ahmad T. Nilotpal Tanveer Ashraf Jaqen H’ghar
    531 replies . 2,893 retweets 7,850 likes
      1. New conversation
      2. Robert Low‏ @RobJLow 26 Aug 2018
        Replying to @fermatslibrary

        A bijection doesn't have to preserve measure.

        4 replies . 3 retweets 148 likes
      3. Ben Hambrecht‏ @BenHambrecht 26 Aug 2018
        Replying to @RobJLow @fermatslibrary

        The inner circle is slipping.

        12 replies . 1 retweet 374 likes
      4. Geoff‏ @RealGeoffErwin 26 Aug 2018
        Replying to @BenHambrecht @RobJLow @fermatslibrary

        Found the engineer.

        1 reply . 3 retweets 129 likes
      5. Ben Hambrecht‏ @BenHambrecht 26 Aug 2018
        Replying to @RealGeoffErwin @RobJLow @fermatslibrary

        Haha, I wish. Physicist.

        4 replies . 0 retweets 97 likes
      6. 𝕲𝖆𝖓𝖌 𝖘𝖍𝖎𝖙‏ @legally_blind_ 26 Aug 2018
        Replying to @BenHambrecht @RealGeoffErwin and

        Better, isn’t it?

        2 replies . 0 retweets 46 likes
      7. Assiye Süer‏ @assiyesuer 27 Aug 2018
        Replying to @legally_blind_ @BenHambrecht and

        ”Better”pic.twitter.com/RgQFcgDuGC

        1 reply . 1 retweet 21 likes
      8. Omar Fawaz ⚫ ⚪‏ @omar01_fawaz 28 Aug 2018
        Replying to @assiyesuer @legally_blind_ and

        Using Sheldon to tell that physics is better than engineering. Ironic!

        1 reply . 0 retweets 10 likes
      9. Assiye Süer‏ @assiyesuer 28 Aug 2018
        Replying to @omar01_fawaz @legally_blind_ and

        I was imagining a room of physicists and engineers, where the physicist looks at an engineer, says that engineering is better, and then turn his/her head to another physicist and blinking so that the engineer doesn't get hurt (even though the engineer is understanding sarcasm)😅

        1 reply . 0 retweets 7 likes
      10. 1 more reply
      1. New conversation
      2. Apsara‏ @Apsaraism 26 Aug 2018
        Replying to @fermatslibrary

        It's only considering the relative displacement of a circle in the horizontal axis. Not the "actual distance" traveled by 'B' or 'C'. Which is known as Cycloid. Equation of cycloid => x = r(t - sin t) , y = (1 - cos t) length => 8 r where r = radius and t = angle of rotation.pic.twitter.com/YDU3m54Itc

        6 replies . 10 retweets 191 likes
      3. Apsara‏ @Apsaraism 26 Aug 2018
        Replying to @Apsaraism @fermatslibrary

        Typo. y = r (1 - cos t) So here the radius is dependent on the position of (x,y) coordinates. Hence it affects the original distance traveled as well. So length of inner cycloid = 8 r (r = inner circle radius) length of outer cycloid = 8 R (R = outer circle radius) 8 R =/= 8 r

        2 replies . 3 retweets 68 likes
      4. M‏ @MDGadzama 26 Aug 2018
        Replying to @Apsaraism @fermatslibrary

        Well of course we know the two circumferences aren't equal, we want to know why they both cover the same length with equal number of rotation. As said, it's a fallacy.

        2 replies . 0 retweets 14 likes
      5. Apsara‏ @Apsaraism 26 Aug 2018
        Replying to @MDGadzama @fermatslibrary

        I already said that. It is just a projection on the horizontal axis (x axis). Not the actual distance covered by outer circle C & the inner circle B. It's applicable to any geometrical shape though, the only criteria is the X value of any two points in that figure should be same

        2 replies . 5 retweets 71 likes
      6. M‏ @MDGadzama 26 Aug 2018
        Replying to @Apsaraism @fermatslibrary

        Oh ok ok ... I just got it. The x-y plane solves the trick. Thsnk you

        1 reply . 1 retweet 7 likes
      7. Apsara‏ @Apsaraism 26 Aug 2018
        Replying to @MDGadzama @fermatslibrary

        You're welcome! 😊

        1 reply . 1 retweet 11 likes
      8. M‏ @MDGadzama 26 Aug 2018
        Replying to @Apsaraism @fermatslibrary

        Again, in another way; Point B is not rolling alongside it's circumference but along the circumference of the bigger circle. So it is simply tracing A. As if it's sliding Thats why they didn't use a dot at the centre, but a much smaller circle to facilitate the illusion.

        1 reply . 0 retweets 26 likes
      9. 2 more replies
      1. New conversation
      2. Neel Mehta‏ @neelmehta247 26 Aug 2018
        Replying to @fermatslibrary

        The inner wheel is turning a lot slower than the outer one is!

        7 replies . 0 retweets 257 likes
      3. M 🐻X DeL 🐻SHMUTT‏ @Max_Delash 26 Aug 2018
        Replying to @neelmehta247 @fermatslibrary

        Regardless of speed, how is a wheel with a much smaller circumference able to cover the same amount of distance as a wheel with a larger circumference, both only making 1 complete rotation?

        2 replies . 1 retweet 66 likes
      4. M 🐻X DeL 🐻SHMUTT‏ @Max_Delash 26 Aug 2018
        Replying to @Max_Delash @neelmehta247 @fermatslibrary

        The falicy is actually that the illustration is compressing the top line as the small wheel rolls across it. Otherwise it would be accumulating a bit of “slack” as it attempted to roll up the same length of line as the large wheel, given a smaller circumference.

        5 replies . 2 retweets 196 likes
      5. José Antonio Puyalto‏ @jpuyalto 26 Aug 2018
        Replying to @Max_Delash @neelmehta247 @fermatslibrary

        Key is both circles have the same center with same angular speed(not linear), So both lines are 2•pi (full rotation) imagine both circles to be part of the same solid: like the inner and outer part of a car tyre, you will see this same effect if you draw a radius on it.

        2 replies . 1 retweet 29 likes
      6. José Antonio Puyalto‏ @jpuyalto 26 Aug 2018
        Replying to @jpuyalto @Max_Delash and

        If you put both circles in the same “ground level” so they don’t share the center, the length of both lines would be different.

        2 replies . 0 retweets 25 likes
      7. M 🐻X DeL 🐻SHMUTT‏ @Max_Delash 26 Aug 2018
        Replying to @jpuyalto @neelmehta247 @fermatslibrary

        Lol I can’t tell if you are disagreeing with me or just expanding upon the explaination.

        1 reply . 0 retweets 4 likes
      8. José Antonio Puyalto‏ @jpuyalto 26 Aug 2018
        Replying to @Max_Delash @neelmehta247 @fermatslibrary

        Just wanted to say there is no compression or any special effect on the .gif as this is something you can see in real life (think about the car tyre)

        2 replies . 0 retweets 6 likes
      9. M 🐻X DeL 🐻SHMUTT‏ @Max_Delash 26 Aug 2018
        Replying to @jpuyalto @neelmehta247 @fermatslibrary

        Please provide a proof a line of a fixed length fits around two different sized circles. There is no way around this. The gif must compress line b in order for it to wrap around the inner circle with one rotation.

        4 replies . 0 retweets 7 likes
      10. 7 more replies

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