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DanielleFong's profile
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@DanielleFong

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@DanielleFong

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Empire of the Future
Joined February 2008

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    1. Emily / aiju  😭‏ @the_aiju 20 Feb 2021

      Emily / aiju  😭 Retweeted Massimo

      someone asked in the reply if this truly saves brick over 2-brick straight line. serpentine line takes average of sqrt(1+sin(x)^2) bricks per one brick of horizontal length. sqrt(1+sin(x)^2)<sqrt(2)<2.https://twitter.com/Rainmaker1973/status/1363133897144426496 …

      Emily / aiju  😭 added,

      Massimo @Rainmaker1973
      A crinkle crankle wall is an unusual type of garden wall built in a serpentine shape typically found in the UK. It economizes on bricks because it can be made just one brick thin. If a wall this thin was made in a straight line, it would easily topple over http://ow.ly/4LY850zYx9T  pic.twitter.com/iBBgZb4UyZ
      2 replies 10 retweets 62 likes
      Show this thread
    2. Emily / aiju  😭‏ @the_aiju 20 Feb 2021

      obviously the answer depends on amplitude of the sine wave but using just y=cos x you get sqrt(1+sin(x)^2) as the length which works out to 1.216 on average (it’s some cursed elliptic integral)

      3 replies 0 retweets 20 likes
      Show this thread
    3. Emily / aiju  😭‏ @the_aiju 20 Feb 2021

      in case you’re wondering why sqrt(1+sin(x)^2), length is sqrt(dx^2+dy^2), length per unit of horizontal distance is sqrt(dx^2+dy^2)/dx = sqrt(1+ (dy/dx)^2) = sqrt(1+sin(x)^2)for y=cos x [mathematicians screaming]

      3 replies 0 retweets 16 likes
      Show this thread
    4. Emily / aiju  😭‏ @the_aiju 20 Feb 2021

      fun fact, this exact problem kind of radicalised me towards physics because mathematics books couldn’t answer a similar problem and it’s trivial with just throwing around dx’s and dy’s

      3 replies 0 retweets 28 likes
      Show this thread
    5. Emily / aiju  😭‏ @the_aiju 20 Feb 2021

      actually, the problem i was interested in back then was this you can make these cute figures using polar coordinates i was curious how to work out the circumference again, easy with dr / dtheta manipulationpic.twitter.com/cm6me1Swjb

      1 reply 0 retweets 15 likes
      Show this thread
    6. Emily / aiju  😭‏ @the_aiju 20 Feb 2021

      before anyone gets mad and mansplains the purpose of mathematics to me, i get it, you guys wanna prove that a solution exists rigorously, but i just wanna calculate stuff and the physicist “non-rigorous” toolkit is much more powerful than standard mathematics

      5 replies 1 retweet 28 likes
      Show this thread
       🤷🏻‍♀️‏ @DanielleFong 20 Feb 2021
      Replying to @the_aiju

      non standard analysis makes the dx/dy manip real so math heads can do it too

      7:47 AM - 20 Feb 2021
      • 2 Likes
      • Imp (71/100 Omelettes) Emily / aiju 😭
      1 reply 0 retweets 2 likes
        1. Emily / aiju  😭‏ @the_aiju 20 Feb 2021
          Replying to @DanielleFong

          yea this is why i said ‘standard mathematics’

          0 replies 0 retweets 2 likes
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