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I Cool Parametric Equations

  1. Mar 24, 2016 #1
    Hi all! I have recently taught myself parametrics, and I stumbled upon the butterfly curve. So, I was wondering about some cool equations I can plug into a parametric graphing calculator.
     
  2. jcsd
  3. Mar 24, 2016 #2

    ProfuselyQuarky

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    Oh, those are a lot of fun -- even better than polar graphing! My favorite is the Hypotrochoid:

    x(t) = (a - b) cos t + c cos ((a/b - 1)t)
    x(t) = (a - b) sin t + c sin ((a/b - 1)t)

    Sorry, I haven't learned LaTeX, yet . . . Here's a bunch of lovely equations you can try:

    https://elepa.files.wordpress.com/2013/11/fifty-famous-curves.pdf

    What calculator do you have?
     
    Last edited: Mar 24, 2016
  4. Mar 24, 2016 #3

    ProfuselyQuarky

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    Oh, another good one:

    x(t) = sin(7πt)
    y(t) = cos(5πt)

    Not so sure if it has a name, but it looks way cool. You can always experiment and make up your own, too :)
     
  5. Mar 24, 2016 #4

    Ssnow

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    The astroid:

    ##x(t)=a\cos^{3}{t}##
    ##y(t)=a\sin^{3}{t}##
     
  6. Mar 24, 2016 #5

    ProfuselyQuarky

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    That one is lovely.
     
  7. Mar 24, 2016 #6

    pwsnafu

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    Special mention should be made of the superellipse
    ##\left| \frac{x}{a}\right|^n + \left| \frac{y}{b}\right|^n = 1##
    which has parametric equations
    ##x(t) = \pm a \cos^{2/n}(t)##
    ##y(t) = \pm b \sin^{2/n}(t)##
    It contains a number of equations above as special cases.

    In turn this is generalized by the superformula.
    As I understand it the 3d version is used by No Man's Sky.
     
  8. Mar 25, 2016 #7

    Ssnow

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    In the Astroid ##t\in [0,2\pi]##, there is also the Archimede spiral:

    ##x=t\cos{t}##
    ##y=t\sin{t}##

    with ##t\in [0,+\infty)##. Have good painting ...
     
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