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DO you think this is real?

  1. Mar 7, 2010 #1
    Do you guys think this really works?
    http://www.xamuel.com/inverse-graphing-calculator.php [Broken]
    I wasn't able to verify it with my graphing software.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 8, 2010 #2

    Mentallic

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    It looks incredible! Really mind-boggling!
    I always wondered if words and pictures could be made out of equations in cartesian form.

    I tried the letter O which should have just been a circle radius 1 unit centre (3,3) by the looks of it, and this is what it gives:

    [tex]\left((x-3)^2+(y-3)^2-1\right)^2+\left(y^2-6y+8+\sqrt{y^4-12y^3+52y^2-96y+64}\right)^2=0[/tex]

    Now, the first part is the correct equation for the circle, but what's this extra nonsense that's tacked on?
     
  4. Mar 8, 2010 #3

    statdad

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  5. Mar 8, 2010 #4

    Mentallic

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    Last edited by a moderator: Apr 24, 2017
  6. Mar 8, 2010 #5
    So it works?
     
  7. Mar 8, 2010 #6

    statdad

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    That expression is added to the ``formula'' for words and sentences as well. Perhaps it's important to the work; perhaps it's a private joke by the programmer.
     
  8. Mar 8, 2010 #7

    Mentallic

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    Yes I believe it does work. And once you start to realize the pattern (go for 1 simple letter at first, such as O and X and work your way from there), it's not as unbelievably impossible as you first might have thought - including myself.
     
  9. Mar 8, 2010 #8

    DrGreg

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    If you look at the structure of the equation for several letters, you will see a pattern emerging, e.g. for 3 letters

    [tex] z_1^2 \, z_2^2 \, z_3^2 \, + \, w^2 \, = \, 0 [/tex]​

    where z1 is a formula for the first letter, z2 is a formula for the second letter, z3 is a formula for the third letter, and w is always the same each time, and all of them functions of x and y.

    Note that the equation is true if and only if w is zero and at least one of the other expressions is zero.

    w is zero if [itex]2 \leq y \leq 4[/itex] and otherwise non-zero, so the effect of adding w2 is to prevent any curves being drawn above y=4 or below y=2. In the case of a circle ("O") it doesn't matter, but for some of the other letters, the formula given creates the correct symbol between heights 2 and 4 but also creates extra lines outside that range, so adding w2 suppresses the unwanted lines.
     
  10. Mar 8, 2010 #9
  11. Mar 8, 2010 #10

    uart

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    Nice explaination of the mysterious extra term. Thanks DrGreg. :)
     
  12. Mar 8, 2010 #11

    Mentallic

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    Yeah, nice explanation DrGreg! :smile:

    I also cannot comprehend why every term is being squared. What is the effect of this?
     
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