i don't remember where exactly, i found in internet this image: beautiful curve

i tried to replicate the formula with python and i tried this:

b = 0.9
y = 2*b + sqrt(x*x) + sqrt((x+b)*(3*b-x))
y1 = 2*b + sqrt(x*x) - sqrt((x+b)*(3*b-x))
plot(x,y, x, y1)

where sqrt is the square root!

but my curve is not very similar to the picture.. mayebe i'm not able to read it because of it is handwritten. some help?

  • 3
    $\begingroup$ I'm fairly certain that it's not $\sqrt{x^2}$... the root and the exponent are probably different so as to give the desired "cusp". $\endgroup$ – The Chaz 2.0 Oct 18 '11 at 14:11
  • 3
    $\begingroup$ The first radical appears to not be a square root, but an $n$th root, which is pretty hard to make out. It'd be silly to use $\sqrt{x^2}$, which is $|x|$, since there's probably a nice function for that in Python. Try experimenting with some other roots, maybe $x^{2/3}$ $\endgroup$ – mathmath8128 Oct 18 '11 at 14:12
  • 1
    $\begingroup$ A related thread. $\endgroup$ – J. M. is a poor mathematician Oct 18 '11 at 14:16
  • $\begingroup$ Perhaps you found the image here: mathematische-basteleien.de/heart.htm (That's what came up when I used Google image search.) $\endgroup$ – PersonX Oct 18 '11 at 15:42
  • 1
    $\begingroup$ @Jeroen "[your text](the http address)" with the [ ] ( ) included $\endgroup$ – Dr. belisarius Oct 18 '11 at 21:20

I did it in Maple...


Vary b to change the picture.

  • $\begingroup$ ok thanks it is perfect! and can i ask you also some little comment about the kind and analysis of this formula? $\endgroup$ – nkint Oct 31 '11 at 9:25

$\sqrt{x^2}$ is the same thing as $|x|$, the absolute value of $x$, whose graph has a sharp corner. When I plot exactly the first equation you wrote above, what I get is quite similar to the part of the graph above the two left and right vertical tangents. But it doesn't have a vertical tangent at the cusp in the middle, although it does have a sharp corner there.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.