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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?

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    @asmeuere: numpy2012-09-12

2 Answers 2

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I did it in Maple...

heart

Vary b to change the picture.

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    ok thanks it is perfect! and can i ask you also some little comment about the kind and analysis of this formula?2011-10-31
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$\sqrt{x^2}$ 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.