LOVE +MATH = can you read this formula?

Question

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?

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". — The Chaz 2.0, Oct 18 '11 at 14:11
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 $x^{2/3}$ — mathmath8128, Oct 18 '11 at 14:12
Perhaps you found the image here: http://www.mathematische-basteleien.de/heart.htm (That's what came up when I used Google image search.) — PersonX, Oct 18 '11 at 15:42
This reminds me of the famous batman equation (http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real) @ J.M., how can you link your text in comment mode? — , Oct 18 '11 at 16:22
Parametric Heart thanks to Dwight Boddorf (MAA's American Mathematical Monthly Volume 115 Number 2 (February 2008) page 113) — Bill Cook, Oct 18 '11 at 19:31
@Jeroen "[your text](the http address)" with the [ ] ( ) included — Dr. belisarius, Oct 18 '11 at 21:20

GEdgar · Accepted Answer · 2013-07-02T16:53:41.500

33

I did it in Maple...

heart

Vary b to change the picture.

edited Jul 02 '13 at 16:53

answered Oct 18 '11 at 14:33

GEdgar

111,679

ok thanks it is perfect! and can i ask you also some little comment about the kind and analysis of this formula? – nkint Oct 31 '11 at 09:25

score 1 · Answer 2 · answered Oct 18 '11 at 15:19

$\sqrt{x^2}$ 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.

LOVE +MATH = can you read this formula?

2 Answers2