
Formula for love: X^2+(y-sqrt(x^2))^2=1 - carusen
http://www.wolframalpha.com/input/?i=x^2%2B%28y-sqrt%28x^2%29%29^2%3D1
======
ck2
Since the human heart looks nothing like the "heart shape" we all know and
use, I wonder where that originated...

Dang, wikipedia knows it all:

<http://en.wikipedia.org/wiki/Heart_%28symbol%29>

 _The seed of the silphium plant, used in ancient times as an herbal
contraceptive, has been suggested as the source of the heart symbol._

Oh, also
[http://www.wolframalpha.com/input/?i=%28x^2%2By^2-1%29^3-x^2...](http://www.wolframalpha.com/input/?i=%28x^2%2By^2-1%29^3-x^2y^3%3D0)

~~~
Jach
I always liked the "Aphrodite's butt" interpretation; it makes me smile
whenever I see heart-shaped boxes of brown chocolate. :)

Also, here's mine:
[http://www.wolframalpha.com/input/?i=%281-%28|x|-1%29^2%29^0...](http://www.wolframalpha.com/input/?i=%281-%28|x|-1%29^2%29^0.5%3D-3%281-%28|x|%2F2%29^0.5%29^0.5)

~~~
Retric
Not bad. I like polar(x + sin(y) = 1) due to the simplicity, but polar(x = y)
seems the most poetic (y from -1.5pi to 1.5pi) or (y from -1.5pi to 1.5pi).

[http://www.wolframalpha.com/input/?i=polar%28x+%3D+%28y%29%2...](http://www.wolframalpha.com/input/?i=polar%28x+%3D+%28y%29%29+%28y+from+-1.5pi+to+1.5pi%29)

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iwwr
Another formula for love:

(NSFW)

[http://www.wolframalpha.com/input/?i=pi%5Epi%2A%28exp%28-x%5...](http://www.wolframalpha.com/input/?i=pi%5Epi%2A%28exp%28-x%5E100%29%2Acos%28x%29%2Babs%280.3%2Asin%28x%29%29%29+from+-3+to+3)

~~~
bajsejohannes
A graph of a penis with 9 upvotes. I hope this isn't where HN is going.

~~~
catshirt
what precisely differentiates this graph from the original post? i feel like
they're equally [relevant/irrelevant].

~~~
bajsejohannes
The original is relevant because 1) it is valentine's day and 2) most people
here appreciate a good math formula.

On it's own the original post was perhaps not too original, but it spurred
some interesting discussion, like where the heart shape originated.

The penis graph on the other hand, only comes of as childish. Sure, it would
have been really funny when I was 15. And to be sure, there are plenty of
clever penis jokes out there ("The hammer is my penis" comes to mind), but
this is not one of them.

~~~
sfphotoarts
Well, I can't agree, I thought it was clever and witty and I'm hanging on to
the 15 year old inside me that still thinks this is pretty funny.

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philh
3d version: (x^2+(9/4)y^2+z^2-1)^3 - x^2 _z^3-(9/80)y^2_ z^3 = 0

[http://www.wolframalpha.com/input/?i=ContourPlot3D[%28x^2%2B...](http://www.wolframalpha.com/input/?i=ContourPlot3D\[%28x^2%2B%289%2F4%29y^2%2Bz^2-1%29^3+-+x^2*z^3-%289%2F80%29y^2*z^3%3D%3D0%2C+{x%2C+-1.2%2C+1.2}%2C+{y%2C+-1.2%2C+1.2}%2C+{z%2C+-1.2%2C+1.3})]

~~~
ot
It's Taubin's heart surface (<http://mathworld.wolfram.com/HeartSurface.html>)

From <http://www.maa.org/mathland/mathtrek_02_11_02.html> :

> The algorithms that Taubin developed worked well even in the vicinity of
> cusps and other singularities. "I discovered the equation of the heart while
> trying to construct surfaces with complex singularities," Taubin says.

Isn't that romantic?

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jacobolus
Mathworld has some better ones: <http://mathworld.wolfram.com/HeartCurve.html>

~~~
scott_s
But the URL gives away the punchline.

~~~
cristoperb
The equation in the submitted link gave away the punchline too.

~~~
scott_s
The text for the URL on HN gives it away, but the URL itself does not. Which
is why I was able to pleasantly surprise a friend of mine with it.

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ehsanul
With bezier curves (it's prettier) in Canvas/Coffeescript (assuming an
existing global canvas context 'ctx'):

    
    
        heart = (scale,x,y)->
          ctx.beginPath()
          ctx.moveTo(x,y)
          p1 = [x-75*scale,y+20*scale]
          ctx.bezierCurveTo(x-20*scale,y-55*scale,p1[0]-50*scale,p1[1]-55*scale,p1...)
          p2 = [x,p1[1]+60*scale]
          ctx.bezierCurveTo(p1[0]+25*scale,p1[1]+22.5*scale,p2[0]-35*scale,p2[1]-40*scale,p2...)
    
          ctx.moveTo(x,y)
          p1 = [x+75*scale,y+20*scale]
          ctx.bezierCurveTo(x+20*scale,y-55*scale,p1[0]+50*scale,p1[1]-55*scale,p1...)
          p2 = [x,p1[1]+60*scale]
          ctx.bezierCurveTo(p1[0]-25*scale,p1[1]+22.5*scale,p2[0]+35*scale,p2[1]-40*scale,p2...)
    
          ctx.strokeStyle = 'rgba(255,40,20,0.7)'
          ctx.stroke()
        
        heart(1.0, 450, 250)

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_corbett
<http://individual.utoronto.ca/sck/vday.html> one of my favorites

"Roses are red. Violets are approximately blue. A paracompact manifold with a
Lorentzian metric, can be a spacetime, if it has dimension greater than or
equal to two."

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jawee
This one was fun at school today:

<http://i.imgur.com/7aofj.jpg>

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nailer
Isn't the square root of x squared just x?

~~~
judofyr
Not for negative numbers. You could also just use the absolute value:
<http://www.wolframalpha.com/input/?i=x^2%2B(y-|x|)^2%3D1>

EDIT: Woah. You got your answer at least.

~~~
pohl
Exactly. It all comes down to abs.

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zerd
In my opinion, this one looks a bit better:

[http://www.wolframalpha.com/input/?i=x^2%2B%28y-sqrt%28abs%2...](http://www.wolframalpha.com/input/?i=x^2%2B%28y-sqrt%28abs%28x%29%29%29^2%3D3)

------
porterhaney
Circles rolling around circles <http://mathworld.wolfram.com/Cardioid.html>

~~~
rosstafarian
kinky.

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hoag
This whole thread is way too cool, loved it!

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scorpion032
Also possible in Polynomial function alone.

[http://www.wolframalpha.com/input/?i=(x2%2By2-1)^3+-x2y3+%3D...](http://www.wolframalpha.com/input/?i=\(x2%2By2-1\)^3+-x2y3+%3D+0)

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ashitvora
One more
[http://www.wolframalpha.com/input/?i=(x^2+%2B+y^2+-+1)^3+-+x...](http://www.wolframalpha.com/input/?i=\(x^2+%2B+y^2+-+1\)^3+-+x^2+*+y^3)

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maddalab
Who does sqrt(x^2) for abs(x) ? Speak about accidental complexity in love

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GanjaHacker
1 * (x^2+(y-sqrt(x^2))^2=1) would be a Bob Marley song.

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zinssmeister
so awesome. that's all.

~~~
websockr
indeed it is

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tintin
And ofcourse: 1 + 1 = 1 ;)

