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Formula for love: X^2+(y-sqrt(x^2))^2=1 (wolframalpha.com)
202 points by carusen on Feb 14, 2011 | hide | past | web | favorite | 41 comments

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:


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...

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...

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).


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

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

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.

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.

I can see your reasons, but to play devil's advocate (because it's more fun):

1) via Wikipedia, the heart shape itself is likely based off the shape of the silphium seed, which was used as a contraceptive, or of course various naughty bits of anatomy. And condom sales spike around V-day. Relevancy #1: check.

2) It's an equation. And it even contains pi raised to the pith power. Relevancy #2: check.

doesn't the comment you addressed suit both your listed criteria for "relevant"?

I think it's actually a "Ď€nus"

edit: wow, crappy pi character. "pinus"

There's a Valentine's card in there somewhere:

You are the sine to my cosine... cos(theta) + cos(2 theta) polar

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


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?

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

Many of these are in W|A already without the need for inputting the full formula; just specify various levels of 'heart curve':


...and the 3D surface is there too:


But the URL gives away the punchline.

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

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.

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

    heart = (scale,x,y)->
      p1 = [x-75*scale,y+20*scale]
      p2 = [x,p1[1]+60*scale]

      p1 = [x+75*scale,y+20*scale]
      p2 = [x,p1[1]+60*scale]

      ctx.strokeStyle = 'rgba(255,40,20,0.7)'
    heart(1.0, 450, 250)

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."

This one was fun at school today:


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

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.

Exactly. It all comes down to abs.


sqrt(-1^2) => 1

When you square root things they become + or -

Not if x is negative.

In my opinion, this one looks a bit better:


Circles rolling around circles http://mathworld.wolfram.com/Cardioid.html


This whole thread is way too cool, loved it!

Also possible in Polynomial function alone.


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

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

so awesome. that's all.

indeed it is

And ofcourse: 1 + 1 = 1 ;)

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