Formula for love: X^2+(y-sqrt(x^2))^2=1

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...

zinssmeister• 15 years ago

so awesome. that's all.

websockr• 15 years ago

indeed it is

philh• 15 years ago

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

http://www.wolframalpha.com/input/?i=ContourPlot3D[%28x^2%2B...]

ot• 15 years ago

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?

porterhaney• 15 years ago

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

rosstafarian• 15 years ago

kinky.

jawee• 15 years ago

This one was fun at school today:

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

maddalab• 15 years ago

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

GanjaHacker• 15 years ago

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

scorpion032• 15 years ago

Also possible in Polynomial function alone.

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

zerd• 15 years ago

In my opinion, this one looks a bit better:

http://www.wolframalpha.com/input/?i=x^2%2B%28y-sqrt%28abs%2...

hoag• 15 years ago

This whole thread is way too cool, loved it!

ehsanul• 15 years ago

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)

_corbett• 15 years ago

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."

ashitvora• 15 years ago

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

Formula for love: X^2+(y-sqrt(x^2))^2=1

Related Stories