Happy sextic (equation) day

Don’t be a pervert. I’m talking about the sextic equation, or the heart equation. Remember college algebra? Remember how this equation graphs a circle:

[pmath size=12]{(x-h)^2+(y-k)^2=r^2}[/pmath]

Well, there has to be a function out there that describes a heart, right? At least that’s what I was asking myself during church today. So google I did, and voila! Here a couple:

[pmath size=12]{x^2+(y-sqrt{delim{|}x{|}})^2=n, where n=3}[/pmath] 1

My favorite comes from Wolfram 2, which is known as the sextic equation:

[pmath size=20]{(x^2+9/4y^2+z^2-1)^3-x^2z^3-9/80y^2z^3=0}[/pmath]

plot of heart surface
plot of heart surface
heart surface
heart surface

Happy Valentine’s Day!


  1. found here, along with many others
  2. home of Mathworld

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  1. Yikes, your question about remembering college algebra was a bit of a head scratcher. I had to think back about that. Can’t say any prof taught us the equation for a heart. Pretty cool.

    I think this could be made into a great Valentine’s card somehow.

  2. You’d have to be the biggest geek in the world to write this equation on a Valentine’s card and hand it to a loved one. I guess I’m gonna try to next year as a joke. It’s no secret that I’m handy with my graphing calculator. But I doubt my g/f will appreciate the gesture.

  3. Whoa! That’s some hard core algebra for Valentine’s Day! I didn’t know that they also coined the sextic equation as the heart equation. This is cool stuff.

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