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Mystery Equation
June 16, 2007 4:34 AM   RSS feed for this thread Subscribe

Mystery Equation: x2+y2=(1-z)z4 A friend of mine has a bet regarding whether anyone can figure out what it represents. It's supposed to be mildly romantic. Ideas?
posted by Firas to grab bag (30 comments total) 15 users marked this as a favorite
If you graph this, does it form the shape of a heart?
posted by effugas at 4:43 AM on June 16, 2007


That was my thought, but no. The graph is entirely unromantic as far as I can tell.
posted by Aloysius Bear at 4:46 AM on June 16, 2007


Yeah she doesn't have much more info…
  • She: did you see the eqn?
  • Me: LOL
    honey you are way overestimating my drive, sparkle, and abstract reasoning skills if you think i'm going ot sit there pondering the hidden meaning behind a random algebraic equality :p
    i'm not that awesome unfortunately
  • She: but oh firas, you are pure genius to me!
    no need to ponder
    you must know some mathematicians
    and if theyre romantic at heart, all the better!
  • She: it represents a surface
    with the z^4
    cant say more
    help me win!
  • Me: something to do with sex?
  • She: no no not sex
    its mildly romantic
    its simple! in the sense, its not the math really; do you know someone who loves math - talks in equations, is romantic with equations, someone like that will crack it!
    point is I win, if someone can look at it and say ahh thats ____
  • Me: is it ok to ask a group of people or does that fall outside the contest terms
  • She: well i suppose you could.
    but they have to come out clean and say
    what it represents
    what surface

posted by Firas at 4:59 AM on June 16, 2007 [1 favorite]


x and y being chromosomal and the multiple zzz's representing bed?
posted by Abiezer at 5:11 AM on June 16, 2007


The symmetry of x and y suggests partners in a relationship, and z's quartic exponent suggests another factor's strong influence...
posted by Mapes at 5:39 AM on June 16, 2007


is she trying to say you both snore?
posted by missmagenta at 5:48 AM on June 16, 2007


Is she really good at maths or has perhaps she been told that it means something that maybe it actually doesnt.

I'm not maths genius but I cant see how that equation can represent a surface - which would *IMO* be a 2 dimensional object - xyz would suggest 3 dimensional.
posted by missmagenta at 5:51 AM on June 16, 2007


Here's a graph as rendered by the OS X grapher utility.
posted by Kikkoman at 5:52 AM on June 16, 2007


My apologies. Here's the revised link.
posted by Kikkoman at 5:54 AM on June 16, 2007 [1 favorite]


Kikkoman, that didn't come out right.

And missmagenta, it's a surface in 3D.
posted by notsnot at 5:58 AM on June 16, 2007


Looks like a breast. I don't think 'romantic' is the right word. I'm not even sure it's 'erotic', but tastes differ.
posted by RussHy at 6:06 AM on June 16, 2007


The equation describes a circle whose radius changes based on the z-value. So, something vaguely spherical or cylindrical would be my guess.
posted by backseatpilot at 6:16 AM on June 16, 2007


Rotating these plots around the z-axis (the dotted line) will give you the 3D surface described by that equation:

A cross-section of the surface
An enlargement where 0≤z≤1, which looks a little bit like a heart
posted by wtdoor at 6:24 AM on June 16, 2007


Maybe it's a MacGuffin. Spending this much effort to assign metaphorical meaning to an unassuming equation, just because some sweet young thing asked you to? Sounds mildly romantic to me. Maybe that's why I'm single.
posted by box at 6:37 AM on June 16, 2007 [5 favorites]


wtdoor's graphs are right. Looks a bit like those snapshots of a raindrop bouncing of a puddle.
posted by springload at 6:52 AM on June 16, 2007


wtdoor's first graph sorta looks like two chins, so maybe two people kissing?
posted by philcliff at 7:48 AM on June 16, 2007


It's a tit.
posted by wsg at 7:58 AM on June 16, 2007 [1 favorite]


It's a Hershey's Kiss.
posted by cardboard at 9:06 AM on June 16, 2007


Whe she asks what surface? it sounds like she's looking for a name. I know some 2D and 3D figures do have names — "Lemniscate of Bernoulli," "Freeth's Nephroid," that sort of thing.

Could it be that this surface's name is some sort of romantic pun?
posted by nebulawindphone at 9:23 AM on June 16, 2007


Aw yr right!
Thanks for the sleuthing all! Mefi delivers again; her bet's so won.
posted by Firas at 9:33 AM on June 16, 2007 [1 favorite]


It's a boobie — well, more like a nipple.
posted by Blazecock Pileon at 10:09 AM on June 16, 2007


Kikkoman's image was right, actually. It just needed to be zoomed in.
posted by brundlefly at 11:13 AM on June 16, 2007 [1 favorite]


Want to show off? Reply with a

(2x2+y2+z2-1)3-(1/10)x2z3-y2z3 = 0

...it's a much more accurate 3D heart.
posted by Wolfdog at 2:05 PM on June 16, 2007 [5 favorites]


It looks a bit melty to be a Hershey's kiss.
posted by monkeymadness at 2:49 PM on June 16, 2007


Wolfdog's is nice once you get the resolution high enough. I hadn't seen that before--thanks. I'd be surprised if there's not a more elegant definition using spherical or cylindrical coordinates.
posted by monkeymadness at 3:00 PM on June 16, 2007


Can somebody show a representation of Wolfdog's equation? Because I'm a girl, and math is hard.

Seriously, someone with better computer skills than I have and a program to graph it.
posted by misha at 3:21 PM on June 16, 2007 [1 favorite]


This is the first one (more or less) in OS X grapher. This is another one I found. If anyone cares I'll post the parametric for it.
posted by monkeymadness at 3:44 PM on June 16, 2007


Wolfdog, do you have Mathematica code for plotting it? I get something like this.
posted by Blazecock Pileon at 4:10 PM on June 16, 2007


Shape of a heart, shape of a kiss, same diff ;)
posted by effugas at 4:32 PM on June 16, 2007


p = ContourPlot3D[(2x^2 + y^2 + z^2 - 1)^3 - (1/10)x^2 z^3- y^2 z^3, {x, -2, 2}, {y, -2, 2}, {z,-2,2},PlotRange->{{-1,1},{-3/2, 3/2}, {-1, 3/2}}, PlotPoints -> 9,MaxRecursion ->1];

Show[Graphics3D[SurfaceColor[RGBColor[1, 0,
0]]], p, ViewPoint -> {-3.042, 1.260, 0.779},
Boxed -> False, ImageSize -> 400]

Should give you pretty nice results. I forgot how tricky it is to get this to render really well in Mathematica. But when I get to the office I will try it in Mathematica 6.0 and expect better things because 6.0 has been, so far, the absolute bomb.)
posted by Wolfdog at 5:02 PM on June 16, 2007 [2 favorites]


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