Comments on: Mystery Equation

Question: Mystery Equation

Firas — Sat, 16 Jun 2007 04:34:01 -0800

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?

By: effugas

effugas — Sat, 16 Jun 2007 04:43:02 -0800

If you graph this, does it form the shape of a heart?

By: Aloysius Bear

Aloysius Bear — Sat, 16 Jun 2007 04:46:16 -0800

That was my thought, but no. The graph is entirely unromantic as far as I can tell.

By: Firas

Firas — Sat, 16 Jun 2007 04:59:44 -0800

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

By: Abiezer

Abiezer — Sat, 16 Jun 2007 05:11:06 -0800

x and y being chromosomal and the multiple zzz's representing bed?

By: Mapes

Mapes — Sat, 16 Jun 2007 05:39:47 -0800

The symmetry of x and y suggests partners in a relationship, and z's quartic exponent suggests another factor's strong influence...

By: missmagenta

missmagenta — Sat, 16 Jun 2007 05:48:01 -0800

is she trying to say you both snore?

By: missmagenta

missmagenta — Sat, 16 Jun 2007 05:51:10 -0800

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.

By: Kikkoman

Kikkoman — Sat, 16 Jun 2007 05:52:27 -0800

Here's a graph as rendered by the OS X grapher utility.

By: Kikkoman

Kikkoman — Sat, 16 Jun 2007 05:54:48 -0800

My apologies. Here's the revised link.

By: notsnot

notsnot — Sat, 16 Jun 2007 05:58:06 -0800

Kikkoman, that didn't come out right.

And missmagenta, it's a surface in 3D.

By: RussHy

RussHy — Sat, 16 Jun 2007 06:06:37 -0800

Looks like a breast. I don't think 'romantic' is the right word. I'm not even sure it's 'erotic', but tastes differ.

By: backseatpilot

backseatpilot — Sat, 16 Jun 2007 06:16:02 -0800

The equation describes a circle whose radius changes based on the z-value. So, something vaguely spherical or cylindrical would be my guess.

By: wtdoor

wtdoor — Sat, 16 Jun 2007 06:24:58 -0800

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

By: box

box — Sat, 16 Jun 2007 06:37:47 -0800

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.

By: springload

springload — Sat, 16 Jun 2007 06:52:41 -0800

wtdoor's graphs are right. Looks a bit like those snapshots of a raindrop bouncing of a puddle.

By: philcliff

philcliff — Sat, 16 Jun 2007 07:48:02 -0800

wtdoor's first graph sorta looks like two chins, so maybe two people kissing?

By: wsg

wsg — Sat, 16 Jun 2007 07:58:22 -0800

It's a tit.

By: cardboard

cardboard — Sat, 16 Jun 2007 09:06:02 -0800

It's a Hershey's Kiss.

By: nebulawindphone

nebulawindphone — Sat, 16 Jun 2007 09:23:40 -0800

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?

By: Firas

Firas — Sat, 16 Jun 2007 09:33:18 -0800

Aw yr right!

She: its called the Kiss surface
http://mathworld.wolfram.com/KissSurface.html
Me: i thought the representation itself has something to do with love
rather than the name of the pattern
http://xkcd.com/c55.html
She: well of course!
the Hershey's kiss!
It is so named because the shape of the lower portion resembles that of a Hershey's Chocolate Kiss.
It is romantic enough
Me: when i think romance, i think handcuffs and miracle whip!!

Thanks for the sleuthing all! Mefi delivers again; her bet's so won.

By: Blazecock Pileon

Blazecock Pileon — Sat, 16 Jun 2007 10:09:56 -0800

It's a boobie — well, more like a nipple.

By: brundlefly

brundlefly — Sat, 16 Jun 2007 11:13:00 -0800

Kikkoman's image was right, actually. It just needed to be zoomed in.

By: Wolfdog

Wolfdog — Sat, 16 Jun 2007 14:05:30 -0800

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.

By: monkeymadness

monkeymadness — Sat, 16 Jun 2007 14:49:16 -0800

It looks a bit melty to be a Hershey's kiss.

By: monkeymadness

monkeymadness — Sat, 16 Jun 2007 15:00:59 -0800

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.

By: misha

misha — Sat, 16 Jun 2007 15:21:53 -0800

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.

By: monkeymadness

monkeymadness — Sat, 16 Jun 2007 15:44:20 -0800

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.

By: Blazecock Pileon

Blazecock Pileon — Sat, 16 Jun 2007 16:10:09 -0800

Wolfdog, do you have Mathematica code for plotting it? I get something like this.

By: effugas

effugas — Sat, 16 Jun 2007 16:32:17 -0800

Shape of a heart, shape of a kiss, same diff ;)

By: Wolfdog

Wolfdog — Sat, 16 Jun 2007 17:02:44 -0800

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.)