Decipher the greeting card $( X^2 +Y^2 -1 ) ^3 - X^2 Y^3 = 0$

Question

A friend of mine just got a rather weird congratulations card through the door

Greeting card image

They have zero idea what it means, I have tried graphing it and nothing spectacular comes out. Is there a standard name for this equation or does it signify anything?

Any help would be appreciated.

Either the card is very weird or your personal situation is quite weird. Is it really true you have a significant other who shares a birthday with you and you have an anniversary on the same day?!! :) Or maybe it is just a card-for-all-occasions... — rschwieb, Sep 03 '13 at 13:08

score 11 · Accepted Answer · answered Aug 28 '13 at 10:28

11

Using Maple it is:

 [> with(plots):
    implicitplot((x^2+y^2-1)^3-x^2*y^3 = 0, x = -10 .. 10, y = -10 .. 10);

enter image description here

answered Aug 28 '13 at 10:28

Mikasa

67,374

3

I love how bad the first couple of plots look. – Simon Hayward Aug 28 '13 at 10:45
Awesome progression! +1 – amWhy Aug 29 '13 at 00:05

score 9 · Answer 2 · answered Aug 28 '13 at 10:13

9

http://mathworld.wolfram.com/HeartCurve.html

Have a look at the second graph here

It is a cardiod curve.

answered Aug 28 '13 at 10:13

Alex Martin

91

lol ! lucky guy !! – lsp Aug 28 '13 at 10:16

Shobhit · Answer 3 · 2018-02-16T09:10:45.303

8

Your friend had a great equation for his greetings, check the graph below

enter image description here

edited Feb 16 '18 at 09:10

answered Aug 28 '13 at 10:17

Shobhit

6,902

Decipher the greeting card $( X^2 +Y^2 -1 ) ^3 - X^2 Y^3 = 0$

3 Answers3