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

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

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.

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your question and title do not match – SHOBHIT GAUTAM Aug 28 '13 at 10:12
Why don't you try plotting it in Wolfram Alpha? :) – Cameron Williams Aug 28 '13 at 10:14
I got curious about the XXX at the end :-D – woliveirajr Aug 28 '13 at 15:21
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 3 '13 at 13:08

Using Maple it is:

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


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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 0:05

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

Have a look at the second graph here

It is a cardiod curve.

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

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

BTW, Happy Anniversary to your friend.

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