## My Mathematical Valentines Message

Here’s a little mathematical exercise with a Valentines theme:

Sketch the curve in the x-y plane described by the equation

for

.

Geddit?

Answer: the equation is that of a cardioid:

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February 14, 2015 at 10:34 pm

Oh, dear. Oh, dear. Oh, dear.

(Or have I got it wrong?)

February 14, 2015 at 11:34 pm

Rewrite in polar coordinates and it reduces to

r = 2a (1 – sin \theta )

at which point I recognised it from prior knowledge. Nice!

February 15, 2015 at 12:05 am

Ah. Now Peter has changed the sign in front of the 2ay term. The original version had a different sign – and that didn’t produce anything like a heart for a>0.

February 16, 2015 at 12:51 pm

You must have been looking at the Australian edition of this blog.

February 16, 2015 at 9:28 pm

Yes, clearly. Or standing on my head.