My Mathematical Valentines Message | In the Dark

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

$\left(x^2 +y^2 + 2ay \right)^2 = 4a^2 \left( x^2 + y^2 \right)$

for

$x<3$ .

Geddit?

Answer: the equation is that of a cardioid:

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This entry was posted on February 14, 2015 at 2:55 pm and is filed under Cute Problems with tags cardioid, mathematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

5 Responses to “My Mathematical Valentines Message”

Bryn Jones Says:
February 14, 2015 at 10:34 pm

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

(Or have I got it wrong?)

Reply
Anton Garrett Says:
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!

Reply
Bryn Jones Says:
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.

Reply
- telescoper Says:
  February 16, 2015 at 12:51 pm
  
  You must have been looking at the Australian edition of this blog.
  
  Reply
  - Bryn Jones Says:
    February 16, 2015 at 9:28 pm
    
    Yes, clearly. Or standing on my head.

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