Archive for cardioid

My Mathematical Valentines Message

Posted in Cute Problems with tags , on February 14, 2015 by telescoper

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:

cardioid-2

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