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Is there a set of equations out there that gives a heart without any other marks? It needs to be in the form of $y = f(x), r = f(\theta)$ or $X_T ,Y_T$ (parametric equations) There needs to be a variable '$a$', which gives a different shape for a different value of $a$.

Edit 1:Also, could you state the best value for $a$? This is opinion based, but it takes me ages to draw one using trial and error

Edit 2: Sorry guys, I am being a bit of a pain aren't I?! This has turned into a challenge now, but could you specify rad/deg, Parameters for $\theta, x/y, and T$? As I have said, I am going to draw this by hand, and I might even LEGO it, so can you give me something suitable for LEGOing?

Xetrov
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1 Answers1

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Try the cardioid, one form of which is given by $$ r=2a(1+\cos\theta) $$

$\theta \in [0, 2\pi[$ say ( so radians.)

To plot by hand plug in the values of $\theta$ e.g.

When $\theta = 0$ then $r=4a$

When $\theta = \pi/2$ then $r=2a$

When $\theta = \pi$ then $r=0$

PM.
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