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Limacon Curves

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What does a limacon look like?

Limaçon curves look like circles. They have various types depending on the values in their equations.

In the image below, for example, the types of limaçon curves are: dimpled, cardioid, and looped (respectively).

mason m · 1 · Mar 27 2016
How do I graph a limacon?

Answer:

It's easiest to watch a video of this.
Here's one I made a while back

Explanation:

I think the video will help you out a lot.

turksvids · 1 · Dec 5 2017
What is the equation of a limacon?

Answer:

$r^{2} = a^{2} cos 2 θ$ $r^2=a^2 cos 2theta$ .
The graph is the fallen eight, looking like the symbol $\infty$ $oo$ ...

Explanation:

For the double loop of $r^{2} = a^{2} cos 2 θ, cos 2 θ \geq 0$ $r^2=a^2 cos 2theta, cos 2theta >=0$ .

So, the range for $θ \in [0, 2 π]$ $theta in [0, 2pi]$ excludes $(\frac{π}{4}, \frac{3 π}{4})$ $(pi/4, (3pi)/4)$ and

$(\frac{5 π}{4}, \frac{7 π}{4})$ $((5pi)/4, (7pi)/4)$ , Here, $cos 2 θ < 0$ $cos 2theta < 0$ ...

A. S. Adikesavan · 1 · Apr 27 2016

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Polar Coordinates

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