## Wednesday, February 4, 2015

### Simple Polar Curves

Simple Polar Curves

** Updated 2/11/2015 - Thank you Mike for pointing out my mistake on the rose curve - it is much appreciated!   Eddie

Here are some of the basic curves in polar coordinates.  These are graphed using the HP Prime Emulator, where 0 ≤ θ ≤ 4*π.

Rose:  r = cos(n*θ)
If n is odd, then the rose has n pedals.
If n is even, then the rose has 2*n pedals.

r = cos(5*θ)
 r = cos(5*θ)

r = cos(6*θ)

 r = cos(6*θ)

Leminscate:  r = +/- sqrt(a^2 * cos (2*θ))

r = +/- sqrt(9 * cos (2*θ))

 R1 = sqrt(9 * cos (2*θ)),R2 = -R1

Cardiod:  r = 2*a*(1 + cos θ)

r = 8 * (1 + cos θ)

 r = 8 * (1 + cos θ)

Limacon of a Pascal:  r = b + a*cos θ

r = 6 - 7*cos θ

 r = 6 - 7*cos θ

And the most basic polar curve of them all:
Spiral of Archidemeds:  r = a * θ

r = 3 * θ

 r = 3 * θ

Source:
Murray R. Spiegel, Ph.D.,  Seymour Lipschutz, Ph.D., John Liu, Ph.D.   "Schuam's Outlines:  Mathematicals Handbook of Formulas and Tables."  3rd Edition.  2009.

This blog is property of Edward Shore.  2015

1. Hey Eddie! Nice blog about polar curves. Brings back awesome memories of when I took calc III.

Anyway, I noticed that to get the rose shaped curves I need to type in r = cos(n*θ) instead of r = n*θ. The later function is the graph of the spiral.

-Mike

1. Mike,

You are correct - I am going to correct the blatant error now. Thank you for catching this. Much appreciated!

Eddie

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