**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

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

ReplyDeleteAnyway, 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

Mike,

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

Eddie