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

2 comments:

  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

    ReplyDelete
    Replies
    1. Mike,

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

      Eddie

      Delete

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