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(6*θ)
Leminscate: r = +/- sqrt(a^2 * cos (2*θ))
r = +/- sqrt(9 * cos (2*θ))
Cardiod: r = 2*a*(1 + cos θ)
r = 8 * (1 + cos θ)
Limacon of a Pascal: r = b + a*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
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
** 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