Mathematics desk
< August 28	<< Jul \| August \| Sep >>	August 30 >

Welcome to the Wikipedia Mathematics Reference Desk Archives
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

August 29[edit]

Interesting curves where θ = f(r) ?[edit]

I'm testing a program I've written which (among other things) graphs polar equations where the angle is a function of the radius. So far all I've tested is θ = r, which is just a basic spiral. Anyone have anything more interesting for me to try ? StuRat (talk) 12:41, 29 August 2012 (UTC)[reply]

You can try

r^{2},\ {\sqrt {r}},\ \exp(r)

. If you had

r=f(\theta )

you would have some nicer options. -- Meni Rosenfeld (talk) 14:21, 29 August 2012 (UTC)[reply]

I have both. For r = f(θ) I found some nice roses and heart plots, the last of which looks like something right off a valentine. StuRat (talk) 14:34, 29 August 2012 (UTC)[reply]

theta = 2 pi r/(r-1) Count Iblis (talk) 16:00, 29 August 2012 (UTC)[reply]

theta = 2 pi sin(r) Count Iblis (talk) 16:10, 29 August 2012 (UTC)[reply]

I like that last one, since it's the only one which isn't some type of spiral. StuRat (talk) 03:29, 30 August 2012 (UTC)[reply]

\theta =\pm \arccos {\frac {r^{2}+d^{2}-m^{2}}{2rd}}

for

0<m<d

is a circle with radius m and the center d apart from the coordinate system's pole. --CiaPan (talk) 06:14, 30 August 2012 (UTC)[reply]

How can the center be a single variable "d" ? Isn't it always 2 coords in 2D, either (x,y) or (r,θ) ? StuRat (talk) 10:13, 30 August 2012 (UTC)[reply]

Sorry for my poor English, I meant the distance from the pole to the circle's center equals d. CiaPan (talk) 11:12, 30 August 2012 (UTC)[reply]

Thanks for the clarification. StuRat (talk) 18:58, 30 August 2012 (UTC)[reply]

Rose (mathematics) expands on the roses mentioned above.--Salix (talk): 10:33, 30 August 2012 (UTC)[reply]

Conic sections have general equation in polar coordinates

r={\frac {l}{1+e\cos \theta }}

(with the pole being the section's focus), see Conic section#Polar coordinates. Solving for θ results in

\theta =\pm \arccos {\frac {l-r}{er}}

(except the circle, which has e=0). --CiaPan (talk) 11:48, 30 August 2012 (UTC)[reply]

Isn't that a division by zero error ? StuRat (talk) 18:58, 30 August 2012 (UTC)[reply]

Congratulations! You've discovered the asymptote through numerical experimentation! Nimur (talk) 20:48, 30 August 2012 (UTC)[reply]

Asymptotic to a circle ? StuRat (talk) 06:42, 31 August 2012 (UTC)[reply]