Wikipedia:Reference desk/Archives/Mathematics/2012 August 29

= August 29 =

Interesting curves where θ = f(r) ?
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)


 * 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)


 * 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)


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


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


 * 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)


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


 * 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)


 * 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)


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


 * Rose (mathematics) expands on the roses mentioned above.--Salix (talk): 10:33, 30 August 2012 (UTC)
 * 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. Solving for &theta; results in    $$\theta=\pm\arccos\frac{l-r}{er}$$ (except the circle, which has e=0). --CiaPan (talk) 11:48, 30 August 2012 (UTC)


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


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


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