Wikipedia:Reference desk/Archives/Mathematics/2012 October 26

= October 26 =

Cylindrical sections
A cylindrical section must be an ellipse or a circle (unless the intersecting plane is vertical). Is there a way to express the eccentricity of this ellipse in terms of the angle of the intersecting plane from the horizontal, and how would it be derived? Double sharp (talk) 10:57, 26 October 2012 (UTC)
 * It the radius of the cylinder is $$r$$ and the angle is $$\theta$$ then the length of the Semi-major axis will be $$\frac{r}{\cos \theta}$$. The eccentricity of an ellipse is
 * $$\sqrt{1-\frac{b^2}{a^2}}=\sqrt{1-\frac{r^2}{\frac{r^2}{\cos^2 \theta}}}=\left|\sin \theta\right|$$
 * --Salix (talk): 12:06, 26 October 2012 (UTC)
 * Thanks! That's what I thought it would be. Double sharp (talk) 14:23, 26 October 2012 (UTC)