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

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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)