MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am a faculty member in the Forensic Science Program at PennState (UP). I am trying to obtain information of a historical nature concerning two closely related topics. I seek historical references for the calculation/determination of the major and minor axes of an ellipse formed by:

  1. the orthogonal projection of a circle onto a plane, where the axes of the resulting ellipse are expressed in terms of the inclination angle of the plane;

  2. the intersection of a plane with a right cylinder (obliquely), where the axes of the ellipse are related to the inclination of the plane relative to the axis of the cylinder.

Hopefully, my descriptions are clear. I believe that Serenus may have described the latter scenario. However, I have been unable to confirm this hunch. This historical research is being done for a project that utilizes these calculations in a forensic science context. Any assistance or guidance you could provide would be greatly appreciated. Thank you!

share|cite|improve this question
While I'm not going to close your question, I just thought I would let you know that this website probably isn't the best place to look for information like this. I suppose you never know who's lurking around, but as you can see, it's of quite a different nature from the other questions on the site. We're mathematicians here, not historians of math. Also, your question is a little unclear: are you looking for the earliest reference? – Ben Webster Nov 2 '09 at 0:18
Yes, the earliest reference(s). Any suggestions on where I could obtain this information? Thanks! – Ralph Ristenbatt Nov 2 '09 at 0:28
This is a little outside the usual range of questions here, but we're not going to close it (barring further discussion on meta!). This sort of question feels like asking a physicist for the first reference to a description of a lever! :-) – Scott Morrison Nov 2 '09 at 2:02
Just to be absolutely clear, you need a reference along the lines of "r radius of base circle, a is angle, axes are r/cos(a) and r?" – Jason Dyer Nov 2 '09 at 2:25
Correct, Mr. Dyer! The earliest reference possible...I realize that this is a daunting task...I wasn't sure where else to turn as this site was recommended by a PennState mathematician. Thanks again! – Ralph Ristenbatt Nov 2 '09 at 14:26

I have found the following avaialable on the web

It is the A History of Greek Mathematics (1921)

by Thomas Little Heath

it has a section discussing the two known works of Serenus "On the Section of a Cylinder" and "On the Section of a Cone" see pages 519 to 526.

share|cite|improve this answer
Thank you! I've got this reference but it doesn't seem to give me what I am looking for with this search. Maybe Serenus laid the foundation but didn't elucidate the relationship between the angle and the ellipse dimensions...Hmmmmmmmm.... – Ralph Ristenbatt Nov 2 '09 at 0:48

The earliest reference I have so far to #1 is The Mathematical Miscellany from 1836.

(page 184)

It quite possibly only came up with the invention of spherical geometry, so earliest references to that might be fruitful.

share|cite|improve this answer
Thank you! Downloading it as I write this! Thanks again! – Ralph Ristenbatt Nov 2 '09 at 17:21

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.