Ask Mr. Perspective

A reader known only as “John” writes in with a somewhat technical question:

Hi, is there a method to measure the degree of an ellipse? I know I can buy an ellipse template, but is there a way to do it without one?

David Chelsea is reading:
by Craig Thompson

This one caused me a bit of mental anguish, because I couldn’t find a rule in the books, and so had to work it out for myself. I started by trying to draw an isometric ellipse, beginning with a line the width of the long axis (which is unforshortened and therefore the same width as the circle in plan), line A-B. I then took that line and tipped it to what I know to be the angle a cube is tipped in isometric projection, approximately 35.264°, line B-C. I then drew another horizontal line D-E, touching C and crossing vertical lines from A and B to form a bounding box for the ellipse, with long and short axes dividing the box in half. The construction basically agrees with the isometric ruling lines already on the paper, and I’m certain the same principle will apply to a circle (in which case B-C will stick straight up at a 90 degree angle), so I will go out on a limb and say this will work for an ellipse of whatever degree. If you have an ellipse of unknown degree, you would work backward to find its inclination.

Next question?