In article ,
Roger wrote:
Ralph wrote:
Turn The leg on two offset centers at 180 degrees with the center point
equal distant from the center.



I guess I'm missing something. How does this form an ellipse? Aren't
the ends going to be circular rather than elliptical in section? Unless
the lathe moves the center while rotating as is possible with some
ornamental lathes the section can't be elliptical.

Roger

Consider a circular cylinder.

Consider what you get if you slice that cylinder at an angle.

Now, construct a cylinder perpendicular to that angled cross-section slice.

You have, obviously, and elliptical cylinder.

It should be "obvious to the casual observer" that you can take an angled
slice of _that_ cylinder in a manner that will yield a circular cross-
section. That cross-section is perpendicular to the minor axis, and at
an angle to the major axis such that the 'diagonal' is the same length
as the major axis. Mathematical "proof" gets a little messy, but is
fairly straightforward -- take the equation of an ellipse, parameterized
as a function of the major and minor axis lengths, set the two lengths
equal, and "reduce".

"A quantitative answer is left as an exercise for the student." *GRIN*