[math-fun] Shape of the Colosseum, again

If we approximate an ellipse of parameters a,b and of eccentricity e by n circular arcs joined in C1 fashion, then we can also equivalently view this picture as approximating a circle by a set of n elliptical segments of eccentricity e (in the orthogonal direction) by dilating the picture in the b direction by a factor a/b. Making this change will make any errors in the approximation more obvious, because lack of circularity is easier to see than non-ellipticity (ellipticality? ellipticalness?).