[trealira]

> Also, that definition of a circle as an ellipse via locus points (which you mentioned) still requires defining ellipses by an imaginary, ideal circle--even if transcendental (and I've mentioned elsewhere, the circle never appears).

How so? I don't understand. It seems like the opposite to me: because a circle can be defined as a special case of an ellipse, then a circle is defined in terms of ellipses, not the other way around. The definition of an ellipse is a generalization of the definition of a circle.

[DiscourseFan]

Its quite a difficult problem...but also one I am actually currently working on, so I should probably put some effort into thinking about it. Give me some time and I'll get back to you. If only there was some way to do private messages on here.