Arclength along an ellipse is notorfiously hard to quantify. But if the ellipse is rescaled to be a circle, points at equal angles apart seem easier to deal with. —Dan Tom Karzes wrote: ----- This suggests the following question: For any three distinct, non-collinear points, does their exist an ellipse such that (1) the points all lie on the ellipse and (2) the distances between the points, along the ellipse, are equal? -----