I may now frame the idea of a mathematical circle, in which all diameters are precisely equal, in express contrast to the series of ellipses, with very unequal diameters, which the floundering hoop has illustrated in its career.
The course was in the shape of an ellipse, with rather sharp turns at either end, where the contestants, if they did not want a spill, or a bad skid, must slacken their pace.
Their ellipses elongate and flatten again to the semblance of circles.
The conical points are clearly visible as the intersections of the ellipse and circle in the (1-3)-plane.
The first of these shows how the ellipse x2 10y2 = 1 is transformed into a circle, the second in what way a dent disappears.
The minimum and maximum ellipse margins are 1.5 and 2.5, respectively.
