I am looking for an adjective or word to describe an ellipse (or ellipsoid, in more dims) where the length of the principal axes are of roughly the same order of magnitude $\mathcal{O}(a) = \mathcal{O}(b)$ (including equal, i.e. a circle).
For instance:
- $a=2$, $b=5$ would be something like an "isometric" ellipse (or ellipsoid)
- $a=2$, $b=50$ would be something like an "asometric" ellipse (or ellipsoid) since they are of different orders of magnitude
I am aware of no special name. But is a name was to be given, I would say very plainly "with high or low" eccentricity due to formula
$$e=\sqrt{1-\frac{b^2}{a^2}} \ \ \text{on a scale} \ \ 0 \le e < 1$$
(the minimum $0$ for a circle, $1$ cannot be attained because we would have then a parabola).
Besides, for the 3D case of an ellipsoid with semiaxes
$$a \ge b \ge c,$$
I would like to attract your attention on two specific names for the case of equality:
if $a = b > c$: "Prolate spheroid" (in fact ellipsoid) (rugby ball),
if $a > b = c$: "Oblate spheroid" (ideal Cinderella's pumpkin...).
The prolate spheroidals, in particular, are connected with various applications:
a 3D coordinates' system
orthogonal functions. See for example this article explaining how that these functions are at the same time orthogonal in $L^2(-1,1)$ and in $L^2(-\infty,+\infty)$...