Axiality has been studied under a definition given here: https://en.wikipedia.org/wiki/Axiality_(geometry)
Consider an alternative definition of axiality as follows: For a convex region C, consider a chord L and the set of chords of C that are perpendicular to L. For each perpendicular chord, consider the ratio: length of smaller segment to length of larger segment into which L divides it. Now, for chord L, define an 'axiality ratio' as the minimum of these ratios over all its perpendicular chords. Now, the best axis of C is that chord for which axiality ratio is a maximum and that value of the axiality ratio could be called the axiality of C itself.
Question: What shape of C minimizes axiality under this new definition?
Note: Some more related thoughts are recorded at http://nandacumar.blogspot.com/2023/01/axiality-of-planar-convex-regions.html and http://nandacumar.blogspot.com/2023/01/centralness-of-convex-planar-regions.html