Some notes about affine diameters of convex figures

Given a pointx in a convex figureM, let(x) denote the number of all affine diameters ofM passing throughx. It is shown that, for a convex figureM, the following conditions are equivalent.

(i)	(x)2 for every pointx intM.
(ii)	either(x)3 or(x) on intM. Furthermore, the setB={x intM:(x) is either odd or infinite } is dense inM.