  We begin by introducing an algebraic structure with three constants and one
ternary operation to which we call mobi algebra. This structure has been
designed to capture the most relevant properties of the unit interval that are
needed in the study of geodesic paths. Another algebraic structure, called
involutive medial monoid (IMM), can be derived from a mobi algebra. We prove
several results on the interplay between mobi algebras, IMM algebras and
unitary rings. It turns out that every unitary ring with one half uniquely
determines and is uniquely determined by a mobi algebra with one double. This
paper is the second of a planned series of papers dedicated to the study of
geodesic paths from an algebraic point of view.
