HYPERCOMPLEX ALGEBRAIC STRUCTURES ORIGINATING ON A SET OF ONE-DIMENSIONAL ELEMENTS

А series of hypercomplex numerical sets having a compositional structure is shown to arise in an abstract environment consisting of randomly oriented 1D geometric objects. We focus on the series’core set which is represented by a groupoid-type algebraic system with one binary operation, associative multiplication, admitting zero-dividers but having no unity; an original Cayley-type table for this set is given. Introduction of the operation of reversible addition extends the set to algebras of real, complex and hypercomplex numbers with units built of the initial simple elements. It is demonstrated that this fundamental mathematics is tightly linked with the origin of the basic equation of quantum physics.