СOMPLEMENTARY ALGEBRA AND ITS APPLICATIONS ON THE REPRESENTATION OF COMPLEX NUMBERS BY COLOR

In many applications negative value and positive value of a variable are of different nature (biochemical mediators and hormones, neural nets, colors in human perception and others), so the sum of equal amounts of complementary substances is invariant in respect to the substances added. For instance, addition of any two complementary colours on colour circle gives white colour. It is natural to interpret the sum of complementary substances as zero regardless of their physical or biological nature.

In the present contribution we demonstrate how one can construct algebra (for instance, real, complex and quaternion numbers) and other algebraic structures based on regular representation of a group and projective geometry on n-dimensional cones with n variables with non-negative values. In particular, all points of a cone, which are projected into zero, are interpreted as having zero value. Any two points on cone, which sum is projected to zero, we will call complementary.  The representation permits to use powerful methods of the theory of analytical functions, differential geometry and topology  in new areas.

See attached article

3 complex number rerpesentation by colors