3D Fractals, Axiom of Algebra (Δ_<i>n</i>)^<i>n</i> = +1

Abstract

After having laid down the Axiom of Algebra, bringing the creation of the square root of - 1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.