Positive approach: Implications for the relation between number theory and geometry, including connection to Santilli mathematics, from Fibonacci reconstitution of natural numbers and of prime numbers

Abstract

The paper recapitulates some key elements in previously published results concerning exact and complete reconstitution of the field of natural numbers, both as ordinal and as cardinal numbers, from systematic unfoldment of the Fibonacci algorithm. By this natural numbers emerge as Fibonacci "atoms" and "molecules" consistent with the notion of Zeckendorf sums. Here, the sub-set of prime numbers appears not as the primary numbers, but as an epistructure from a deeper Fibonacci constitution, and is thus targeted from a "positive approach". In the Fibonacci reconstitution of number theory natural numbers show a double geometrical aspect: partly as extension in space and partly as position in a successive structuring of space. More specifically, the natural numbers are shown to be distributed by a concise 5:3 code structured from the Fibonacci algorithm via Pascal's triangle. The paper discusses possible implications for the more general relation between number theory and geometry, as well as more specifically in relation to hadronic mathematics, initiated by R.M. Santilli, and also briefly to some other recent science linking number theory more directly to geometry and natural systems.