Number Theory   Natural Numbers and Their Square Roots Expressed by Constant Phi and 1

Authors: Harry K. Hahn

All natural numbers ( 1, 2, 3,…) can be calculated only by using constant Phi (ϕ) and 1. I have found a way to express all natural numbers and their square roots with simple algebraic terms, which are only based on Phi (ϕ) and 1. Further I have found a rule to calculate all natural numbers >10 and their square roots with the help of a general algebraic term. The constant Pi (π) can also be expressed only by using constant Phi and 1 ! It seems that the irrationality of Pi (π) is fundamentally based on the constant Phi and 1, in the same way as the irrationality of all irrational square roots, and all natural numbers seems to be based on constant Phi & 1 ! This is an interesting discovery because it allows to describe many basic geometrical objects like the Platonic Solids only with Phi & 1 ! The result of this discovery may lead to a new base of number theory. Not numbers like 1, 2, 3,… and constants like Pi (π) are the base of number theory ! It seems that only the constant Phi and the base unit 1 ( which shouldn’t be considered as a number ! ) form the base of mathematics and geometry. And constant Phi and the base unit 1 must be considered as the fundamental „space structure constants“ of the real physical world !

Comments: 5 pages, 1 drawing