Hilbert's Fourth Problem as a Possible Candidate on the MILLENNIUM PROBLEM in Geometry
Alexey Stakhov *
Institute of the Golden Section, Academy of Trinitarism (Russia), Ontario, Canada.
Samuil Aranson
Russian Academy of Natural Sciences, San Diego, USA.
*Author to whom correspondence should be addressed.
Abstract
Hilbert’s Fourth Problem is one of the most important mathematical problems, formulated by Hilbert in 1900. Unfortunately, attempts to solve this problem during 20th century did not lead to the generally recognized solution, and now modern mathematicians believe that the problem has been formulated by Hilbert "very vague" and therefore it can not be solved. The main purpose of this article is to develop a new view on authors’ original solution to this problem and to interpret this problem as MILLENNIUM PROBLEM in Geometry what has an interdisciplinary importance and affects not only on geometry, but also on all theoretical natural sciences. The source of a new approach to solving this problem is a new branch of mathematics, the Mathematics of Harmony, which goes back in its origins to Euclid’s Elements and has interdisciplinary importance for modern science.
Keywords: Millennium problems, Hilbert’s fourth problem, the golden ratio, Fibonacci and Lucas numbers, Binet’s formulas, Bodnar’s geometry, Gazale’s formulas, recursive hyperbolic functions, original solution to Hilbert’s fourth problem.