The article proves the insolvability of the 4-th Hilbert Problem for hyperbolic geometries. It has been hypothesized that this fundamental mathematical result (the insolvability of the 4-th Hilbert Problem) holds for other types of non-Euclidean geometry (geometry of Riemann (ell...
Open access
Research Article10.9734/jamcs/2019/v31i130099
The main goal of the article is to explore two unusual numeral systems, which alter radically our ideas on the positional numeral systems. We are talking on the numeral systems with irrational bases. The first of them is the binary (0,1) numeral system with the irrational base ...
Open access
Research Article10.9734/BJMCS/2016/28262
In the 70s and 80s years of the past century, the new positional numeral systems, called Fibonaссi p-codes and codes of the golden p-proportions, as new informational and arithmetical foundations of computer science and digital metrology, was considered as one of the most importa...
Open access
Research Article10.9734/BJMCS/2016/25969
This article substantiates a new look on Euclid's Elements and mathematics history, based on Proclus hypothesis. Proclus hypothesis answers the question about Euclid’s goal for writing his Elements. Two Greek mathematical achievements underlie Proclus hypothesis: the golden ratio...
Open access
Research Article10.9734/BJMCS/2016/23100
This article solves the problem of variation of fundamental physical-mathematical constant (the fine-structure constant) in dependence of the age of the Universe. This problem has been named by as one of the MILLENNIUM PROBLEMS. The mathematical model of the evolution of the Univ...
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Research Article10.9734/PSIJ/2016/21966
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...
Open access
Research Article10.9734/BJMCS/2016/21849