Alexey Stakhov

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 (elliptic geometry), non-Archimedean geometry, and Minkowski geometry). The ancient Golden Section, described in Euclid’s Elements (Proposition II.11) and the following from it Mathematics of Harmony, as a new direction in geometry, are the main mathematical apparatus for this fundamental result. By the way, this solution is reminiscent of the insolvability of the 10-th Hilbert Problem for Diophantine equations in integers. This outstanding mathematical result was obtained by the talented Russian mathematician Yuri Matiyasevich in 1970, by using Fibonacci numbers, introduced in 1202 by the famous Italian mathematician Leonardo from Pisa (by the nickname Fibonacci), and the new theorems in Fibonacci numbers theory, proved by the outstanding Russian mathematician Nikolay Vorobyev and described by him in the third edition of his book “Fibonacci numbers”.

This article deals with a wide range of issues related to the design of specialized computing and measuring systems for mission-critical applications, in which the requirements of reliability and noise immunity are put to the fore. Among these issues, we consider: paradox of the Hamming code, the ‘row hammer effect’, the ‘Trojan horse’ of the binary system. It is discussed the issue of the use of numeral systems with irrational bases (Bergman’s system, ternary mirror-symmetric arithmetic, Fibonacci p-codes and codes of the golden p-proportions) for the design of specialized computing and measuring systems for mission-critical applications.