THE GOLDEN RATIO IN PROBABLISTIC AND ARTIFICIAL INTELLIGENCE

The problem of the line section based on the golden ratio iota = 1,618033 has the analogy in probability. The solution of the elementary exponential distribution relies on the value 2ln iota in particular. This value also plays a key role to Riccati hyperbolic functions with Fibonacci and Lucas numbers in continuous domain. This establishes a close relationship between the constants e and iota . Two new theorems on the convergence between the constants iota and e were derived. The number e is the foundation of Markov processes, which find applications in probabilistic and artificial intelligence theory. The ratio between the constants iota and e, as well as many other natural phenomena based on the golden ratio, highlight the need to expand the field of probabilistic and artificial intelligence.Original Abstract: Problem linijskog odsjecka utemeljenog na omjeru zlatnog reza iota = 1,618033 ima analogiju u vjerojatnosti. Rjesenje elementarne eksponencijalne raspodjele, posebice isti iota ce vrijednost 2ln iota . Ova vrijednost takoder ima kljucnu ulogu u odnosu Rikatijevih hiperbolicnih funkcija s Fibonacijevim i Lukasovim brojevima u kontinuiranom podrucju. Time se uspostavlj a bliska veza izmedu konstanti e i iota . Izvedena su dva nova teorema o konvergencij i konstanti iota i e. Broj e je temelj Markovskih procesa, koji su nasli primjenu u teoriji vjerojatnosni i umjetne inteligencije. Omjer konstanti e i iota , kao i mnogi drugi prirodni fenomeni na temelju zlatnog reza, isticu potrebu zaprosirenjem podrucja vjerojatnosni i umjetne inteligencije.