Review article

The golden ratio in probablistic and artificial intelligence

Ilija Tanackov ; University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia
Jovan Tepić ; University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovica 6, 21000 Novi Sad, Serbia
Milan Kostelac ; University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Ivana Lucica 5, 10000 Zagreb, Croatia

Abstract

The problem of the line section based on the golden ratio φ = 1,618033 has the analogy in probability. The solution of the elementary exponential distribution relies on the value 2lnφ 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 φ. Two new theorems on the convergence between the constants φ 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 φ 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.

Keywords

artificial intelligence; golden ratio; Markov processes

Hrčak ID:

75415

URI

https://hrcak.srce.hr/75415

Publication date:

27.12.2011.

Article data in other languages: croatian

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