The golden ratio in probablistic and artificial intelligence

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 2ln φ 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.