The structure of the decimal expansion of the Golden Ratio is examined in decimal and modular forms through the use of various properties of the Fibonacci numbers, particularly the roots of the associated polynomial and the golden ratio. While the ratio Fn+1/Fn approaches the golden ratio it cannot have both terms even, whereas the ratio Fn+6/Fn can. The decimal string of the golden ratio is given in ratio and binomial forms and analysed with the modular ring Z4 and the sequential structure. The decimal part of the golden ratio is also related to pi
Taking the reciprocal of the golden ratio and summing its non-negative integer powers, we obtain a s...
We discuss the well-known importance of the golden ratio in Science and Art with few examples: its t...
The numbers in the so-called Fibonacci Sequence express Euclid’s division in extreme and mean ratio ...
The Golden Ratio, also known as the Golden Section, exists as a proportion of lengths. Calculated to...
Expansions in the Golden ratio base have been studied since a pioneering paper of Rényi more than si...
The golden ratio, or phi (φ = 1.6180339887...), is a ratio that has interested mathematicians as wel...
We consider thewell-known characterization of theGolden ratio as limit of the ratio of consecutive t...
The Golden Ratio appears in many situations: in geometry, in lists with special numbers drawn up by ...
We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive...
The sequence of Fibonacci numbers is given by 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 6...
The main purpose of this paper is to give many new formulas involving the Fibonacci numbers, the gol...
The ratio of two successive Fibonacci numbers approaches the value of the golden ratio (1+sqrt(5))/2...
The golden ratio and the Fibonacci numbers have a very noticeable presence in many mathematical appl...
The Fibonacci number sequence is famous for its connection to the Golden Ratio and its appearance wi...
In this article, we illustrate the use of a scientific calculator for exploring the Fibonacci sequen...
Taking the reciprocal of the golden ratio and summing its non-negative integer powers, we obtain a s...
We discuss the well-known importance of the golden ratio in Science and Art with few examples: its t...
The numbers in the so-called Fibonacci Sequence express Euclid’s division in extreme and mean ratio ...
The Golden Ratio, also known as the Golden Section, exists as a proportion of lengths. Calculated to...
Expansions in the Golden ratio base have been studied since a pioneering paper of Rényi more than si...
The golden ratio, or phi (φ = 1.6180339887...), is a ratio that has interested mathematicians as wel...
We consider thewell-known characterization of theGolden ratio as limit of the ratio of consecutive t...
The Golden Ratio appears in many situations: in geometry, in lists with special numbers drawn up by ...
We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive...
The sequence of Fibonacci numbers is given by 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 6...
The main purpose of this paper is to give many new formulas involving the Fibonacci numbers, the gol...
The ratio of two successive Fibonacci numbers approaches the value of the golden ratio (1+sqrt(5))/2...
The golden ratio and the Fibonacci numbers have a very noticeable presence in many mathematical appl...
The Fibonacci number sequence is famous for its connection to the Golden Ratio and its appearance wi...
In this article, we illustrate the use of a scientific calculator for exploring the Fibonacci sequen...
Taking the reciprocal of the golden ratio and summing its non-negative integer powers, we obtain a s...
We discuss the well-known importance of the golden ratio in Science and Art with few examples: its t...
The numbers in the so-called Fibonacci Sequence express Euclid’s division in extreme and mean ratio ...