FibonacciVerhältnissen

FibonacciVerhältnissen, often translated as Fibonacci Ratios, refers to the relationship between successive numbers in the Fibonacci sequence. The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. Thus, the sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

As the numbers in the Fibonacci sequence grow larger, the ratio of any number to its preceding number approaches a specific irrational number. This limit is known as the golden ratio, often denoted by the Greek letter phi (φ). The value of φ is approximately 1.6180339887. For instance, 34 divided by 21 is approximately 1.619, and 21 divided by 13 is approximately 1.615. The closer you get to higher numbers in the sequence, the more accurate this ratio becomes to the golden ratio.

These Fibonacci ratios and the associated golden ratio appear frequently in nature, art, architecture, and design. In nature, they are observed in the arrangement of leaves on a stem, the branching of trees, the fruitlets of a pineapple, the flowering of an artichoke, and the spiral arrangement of a pine cone's bracts. In art and design, the golden ratio is often used to create aesthetically pleasing proportions and compositions. This widespread occurrence has led to much discussion and study regarding its significance and implications.