28th June 2022

Practical Applications of the Fibonacci Sequence

While the Fibonacci sequence might not appear significant, it has been rediscovery in an amazing diversity of forms, ranging from branches of higher mathematics to applications in computing, statistics, natural sciences, and Agile development. While using the familiarity to predict market movements is far less determinative than using it to compute patterns in sunflower seeds, the appearance of the sequence in finance is yet another indication of its power in engaging human imagination. Humans are hardwired to recognize patterns, and when it comes to the Fibonacci number, we are not limited to looking for and celebrating the sequences found in nature. Some do make predictions using the level of the Fibonacci retracement, which comes from the familiar.

Technical analysts can examine an entire set of numbers that match the proportions of numbers in the Fibonacci series, but a couple important ones are 61.8% and 38.2%. These numbers, 34 and 21, are numbers in the Fibonacci sequence, and their ratio, 1.6190476, is close to Phi, 1.6180339. The squares are arranged exactly as they should be, since the ratio of numbers in the Fibonacci series is extremely close to the Golden Ratio , approximately 1.618034. We can see each successive number in the sequence is approaching, or getting nearer to, the Golden Ratio.

We can begin any Fibonacci-like number sequence with any two whole numbers, so long as every succeeding number is still following the rule that it is the sum of the preceding two numbers. The third equation is a recursive formula, meaning each number in a Fibonacci sequence is defined using the preceding numbers. Every third number in the sequence is an even number, and, in general, every kth number in the sequence is a multiple of F k.

The Fibonacci sequence is a series of numbers starting with a single one, followed by one, and proceeds according to the rule that every number (called the Fibonacci number) is equal to the sum of its preceding two numbers. The Fibonacci sequence is a set of integers (the Fibonacci numbers) that starts with zero, followed by one, followed by another one, then by a sequence of continuously increasing numbers. This method is named for, and derived from, the familiar.

Applications of the Fibonacci numbers include computing algorithms, such as the Fibonacci Search Technique and Fibonacci Heap Data Structure, as well as graphs called Fibonacci Cubes used to interconnect concurrent and distributed systems. It is frequently used to introduce the concept of recursion to new programmers,1 and is a common interview question.2 There is also an algorithm to search through ordered arrays using Fibonacci numbers called fibonacci searching. Music uses the Golden Ratio and Fibonacci sequence, and there is even a composition technique devoted to using the sequence, Schillingers system.

The question about the Fibonaccis, concerning the rabbit, is an unrealistic scenario, and the sequence can be observed in nature, for example, in the arrangement of sunflower seeds and other plants, as well as the shapes of galaxies and hurricanes. Fibonacci number sequences are found in nature, not just his experiments on rabbits, but in beautiful flowers.

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