The Fibonacci sequence is a mathematical sequence that starts with 0 and 1, and each subsequent number is the sum of the two preceding ones. So the sequence begins: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.
Pattern recognition can be applied to the Fibonacci sequence in various ways. Here are a few examples:
Ratio between consecutive Fibonacci numbers: As the Fibonacci sequence progresses, the ratio between consecutive numbers approaches the golden ratio, approximately 1.6180339887. This ratio is found by dividing any number in the sequence by the previous number. For example, 21 divided by 13 is approximately 1.615, which is quite close to the golden ratio.
Spiral pattern: By drawing squares with sides equal to the Fibonacci numbers and connecting their corners with a curve, known as the Fibonacci spiral, you can observe a pattern found in nature. Many natural phenomena, such as the arrangement of seeds in a sunflower, the shape of seashells, and the branching of trees, exhibit a similar spiral pattern.
Sum of even Fibonacci numbers: If you sum up only the even numbers in the Fibonacci sequence, you get a separate sequence: 0, 2, 8, 34, 144, and so on. This sequence also exhibits its own pattern, where each number is approximately four times the preceding number.
Prime numbers: Although most Fibonacci numbers are not prime, there are some notable exceptions. For example, the 2nd, 3rd, 5th, 13th, and 89th Fibonacci numbers are all prime. However, prime numbers do not occur regularly in the Fibonacci sequence.
These are just a few examples of pattern recognition in the Fibonacci sequence. The sequence has fascinated mathematicians and enthusiasts alike due to its numerous connections to nature, art, and mathematics.
