Mathematicians discovered a strange sequence of Fibonacci after Liverpool was champion

Liverpool FC’s victory over the weekend secured them the second Premier League title, but also resulted in a curious thing-produced a strange number of numbers in the league record books.

Something has just happened extraordinary in English football. Liverpool became Premier League champion for the second time. Sound to its 18 titles prior to Premier League, the club equals the record of Manchester United, which became an English champion 20 times. But while club supporters will undoubtedly celebrate this moment of triumph, another amazing facet of their feat caught the attention of mathematicians.

The winning of the title by Liverpool completed the opening of a exceptional set of numbers which has been prepared for 33 years. The sequence comes when we put Liverpool alongside the other clubs who have won the Premier League since its inception in 1992, listing them with the number of titles won, starting with the lowest.

As you can see in the table below, the number of Premier League titles is as follows: 1, 1, 2, 3, 5, 8, 13.

For those who do not know, this sequence may not seem significant. But it will be sufficient to enthusiastic many math aficionados. Will recognize this sequence as the Fibonacci sequencewhere each number (after the first two) is the sum of the previous two of the sequence.

The sequence can be found in a amazing variety of places – From the spirals of the seeds in the heads of sunflowers and the bracts of the pine cones to the standards of the genealogical trees of some species of animals.

Fibonacci sequences (plural sequences, because starting with a different pair of initial numbers and following the rule of adding consecutive numbers to generate the following gives us a different but related sequence were introduced by first time in European science in 1202 by Leonardo de Pisa, also known for his nickname Fibonacci (which means son of Bonaccio).

However, long before Fibonacci popularizes sequences in his book Free abacisequences were already known to Indian mathematicians. They had appealed to the sequences to help them enumerate the number of possible poems of a given extension, using short syllables of a unit of duration and long syllables of two units.

Indian poets/mathematicians knew that a poem could be made in length n Taking a poem of length n-1 and adding a short syllable or in a poem of length n-2 and adding a long syllable. Consequently, they found that to calculate the number of poems of a certain length, it was sufficient to add the number of poems with a syllable less to the number of poems with two less syllables – the exact rule we use today to define a sequence of Fibonacci.

Hidden in the sequences is another important and related mathematical base – The Golden Proportion. As the terms of a fibonacci sequence increase, the ratio between each term and the previous one is increasingly approaching the golden reason-approximately 1.61803 by the first houses in its decimal expansion. It is assumed that the golden ratio governs the willingness of the leaves in the stem of some plant species and allegedly leads to aesthetically pleasant results when applied to art, architecture and music.

Fibonacci sequences are often considered by mathematicians as Examples of the beauty of mathematics. They can provide vivid visual examples of real -world mathematics, without which many non -mathematicians may have difficulty understanding the elegance we see in our discipline.

However, in our excessive enthusiasm in doing proselytizing, there is a temptation to present the sequences of Fibonacci or the golden proportion as a kind of kind of comprehensive natural law which governs phenomena of various orders of grandeur, from the spiral forms of the nautilus shells to the vortices of the hurricanes and curved arms of the galaxies.

In fact, although these natural characteristics are aesthetically pleasant, very few are in accordance with the rules of the Fibonacci sequence or display the golden proportion. We have to be careful not to try to fit all beautiful patterns in the delicate Fibonacci crystal shoe – to suggest causality and impose meaning where it does not exist.

Sometimes coincidences can lead scientists to error, seeming to point to a conclusion when, in reality, there is an alternative explanation for the observations that is best supported by the facts.

What then means for football, the fact that the beautiful and almost mystical sequence of Fibonacci appeared in the data on the number of titles won in the Premier League? Without any plausible mechanism that may have given rise to the sequence, The answer is almost certainly nothing.

It is wonderful to have discovered this mathematical sequence in such an unlikely place, giving us the opportunity to reflect on the importance of Fibonacci numbers. But a pattern does not always mean causality – a coincidence is sometimes just a coincidence.