Liverpool FC, Fibonacci sequence, Indian mathematicians and cute coincidences | Football News

When ranked from least number of titles to most since the new era of English Premier League started in 1992, this is how teams stack up: 1, 1, 2, 3, 5, 8, 13. That’s a title each for Blackburn Rovers and Leicester City, two now for Liverpool, three for Arsenal, five for Chelsea, eight for Manchester City and 13 for Manchester United.
Aligning this specific sequence took 33 years in the making, and BBC’s Kit Yates discovered that when led from least to most, the 1, 1, 2, 3, 5, 8, 13 comprises the famous mathematical wonder, the Fibonacci sequence.
What is a Fibonacci Sequence?
Fibonacci sequences (sequences in the plural because starting with a different pair of initial numbers and following the rule of adding consecutive numbers to generate the next gives you a different, but related sequence), as per BBC, ‘were first introduced to European science in 1202 Leonardo of Pisa, also known his nickname Fibonacci (meaning son of Bonaccio).’
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So, 1+1=2 and then 1+2=3 and then 2+3=5 and then 3+5=8, so on and so forth. The happenstance, which BBC ultimately calls a “cute coincidence” or “misleading coincidence”, could only be possible after 33 years. The next one? 8+13=21. Hence, possible only after the 54th edition, should any teams get to that mark of 21 in those years, and the rest of the numbers align as well.
Its meta relevance? None. But Liverpool FC’s victory, which helped them become the English champions a 20th time, same as Manchester United in all hory, did help hang the math geek’s mletoe when Chrmas came early.
The exceptional set sees each number (after the first two) as the sum of the previous two in the sequence, the BBC noted.
‘The sequence can be found in an astonishing array of places – from the spirals of seeds on sunflower heads and the bracts of pinecones to family tree patterns in some species of animals,’ BBC wrote.Story continues below this ad
But long before Fibonacci popularised the sequences in his book Liber Abaci, the sequences had been known to Indian mathematicians, Yates noted. These were concerned with tenor notes of poetic schemes.
“They had drawn upon the sequences to help them enumerate the number of possible poems of a given length, using short syllables of one-unit duration and long syllables of two-unit duration. The Indian poet/mathematicians knew that you could make a poem of length ‘n’ taking a poem of length n-1 and adding a short syllable or a poem of length n-2 and adding a long syllable. Consequently, they figured out that to work out the number of poems of a given length you just had to add the number of poems that were one syllable shorter to the number that were two syllables shorter – the exact rule we use today to define a Fibonacci sequence,” the BBC wrote.
The Fibonacci sequence is closely interlinked with the golden ratio. ‘Hidden in the sequences is another important and related mathematical mainstay – the golden ratio. As the terms in a Fibonacci sequence get larger, the ratio of each term to the one preceding it gets closer and closer to the golden ratio – approximated to 1.61803 the first few places in its decimal expansion. The golden ratio is hypothesised to govern the arrangement of leaves on the stem of some plant species and supposedly leads to aesthetically pleasing results when applied in art, architecture and music’ the BBC further raved.
Mathematicians who deal with dull lifeless numbers all their lives, take great glee in finding patterns (it’s their magic world), and Fibonacci has been one of those sequences fetishised whenever spotted. ‘Fibonacci sequences are often held up mathematicians as exemplars of the beauty of mathematics. They can provide vivid visual examples of maths written into the patterns of the real world, without which many non-mathematicians can struggle to understand the elegance we see in our subject,’ the BBC further added.Story continues below this ad
The safety catch was inbuilt in the piece though, as Yates warned, “In our over-enthusiasm to proselytise, however, there is a temptation to cast Fibonacci sequences or the golden ratio as some sort of all-encompassing natural law governing phenomena across orders of magnitude, from the spiral shapes of nautilus shells to vortices of hurricanes to the curved arms of galaxies. It’s extraordinary, then, to find the Fibonacci sequence cropping up in a place as unexpected as the Premier League. When, as scients, we spot a well-known sequence like this appearing seemingly out of the blue, we should start to ask ourselves whether it tells us anything important about the process that generated the sequence. Is there some surprising unseen process underlying Premier League title battles or is it nothing more than a cute coincidence? Just because we can see a Fibonacci sequence in something doesn’t mean it is there for a reason,” Yates says.
A pattern doesn’t always mean causality – a coincidence is sometimes just a coincidence, the real stresses adding, “…the Premier League records is just that – nothing more than a spectacular but ultimately misleading coincidence.”
The Liverpool faithful meanwhile are just ‘Slot’s happy lots’, to win their second, a fab-onacci sequence for them.