Friday, August 29, 2014

The Son of a Simpleton

They call him the man with many names. They call him Leonardo Pisano Bigollo, or Leonardo Pisano, or Leonardo Bonacci. They call him Leonardo Fibonacci and even, by some, “the most talented Western mathematician of the Middle Ages.” He did not however, actually discover the number sequence named after him (the Fibonacci numbers) as most would otherwise suspect. Most of Fibonacci’s fame should be attributed to his 1202 composition of “Liber Abaci” — a book that spread the Hindu-Arabic numeral system throughout Europe. 

Fibonacci’s early life appears to be a bit of a mystery. There are two separate theories which shed some light on why Fibonacci came to adopt so many names. The first theory presents Fibonacci’s father as a wealthy merchant named Guglielmo Bonacci. Some even go further claiming that Bonacci was the consul for Pisa. 

(Fibonacci was from Pisa, you know, the place with the off-kilter tower.) 

Alternatively, according to a history text by mathematician Tobias Dantzig, his father was "a lowly shipping clerk nicknamed Bonaccio, which, in the idiom of the period, meant 'simpleton’. This would explain the name given to his son... 'Fibonacci,' the 'son of a simpleton.’” Someone on Yahoo divulges that Leonardo's father, Guglielmo Bonacci, was a kind of customs officer in the North African town of Bugia now called Bougie where wax candles were exported to France. They explain that this is why candles are still called "bougies" in French. Despite the controversy concerning Bonacci’s profession, Fibonacci described his father in the introduction to “Liber Abaci” as “a public official… in the Bulgia customs house established for the Pisan merchants.” 

So why, if the sequence of numbers most commonly referred to as the “Fibonacci numbers” weren’t actually discovered by Fibonacci, what gives with the name? In “Liber Abaci,” the middle-age mathematician (that is, the mathematician from the middle ages, not to be confused with a middle-aged mathematician) posed, and solved a problem regarding the rate of reproduction in rabbits. The solution, generation by generation, turned out to be the same sequence of numbers we associate with the formula for the Golden Ratio: which occurs when a ratio is the same as the ratio of their sum to the larger of the two quantities. 

In the Fibonacci sequence of numbers, each number is the sum of the previous two numbers. Fibonacci began the sequence not with 0, 1, 1, 2, as modern mathematicians do but with 1,1, 2, etc. He carried the calculation up to the thirteenth place (fourteenth in modern counting), that is 233, though another manuscript carries it to the next place: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377. Fibonacci did not speak about the golden ratio as the limit of the ratio of consecutive numbers in this sequence.

Rabbits are far from the only animals affected by the Fibonacci number sequence. One of my favorite connections actually has to do with bees. The most profound example is by dividing the number of females in a colony by the number of males (females always outnumber males). The answer is typically something very close to 1.618. In addition, the family tree of honey bees also follows the familiar pattern. Males have one parent (a female), whereas females have two (a female and male). Thus, when it comes to the family tree, males have 2, 3, 5, and 8 grandparents, great-grandparents, gr-gr-grandparents, and gr-gr-gr-grandparents respectively. Following the same pattern, females have 2, 3, 5, 8, 13, and so on. Anyway, it seems as though Fibonacci has been a buzz word for a while now. 

We know Fibonacci is a man of many names, but he’s also a man with many things named after him.  For instance, there are many mathematical concepts named after Fibonacci, usually due to their connection to the Fibonacci numbers. Examples include the Brahmagupta–Fibonacci identity, the Fibonacci search technique, and the Pisano period. Beyond mathematics, namesakes of Fibonacci include the asteroid 6765 Fibonacci and the art rock band The Fibonaccis

It is my belief that every member of “The Fibonaccis” band would have burned at the stake if they presented this during Fibonacci’s time. 

While we’re on the topic of music, I’ll end by presenting a beautiful musical translation of the Fibonacci number sequence. Enjoy. 

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