Fibonacci Numbers and Other Very Meaningful Things

Fibonacci Numbers and Other Very Meaningful Things

1, 1, 2, 3, 5, 8, 13, 21, 34. At first glance these numbers don't seem to follow any real pattern. Or maybe they do if you're one of those math weirdos who instantly recognizes patterns in sequences like 43, 2.7, 1001, pi, etc. Well, they don't seem to have a pattern to the layman. And by "layman" I mean "average Joe," or "a normal person." But the truth is, that these numbers do have a pattern. After the first two numbers, every number is the sum of the preceding two numbers.

If you wanted to look really smart you could define the series as F₁ = 1, F₂ = 1, and F_n = F_n-1 + F_n-2 for n > 2. All the numbers in this wonderful sequence are called Fibonacci Numbers. This is very similar to prime numbers. They are both odd sequences of numbers that many people think are Very Meaningful, and they both don't seem to follow a set pattern at first. Of course, prime numbers never do follow a pattern.

The Mathematical Genius who invented these numbers (imagine someone near you suddenly bursting out: "Hey! I just invented a new sequence of numbers!") was named Leonardo Pisano. This may lead you to wonder why the numbers are called Fibonacci Numbers. I did some research, and found: only four of the letters in "Fibonacci" are also in "Leonardo Pisano," making them very dissimilar. But here's how it works. Evidently, Leonardo's dad was named Bonaccus, because they nicknamed him Filius Bonacci. If you know Latin, then you know that this nickname means "son of Bonaccus." But, his friends must have soon realized that this was not a very good nickname. It was actually longer than the name Leonardo, making it a very poor nickname. So they shortened it to Fibonacci, which, though it has the same amount of syllables, is more fun to say than Leonardo. This is something few people know. I am not making this up.

Even though I was never a close personal friend of Leonardo Pisano, mostly because I was not alive, I shall still refer to him as Fibonacci. One of my sources claims that he "played an important role in reviving ancient mathematics and made significant contributions of his own." For example, inventing neat little sequences of numbers. He lived circa 1175-1250. Basically, circa means "around." And yes, Pisano does mean "of Pisa." Which means that Fibonacci was from Pisa. If you don't know where that is, just remember the Leaning Tower of Pisa, which is in Italy. Fibonacci was born in Italy.

One thing that some people think is important about mathematicians is what the names of their books are. All mathematicians write books, but they aren't ordinary books like you find in a library. They're math books, full of formulas, theorems, and the like. In any case, Fibonacci was a mathematician, which means -- you guessed it -- he wrote books. They all have interesting unintelligible names. Liber abaci is one such book with one such name. It was published in 1202 and is simply based on algebra and arithmetic, which, though no one cares today, was pretty big stuff back in the 13th century. The Important Thing about this was that it "introduced the Hindu-Arabic place-valued decimal system and the use of Arabic numerals into Europe." There was also a problem in this book which led to the formation of the Fibonacci sequence. This is really the only thing in his book that anyone cares about today.

FACT: if you were to take all the Fibonacci numbers in size twelve Times New Roman and put them end to end, the line would go on forever! That is entirely true.

Another of his books, and this I'm sure is Very Meaningful, is Practica geometridæ in 1220 which contains a bunch of geometry and other stuff we learned two years ago. Another of his books was Liber quadratorum in 1225. In this book, ladies and gentlemen, the amazing Fibonacci "approximates a root of a cubic obtaining an answer which in decimal notation is correct to 9 places"!

FACT: if you were to start at the beginning of January, and, starting with 1, every day you earned the next consecutive Fibonacci number of dollars, by the 31st you would have earned $3,524,577.

Yet another of his books was Mis practica geometriæ, the only one of all his books with a three-word title.

Another little-known fact about Fibonacci numbers is that they have real-world applications. You may not have suspected this from a mathematician, but this was the 1200's, and real math, math with no applications to the real world, had yet to be developed. But it's true. Fibonacci numbers are everywhere. Perhaps you've heard of the book Math Curse by I don't know who, in which some kid begins to see everything in life as a math problem. It is tempting to do that here with Fibonacci numbers, but I won't. The kid probably got sent to Happy Acres ten minutes after the book was written, so that's probably what would happen to me if I did that here. Many plants' flowers have a Fibonacci number of petals. Few don't. Artistically, the Fibonacci numbers are very balanced. This is why I try to have only Fibonacci numbers of fish in all my tanks. I have 1 red-tailed shark, 2 kribs, 13 cardinal tetras, and so on. This has been one of my personal goals, and I have to admit, it looks balanced.

FACT: the 40th Fibonacci number is 102,334,155.

I remember somewhere in my science book during my freshman year, it talked about Fibonacci numbers and how they are very common in nature, especially the smaller ones. It also talked about the Golden Ratio and how the spiral of a nautilus shell follows the Golden Ratio exactly. I'm not sure quite how. I have this feeling that sometime in the future, some down-to-earth genius mathematician will discover a huge link between Fibonacci numbers and the Golden Ratio. I would not be in the least bit surprised. In fact, I would probably walk up to him and show him this paper, and say, "See?"

Another interesting thing about Fibonacci is that he was educated in North Africa. My source claims that his father "held a diplomatic post" there. I'm not sure what his father did with the diplomatic post while he was holding it. Maybe he diplomatically hit people with the post. Or maybe it was part of a fence.

FACT: Egypt is considered part of North Africa.

My source further insists that while he "traveled widely" with his father, probably avoiding being hit by the post, he was "recognising and the enormous advantages of the mathematical systems used in these countries." You should probably omit that first "and." My source apparently had a typo. This is, of course, why Fibonacci wrote Liber abaci. I'm wondering whether that's Italian or Latin. I don't know, not speaking either.

FACT: Brazil is not considered part of North Africa. It is not even on the same continent.

A man named Hankel once said something I think is very appropriate. He said: "If we compare a mathematical problem with a huge rock, into the interior of which we desire to penetrate, then the work of the Greek mathematicians appears to us like that of a vigorous stonecutter who, with chisel and hammer, begins with indefatigable perseverance, from without, to crumble the rock slowly into fragments; the modern mathematician appears like an excellent miner who first bores through the rock some new passages, from which he then bursts it into pieces with one powerful blast, and brings to light the treasures within." One must take into consideration that, if we are in fact comparing a math problem to a huge rock, the "treasures within" are actually just some very old fossils of dead things which used to be alive a long time ago. But all this to say that yes, mathematics is far more complex and I dare say, more knowledgeable than it was in Fibonacci's day. Even still, one must admire the man who realized that he had invented a sequence of numbers, knew they were Very Meaningful, and wrote it down, if only for his originality. Today mathematicians are doing Who Knows What with the sequence of numbers discovered by Fibonacci. There is actually a mathematical society called The Fibonacci Association, and it even publishes an actual journal filled entirely with stuff about Fibonacci numbers.

FACT: this journal is called "The Fibonacci Quarterly".

FACT: North Africa exists today.