book review...

Lately I've been fiddling around trying to read different genres of book and it hasn't been going as well as I'd hoped. In an effort to read something intelligent, I picked up a copy of The Golden Ratio by Mario Livio. It is about the number phi, 1.6180339887...; which is expressed more precisely as the ratio of the diagonal of a pentagram to its side. This number is often referred to as the golden ratio, or the golden number because it often appears in plants, artwork, poetry, architecture and music (and in geometry it's called the golden angle). It has been studied by many and has some very interesting properties.

What I thought was interesting about the book was the author discusses how we as people understood the concept of counting higher than the number of fingers we have. Have you ever though about how cavemen went about bartering antelope meat for lima beans? One antelope carcass has got to be worth a whole horde of lima beans, but how does Iggy (the hunter) tell Narg (the gardener) that he owes him 20 meals of beans for his one killed antelope. Well, it seems that there were some archeologists that found a baboon thigh bone from 10,000+ years ago that had notches on it. So I would guess that Iggy just notched his bone for every meal of beans he recieved from Narg.

Something else that I found interesting is how we ended up with 60 seconds as our time base when we have a base 10 numbering system. The author explained that way back when, different cultures had different numbering systems. And as one culture was overrun by another the numbering systems were adopted, meshed or thrown out.

One other common theme of this book is the Fibonacci sequence and how the sequence approaches the golden ratio as the sequence approaches infinity. The Fionacci sequence is this: 1, 1, 2, 3, 5, 8, 13, 21, 39, ... and is achieved by taking the previous two numbers in the sequence and adding them (1+1=2, 2+3=5, and so on). What is neat about this sequence is how it appears in nature as well. It is called phyllotaxis and it is when plant leaves or flower petals arrange themselves in this manner. This appears in the pineapples, sunflowers and roses. In some plants it also describes the arrangement of branches on a tree in relation to the trunk. Very neat.

There are also some very cool mathmatical examples which were shown in the book, like how Fibonacci numbers are related to Pythagorean triples. For example, if you take any four consecutive Fibonacci numbers, such as 1, 2, 3 and 5;
The product of the outer numbers 1x5=5,
twice the product of the inner terms 2x2x3=12, and
the sum of the squares of the inner terms 2^2+3^2=13...
gives the 3 legs to a Pythangorean triple. Also, note that the third number, 13 is a Fibonacci number. Pretty sweet, huh!

So I was able to find some gems in the dry roughage of this book. I really found it boring how he presented arguements concerning plagerism of certain mathematicians of the 1600's. And the chapters on poetry and music I skimmed them (that's being generous). But will admit that I would pick up another book by this author if I had the chance.