Love & Math

For my project, I decided to read the book Love and Math by Edward Frenkel. I was originally attracted to this book because of it’s cover and it’s interesting sounding title. After reading the description of the book, it seemed like something that could be pretty interesting.

I ended up reading only about half of the whole book. The parts about Edward Frenkel’s life I found very interesting. A little bit about Edward Frenkel’s life:

He’s a mathematician that was originally interested in quantum physics, but was converted to mathematics by Evgeny Evgenievich, who became one of his mentors at a young age. He wanted to study mathematics at Moscow State University, but was not accepted due to the extreme discrimination against Jewish people. Instead, he had to enroll in the applied mathematics program at the Moscow Institute of Oil and Gas. He snuck into lectures at MGU, attended Israel Gelfand’s seminar and worked with mathematicians like Dmitry Fuchs. Frenkel received his PhD from Harvard University in 1991, and now has been a professor at UC Berkeley since 1997.


The math parts of the book I found….not so interesting.

Frenkel talks about some pretty advanced stuff, and a lot of it was  over my head. It took a while to even get through a chapter because I constantly had to keep re-reading to try to understand what he was talking about.

At one point in the book, Frenkel talks about Fibonacci numbers briefly, and I was like woah something I actually understand!

So, I decided to take this topic from the book and research it a little more.


We all know that the Fibonacci numbers are defined as each number being equal to the sum of the preceding two numbers. (1,1,2,3,5,8,13,21,34,…)

Using this rule, you can only find the nth Fibonacci number if you know the previous two, which isn’t very effective.

Is there a way to find the nth Fibonacci term without finding all the previous numbers?

In his book, Frenkel talks about how the Fibonacci numbers can be generated using the following series:

q+q(q+q^2)+q(q+q^2)2+q(q+q^2)3+q(q+q^2)4+…

When expanded out, the coefficient in front of q^n should be the nth Fibonacci number.

I did this for n=1 through n=4 and showed that the coefficients do come out to be the Fibonacci numbers.

Scan0001

I also was researching the Fibonacci sequence online and found another way to find the nth term of the sequence. This can be done using Phi (comes from golden ratio) and phi (the reciprocal of Phi).

Scan0002

Obviously by hand is not the most efficient way of going about that, and it would be much easier to do with a calculator. Using this, we can find essentially any Fibonacci number we want. For example, we can find the 50th term.

Scan0003


 


The Fibonacci sequence appears a lot in nature, and it also occurs in the sums of the diagonals of Pascal’s Triangle.

pascals-triangle-fibonacci


 

So this was me expanding on a topic I could fully comprehend from the book I read, Love and Math, by Edward Frenkel.

I’m sure this book is really good if you’re smarter than I am and can get more out of it.

 

Credits:

http://www.motherjones.com/files/Frenkel-LM.jpghttp://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibFormula.htmlhttp://www.goldennumber.net/wp-content/uploads/2012/05/pascals-triangle-fibonacci.gif

 

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OArianna

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