Monday, February 24, 2014

Book Review-The Math Book

For the past several weeks, I have read The Math Book by Clifford A. Pickover. Overall, I like the idea of this book. It is a book of the 250 most important mathematical innovations. Each page gives you a new and exciting discovery in math. This all happens in the order they were discovered.

I feel as though the discoveries at the beginning of the book were way more interesting than the later ones. This is probably because the discoveries at the beginning lead towards the discoveries that happened later in history.

The invention that I felt was the most interesting was the simple game of Tic Tac Toe. This game is traced back to 1300 BC.  It is considered the "atom" of board games because many other games are based off of Tic Tac Toe. Interestingly, there are 362,880 ways to place X's and O's. Of these possibilities, there are 255,168 possible games that can be played that end in 5,6,7,8, and 9 moves.

Along with Tic Tac Toe, I found the pages that were on items such as the Mobius Strip and the Klein Bottle were interesting. They are objects that are in at least three dimensions but they are only one sided objects.

This book shows us many interesting discoveries in math and tells us everything they can in a one page summary.

One of the major flaws with this book is that the author deviates from the math quite often. He tells us a lot about the mathematicians as well. The flaw comes in the way he does this. He touches on the families of the mathematicians but only seems to do it for the female mathematicians. He also points out the religions of the mathematicians if they are not a white Christians. This happened mostly when they were Jewish. I feel as though it is demoralizing being a female mathematician that he would say this stuff. It is more important to talk about their contributions than to tell us how many children the females have or of what religion they are.

Overall, I do believe that this book has a good idea about it. I just feel that it would be better if it stuck more to the math than the other stories that aren't of any importance.

Thursday, February 20, 2014

History of Math-Fibonacci

Growing up, we always here about this thing called a Fibonacci sequence. I never really understood it until I reached high school. Now I look at this sequence and these numbers all the time. But where did these magic numbers come from?

Fibonacci, also known as Leonardo of Pisa, was an Italian mathematician from the 13th century. He is considered one of the greatest mathematicians from the medieval times. In the year 1202, Fibonacci traveled around Europe and Northern Africa promoting his book, Liber Abaci (The Book of Abacus). This book gained widespread recognition. First of all, in this book Fibonacci introduced the Hindu-Arabic number system into Europe. Secondly, n this famous book was the Fibonacci sequence; one of the world's most famous sequences.

This sequence is famous for a couple of different reasons. I would say that the most important reason is because we see this sequence of numbers everywhere in nature. Even in Fibonacci's original question asking "How many rabbits are created in one year with one pair of rabbits?"

It is unknown how Fibonacci created this sequence. Some believe that he was not the one to create it. He is just the one to make it famous.

Tuesday, February 4, 2014

Nature of Mathematics-Algebra Vs Geometry

Today I was thinking about the differences between algebra and geometry. It is clear that they are both part of mathematics but why? They are considered two different subjects. Or at least that is what we think. When really looking into the basics and the foundation, they are more similar than people or even myself think. I have come to realize that we can't have geometry without algebra and we can't have algebra without geometry.

The obvious one to discuss is that we can't have geometry without algebra. This is seen within every calculation for geometry. For instance, we try to find the angle measurement of a circle by setting an equation equal to alpha and solving for alpha. Or if we know that volume of a cylinder and we can find the height. We do all of this using algebra.

Looking at the other direction is a bit more difficult. How can we relate algebra to geometry. We learn this in the most simple form. We use it when we are looking for a variable, x, and are given a square or a rectangle. We also see it in slopes. Finding the "rise over run" of a simple geometric figure, a line.

There are many difference when comparing algebra to geometry but there are even more similarities. These are just a few examples. Algebra and geometry go hand 'n hand.