I've been studying and working problems on topics with names such as: "Connecting Euler's Formulas for Planar Networks and for Polyhedra," "Working With Angles in Regular n-Gons," and "Determining the Interior Points of a Simple Closed Curve in the Plane," to name a few. Those are topics from my Mathematics For Elementary Teachers II class. This blog is actually designed as part of my studies for Mathematics For Elementary Teachers I class. I mention both classes simply to say that while summer is normally the time for outdoor fun and swimming in the sunshine, the only thing swimming around here right now is my mind. It's a good thing. Don't get me wrong, but it is a new thing. New things always take a little getting used to.
I did give myself a break from the studies the other night and went outside to play on the trampoline in the dark with my daughter. We laughed and jumped and sang songs like a couple of dorks. After a long time we laid down on our backs and looked up. I laid there looking at the stars and feeling the breeze of a cool summer night. As I noticed the hexagonal shape of the net that surrounds the trampoline, I thought to myself, "I bet I could figure out the angles of each adjacent side of the net." That's when I realized, this math stuff gets in your head. I suppose that's the whole point.
After spending several hours this past week learning about numeration systems of other cultures from both the past and the present, I have a new found appreciation for all things math but especially for our numbering system, which now seems so much "easier" than others. It's only my second blog post and I am already referring to math as "easier?" Huh.
In all seriousness, we can be glad to have the system that we do for counting and combining numbers. I learned about the Egyptian, Babylonian, Mayan, Indo-Arabic, and Roman numeration systems. I even learned something called "The Russian Peasant Algorithm" for Multiplying." It consists of making two columns of numbers beginning with the first number to be multiplied placed at the top of a column on the left and the second number to be multiplied placed at the top of a column to the right.
From there, the numbers in the left column are halved and the numbers in the right column are doubled until the last remaining pair of numbers begins with a 1. The pairs of numbers are set up in a table. Rows of numbers beginning with an even number are crossed off of the list. At the end, the sum of all numbers remaining in the right column are added together to find the answer to the original multiplication problem. It is time-consuming, but really rather amazing. You'll want to try it. Go ahead. Just do it.
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| Multiplying Using the Russian Peasant Algorithm |
http://www.cut-the-knot.org/Curriculum/Algebra/PeasantMultiplication.shtml
Each of these systems is equally impressive. The Mayan and the Babylonian systems were pretty incredible and left me scratching my head. It's one of those things that at first is like a puzzle that you have to try to wrap your mind around and then once you get it, you get it and you can appreciate it. If you've ever mastered one of those metal "brain teaser" types of puzzles, you'll know exactly what I mean. You know, the ones where you have to get one part of this metal puzzle separated from the other and it seems impossible...until you do it...and after that you can't not know how to do it?
Mathematics is a language of its own, but it is one that has been spoken in every culture across all times. The wording and the symbols may be different, but the ideas are the same. As for me, I all of a sudden really really like the way that we "do" math here in America. And with that, I have some math to do... ...
Here is a chart of the Egyptian symbols for the powers of 10:
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| https://www.google.com/search?q=Egyptian+Symbols+for+powers+of+10&client=firefox-a&hs=FJV&rls=org.mozilla:en-US:official&channel=fflb&source=lnms&tbm=isch&sa=X&ei=dXCoU4XgNtevyASshoD4Bg&ved=0CAgQ_AUoAQ&biw=1218&bih=638 |
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