Today is pi day and I really like to celebrate it. I mostly like to do this because I never let my kids have a day off. It's nice for them to get some relief from the normal day and also do something fun. We were talking a little bit about pi in the teacher's lounge and a fellow teacher asked, "Does pi really go on forever without repeating?"
"Yes, it's irrational," several math teachers responded at once.
"Irrational, what's that mean?"
"That it goes on forever without repeating," I responded.
"But how do you know? Are there other numbers that do this?"
I was a little surprised, but I continued on and with the assistance of other math teachers, we started to explain about square roots of numbers like 7 or 10 and how we can approximate the decimal value of those numbers by multiplying by a series of more precise decimals that narrow down the upper and lower bounds, but that you can never find the exact decimal value of your answer. It makes more sense if I can explain it with a white board and some markers, but he understood.
"But what's it for?"
What's it for? That threw me. Does it have to be for something? It's like teaching someone colors and they point to a swatch of color and ask, 'what's that?' and you say, 'purple' and they say, 'what's it for?' Purple's not for anything. I guess we use the word to describe things that are that color, but it's not like we'd be in an emergency situation asking if anyone nearby has some purple.
I finally figured out that he was asking how it was used in math or life and I explained that you would use irrational numbers to describe the length of the hypotenuse of certain right triangles. Kind of like asking, "What things are purple?" which is a much more valid question.
It made me realize that people think that math is like art or poetry or movies. And in one sense, it certainly is like those things in that it is beautiful, allows people to be creative, stimulates the mind and fills up a lot of our time. But it is different in that it is not made up. I mean there are parts of it that people just make up and we all agree on it, but in principal, math is not created, it is discovered. He thought that someone made up the idea of irrational numbers and then tried to use it, when really irrational numbers exist and someone finally found them and named them.
Let's take pi, for instance. Pi was named pi by a Welsh dude in 1706 (William Jones). Why? Because he made up the name. With good reason and all that, but he made it up. That was his creative choice and a bunch of people agreed and now math cannon causes us all to follow this choice (or not, if you feel a little rebellious). But the essence of pi, it's existence and the refinement of our knowledge about pi is not created by the whim of a smart nerd. It is discovered. A bunch of people from ancient times on noticed that the circumference of a circle divided by its diameter is always equal to the same number, no matter what circle. When you get a constant like that, it seems like it might be interesting to study. So people did: Greeks, Egyptians, Babylonians, Israelites (Pi is mentioned in the Bible!!), and Chinese among others.
Archimedes (on my top ten list for cool dead guys) refined our knowledge about pi and even gave it some upper and lower bounds. Not because he arbitrarily and creatively sat down to make up some number, but because he studied this number and found out some true things about it.
So to summarize: Edison did not create electricity, neither did Ben Franklin, math and science are discovered. No group or body of people said, " What do you think we should make 2 + 5 equal?" 2 + 5 = 7 because we labeled (the creativity part) ** + ***** = ******* with certain symbols. This creativity part doesn't change the number of cows I have if I had 2 and you gave me 5. Who decided it was 7? It just is! The label may change, but the amount of cows I have does not.
So there is my rant about how people think math is some made up set of arbitrary rules that people memorize so they can be super nerdy and prove that they have better memories than you. Math is about logical analysis of the world around us and it is described using a specific language. Ok, I feel a little better, thanks.
I'm going to end this with my Pi-Ku for today. It's like a Haiku only with a 3-1-4 pattern
Oh, pi day,
joy
you bring to all
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