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Fractured Memories

Some fractions are a part of everyday life; dimes, quarters, nickels, hours, minutes, seconds, etc. These are relatively easy to manage mainly because we deal with them so often. Everyone just “knows” that 1/2 is 0.5, and 1/4 is .25, and 1/10 is 0.1; we’ve had it ingrained in us through massive amounts of repetition. I go one step further; I can usually estimate the decimal equivalent of just about any fraction that comes up in my life. Super useful? Maybe not, but it has good show-off value, and I think it’s fun!

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Mom was right

Ah, Mother’s Day. Admittedly, Math isn’t the first thing you think about when scrambling for that 1-800-Flowers phone number (I always forget that one) or that last box of chocolate from the drugstore. However, one of the memories that sticks in my mind most about my Mom is arguing with her about Math during dinner about .9 repeating and 1. Before you think we’re crazy, please keep in mind she’s a Math teacher, and I have some small interest in the subject myself. So here’s to you, Mom. I finally realized you were right some time ago, but don’t think I ever said so.

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Discretely simple

I’ve said it before, and I’ll say it again – I like math. Now, don’t get me wrong; I don’t run around solving Fermat’s Last Theorem for fun on Sunday nights, or anything like that. Perhaps it would be more clear to say I enjoy math, for many reasons, not the least of which is, when you prove something in math, it’s true every time!

Since merely saying, “I can’t find a contradictory example” is never accepted as “it’s always true”, mathematical proofs are often filled with a multitude of complex concepts and references to other also very complex proofs. It’s very refreshing, I think, to find a few that are so simple and elegant, they make you wonder if there aren’t very simple proofs for those other theorems, that we just haven’t discovered yet. Here I present two of my favorite math proofs. I hope you’ll enjoy them as much as I do.
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Litter By Numbers

About two years ago, I got interested in Geocaching1. I call it “organized littering”. Essentially, people have taken the time to hide caches (usually tupperware containers full of bric-a-brac) all over the world. They then log the lat/long coordinates of their stash, and enter them along with a description on the GeoCaching site2. The rest of us use that site to find caches near where we’ll be, and off we go using our portable GPS units to find these little pockets of fun all over the world.

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Alternative Math Methods


A lot of math is broken down into processes. Start with a problem, do this, do that and, voila, you have the answer. Most people in America learn the same processes for doing most basic arithmetic, and it’s easy to forget there might be other ways to solve these problems. The positional decimal system developed by the Indians (of India) is the standard taught in every school I’ve ever been in, but it’s not the only way to multiply two numbers1. The following is a description of another method I like for its enforced structure and visual guides.

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The shortest path

Shortcuts are a great way to do a lot of math in your head. You know the guy in the office that always responds when you ask “What’s 25 times 56?” He’s using shortcuts, and so can you. The best thing about these so-called tricks? They always have a real math basis, or they wouldn’t work! Here are a few multiplication shortcuts. Learn them, and you’ll see how often the situations for which they are useful show up.

What’s the square of [some number > 20]? Does this come up for you very often? Well, maybe not, but from the square you can get great estimates on other products, and you’ll be surprised how often you come across the problems when you can easily solve them. Now, no one really expects you to memorize all the squares to 100 but, with a few shortcuts, you can compute most of them fairly easily.
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