I Am a Geek
Talking Basically About Bases
You may or may not know that we operate in a base-10 number system, which is a beautiful thing. It spares us from the agony of Roman numerals, where years looked something like this:
Instead of like this:
Remember all that talk about place value in elementary school? Ones, tens, hundreds, thousands, and so on? That’s the base-10 idea. Multiply 10 by itself successively, and you get the next place value.
Ten isn’t the only number to base a system on, though. Convenient with our ten-fingered anatomy, but it’s not even the only base we use on a regular basis. Time notoriously operates on non-ten bases. (Makes figuring elapsed time tricky for some students.) And since this particular country refuses to go metric, most of our measurements avoid the ease of base-10.
There are plenty of practical applications for other bases, but when I first learned about them in school, I remember just thinking it was cool to write a number that meant something other than what it looked like. Sort of a mathematical code.
For example, take base-8. We have to reassign all the place values. The ones place is still the ones place. The next place to the left is now the eights place. And the next is the eight-squareds (or sixty-fours) place, followed by the eight-cubeds (or five-hundred-twelves) place. So earlier I mentioned the year 1988. In base-8, that’d be
3 five-hundred-twelves
7 sixty-fours
0 eights
4 ones
So the year 1988 converts to 3704.
If someone gave me a worksheet of numbers to convert to different bases right now, I’d probably be a happy camper working through it.
And that concludes our Yes-I-Am-A-Geek moment for this week.
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1 commentConfessions of a Math Geek
I love calculus.
If there’s anything that cements and seals my “I’m a Geek” badge, that statement is it. And I’m okay with that.
Do you know what you can do with calculus? I’ve found most people who never took calculus have no idea what it involves, so here are some highlights.
You can find the slope of curves. Remember slope? You learned about it in algebra, probably with some variety of “rise-over-run.” It tells you how steep a straight line is, the rate at which it increases or decreases.
Well, with calculus, you can find that rate at a specific point on a curvy line. It’s starts off a little ugly and scary, with a formula that looks like this (or a variation on it):
After laboring through several problems with this not-so-fun process, your teacher reveals that there are ridiculously easy shortcuts.
You want to kill your teacher. (I warn my students ahead of time that this will happen.) Then you get over it and get to work.
This may not sound that useful, but think about all the things that involve rates. Velocity, acceleration, how quickly something is growing or shrinking, etc.
Later on, you learn how to find the area under curves. Again, it starts with a slightly complex process that you soon simplify (until it gets harder again). This concept extends to taking the graph of an equation, imagining that you’re spinning it around an axis, and finding the volume of that 3-D shape.
There are ways this is useful, too. But from the time I learned it, I thought it was just insanely cool all by itself.
Yup. A geek, for sure.
You know what’s even stranger? That slope-finding process and the area-finding process turn out to be inverses of each other. Totally unexpected, but it’s part of what makes it easier in the long run.
Anyone else have a topic they learned about in school that just makes them geek out to an irrational degree? A certain period in history, or a concept in science? It’s safe to share. All geeks are welcome here.