## Tuesday, July 30, 2013

### Let's make a nerdy clock

This was a gift from a student, and I love it very much. But there are some problems, mathematically speaking. (See 'em?)

And, anyway, 6 times 2 isn't nearly nerdy enough.

Here's what I figure: I've got a can of blackboard paint in the closet, and I can remake the clockface for mathematical correctness and interest.

But what should I put for 1 o'clock? For 7 o'clock? Midnight/noon?

You'll help me out with this, right? In the comments?

1. pi - .14 times 3 isn't 9, for the most obvious one. I'd want 9 to be a lovely, perfect square... (3/4 x 2^2)^2 ...

2. I did this with a clock years ago. I put π and φ on it. If my students knew how to read an analog clock, it would have been way funnier.

3. I don't have a great idea for 7, but there are some good options for the other two, e.g.:
1 = e^{2πi}
12 = 1!2!3! (h/t Wikipedia)

4. I contend that it's ok to have 3(pi-0.14), as long as it's very slightly above where the 9 should be. Of course, that complicates the location of the minute hand as the clock transitions from 8:59 to 9:00.

I say go easy on the radicals. Maybe do some more exponents and factorials as mentioned above. Throw 0! in there. That will mess with kids.

1. For 1 o'clock, how about 8,543^0?
A little zero exponent action?
Make up whatever base you want, but make it extreme. I don't recommend a number like 2,069.

5. I have this clock and a couple of others on my office wall. None of them are cool enough for me, but they do serve to signal that I'm a bit of a nerd.

6. My nerdy clock is a backwards clock with the times represented by the radian measure of the angles. Its at work or I'd offer a pic. I still have the doc fil I used to make it somewhere.

7. My favorite clock is the marble clock described here:
http://mcsp.wartburg.edu/zelle/cs220/marbleclock.html

It is mesmerizing to watch and is a nice example of a number system of a different base.

8. One more try...

How about a classic math mistake, 3^0, for 1? In one version of my nerdy clock, I used mostly powers, roots, and logs. I liked log_2 2^7. Obvious if kids think “What power of 2 is 2 to the 7?” rather than reach for the calculator. In the same spirit, I also like 100 000 – 99 999 for 1. I saw that you’re going to be teaching grade 4. You want them in on the joke, right? I think they’ll see 6*2 as being sufficiently nerdy. I’d lose the long division ones– dividing by 3 digit divisors belongs on the clock of the History teacher.