Math Alert
I guess I can ramble a bit about some math stuff. A couple of weeks ago at the card shop, a friend of mine was talking about a couple math problems he was given as part of a phone interview. The first was about the hands of a clock. How many times do the hour and minute hand overlap in the course of a day on a 12 hour clock? We talked about it, and I tried to get all technical on it. I wanted to graph the sine curves for each hand, and the second hand, too, for shits a giggles. I don't remember equations (or technical terms) very well. The graph would be of time in minutes. The second hand's period is 1 minute (y=sin (pi/30)x), the minute hand's period is 60 minutes (y=sin (pi/1800)x), and the hour hand's is 720 minutes (y=sin(pi/43200)x). They all start from zero obviously. Anyway, I was going to look at this graph and see where the hands intersected, and that would give me my answers. The equations I gave in parenthesis are what I think these graphs would be, based on a cursory inspection of sine waves on wikipedia. I'm trying to fins an online graphing tool which will show you what I'm talking about, but it's going slowly. I'll reply to this with it if I find one.
Unfortunately for me and all the time I spent on this, the question isn't nearly as difficult as that. Think about it: where do the two hands intersect? Well, at 12, 1:05ish, 2:10ish, etc. If you look at them, you'll realize that the hands do not meet in the 11 hour, so they intersect 22 times a day, at an exact 12/11 hours, which is something like 65.4 minutes. Leave it to me to waaaaaay overthink this.
A second question was to consider every prime pair. These are prime numbers separated by one number, such as 11 and 13. Can you prove that the number in between is divisible by six? This one didn't take nearly as long, but I still had to think about it because I'm really rusty with this sort of thing. First off, we know the number in between is even, which makes it divisible by two. We also know that every third number is divisible by three, and that the two numbers around the middle one aren't. That means the middle number is compelled to be divisible by 3. If a number is divisible by two and by three, guess what it's divisible by? BAM!
Another geeky math thing I discovered a couple weeks back is how to hand calculate square roots. To my recollection, I never learned to do this. Yes, I know that's what a calculator is for. But when shit hits the fan, and you don't have a calculator, and the fate of the world rests of you calculating the square root of 67, you'd damn well better know how to etch your work onto your stone tablet! I found this tutorial on it, and I'm wondering why it doesn't look familiar to me at all. I must have been taught this at some point in my life, right?
Unfortunately for me and all the time I spent on this, the question isn't nearly as difficult as that. Think about it: where do the two hands intersect? Well, at 12, 1:05ish, 2:10ish, etc. If you look at them, you'll realize that the hands do not meet in the 11 hour, so they intersect 22 times a day, at an exact 12/11 hours, which is something like 65.4 minutes. Leave it to me to waaaaaay overthink this.
A second question was to consider every prime pair. These are prime numbers separated by one number, such as 11 and 13. Can you prove that the number in between is divisible by six? This one didn't take nearly as long, but I still had to think about it because I'm really rusty with this sort of thing. First off, we know the number in between is even, which makes it divisible by two. We also know that every third number is divisible by three, and that the two numbers around the middle one aren't. That means the middle number is compelled to be divisible by 3. If a number is divisible by two and by three, guess what it's divisible by? BAM!
Another geeky math thing I discovered a couple weeks back is how to hand calculate square roots. To my recollection, I never learned to do this. Yes, I know that's what a calculator is for. But when shit hits the fan, and you don't have a calculator, and the fate of the world rests of you calculating the square root of 67, you'd damn well better know how to etch your work onto your stone tablet! I found this tutorial on it, and I'm wondering why it doesn't look familiar to me at all. I must have been taught this at some point in my life, right?