Too late, too late...

[cactuswatcher]

It's too bad there isn't anyone interested in math on my friends list.

I was thinking the other night in sci-fi terms about how an alien society might be different, if, say, they had a different sort of clock. The reasons for dividing a clock and other circles into parts divisible by 60 is pretty obvious. You can get half a circle, a third of a circle, a quarter of a circle, a fifth of a circle, and even a sixth or a tenth of a circle pretty easily without fancy math. However if you are not the ancient Greeks or Romans without decent mathematics, perhaps dividing a circle into 360 degrees isn't all that necessary. I tried 400 pieces (a right angle would =100 degrees instead of 90) and it works just fine, as long as you have decimals at your disposal. I thought I'd found something really profound about using 100 degrees for a right angle, when I checked back about how 90 degree right angles work. I realized that something I'd really struggled with back at the dawn of time when I took trigonometry was really dead simple. It was just that as far as I can remember, it was never explained to me. I have a very fine book of math tables and formula definitions (from the days when such books were necessary) and the critical formula isn't there!

The problem is this: what is the relationship between the tangent of an angle and the number of degrees in an angle? I remember problems at the end of homework assignments in trig class that took forever to puzzle out. I remember being given a problem on the SATs where I was given a complex figure, the length of a stray side and an inconvenient angle in degrees somewhere else, where I was supposed to figure out the rest of it using geometry (ie ancient Greek methodology). It seemed like it took forever to think of a way to approach the problem. I did it and I'm pretty sure I got the right answer, but how much simpler the whole thing would have been if I'd known the simple formula.

For a right triangle with sides a, b and c, with c being the hypotenuse, the tangent of the angle formed by side a and side c = b/a
The angle in degrees between side a and side c = 90(b/a+b)

How much time on the job I could have saved if I'd known that!

Comments

[cactuswatcher.livejournal.com]

My geometry teacher was my only high school teacher that nearly put me to sleep every time he said anything. I can remember my older brother coming home when he was in high school just thrilled about what they were doing in geometry class. The right teacher makes so much difference. I was interested enough in math that I learned geometry, but I sort of had to take it home and figure it out for myself. My father (an engineer) was much happier if I learned on my own. But he would help and was very good at finding ways fairly quickly to get the right idea to strike home.

I took a lot of math in high school. Most people wouldn't need half of the math I learned. I'm not sure all the class time was worth it for most of the kids I took those classes with, who didn't actually go into engineering. It just happened that I got into a job that including programming robotics at a time when computer assistance for that was minimal. Didn't really need the calculus, but did need all the other math and lots of time to work out some really nasty puzzles.

Yeah, I learned to do square roots in school. It was something they didn't emphasize at all. I don't think I ever had a use for cube roots when I didn't have a table or a good calculator handy. But I suppose not everybody my age has engineering quality math tables on the shelf in their home. ;o)

[anomster.livejournal.com]

Ooh, do you have Glover's Pocket Ref? @>)

[cactuswatcher.livejournal.com]

Nope, CRC Standard Mathematical Tables. From the same folks who published the Handbook of Chemistry and Physics.

[atpo-onm.livejournal.com]

Hey, I have one of those, bought back in my high school days! And the Handbook of C&P. Haven't cracked one of them open for years (decades) now, but, you never know!

[cactuswatcher.livejournal.com]

I have a 51st edition of the Handbook. I think they are up to 94 now. That'll make you feel old. ;o)