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]

I retook analytic geometry in college. Not too surprisingly, the stuff we'd covered in high school was dead simple the second time through. But my 'dyslexia' caught up with me when we started to do translations and rotations. With umpty signs to keep track of in every problem I just couldn't do better than "C" work. Fortunately it was the less messy stuff that turned out to be valuable later in life.

They told me in high school that mathematicians do their best work in their twenties. I guess we 60+ folks showed 'em. ;o)