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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!
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!