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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!
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Who says? I am! I almost majored in math in college. (I majored in Spanish instead, thinking I'd go on to a master's in linguistics; I already knew Spanish quite well, which freed me to take undergrad linguistics courses. Then I didn't end up going to grad school.) I was the geek who realized in high school that Fahrenheit & Celsius temp's. had to coincide at some point & worked out the algebra (it's -40°). The only one who didn't laugh when the 1 European student in bio class said normal body temp. was 37°, 'cause I'd worked it out on my own time (so I called out, "It is in Centigrade!") Who wanted to take calculus because everyone talked about it like it was impossible (& then was disappointed that I had to take trig 1st, & again that I had to retake it in college because I'd learned it w/degrees & needed to learn it w/radians before I could take calculus). Who worked out quick-&-dirty conversion shortcuts, like dividing cm by 10 & multipying by 4 to get the approximate equivalent in inches & subtracting 10 from degrees C, doubling, & adding 50 to get approximate degrees F (yep, 10°C = exactly 50°F; works well enough for most atmospheric temp's. that humans are likely to encounter).
That last one occurred to me (I think) several years after the -40° equivalency; I'm not sure if I was out of college yet. It took me till I was 60 to realize there's a cycle every 50°/90°! It was when I heard a weather report this winter saying that the temp. in some places was -30°F & just had to figure out what that was in Celsius.
Anyway, yeah, so, math geek here. You wanna post on math? Please go ahead! This one was cool, & even your pizza post had a math aspect! (Now I have "♪There's a little bit of math in everything♪" going through my head!)
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They told me in high school that mathematicians do their best work in their twenties. I guess we 60+ folks showed 'em. ;o)