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

[atpo-onm.livejournal.com]

This lack of proper explanation of things was a continual pet peeve of mine throughout much of Jr high and high school. SOme teachers did a good job at explaining the fundamentals, others concentrated mostly on having you memorize things such as formulas and how to look up things in tables. And of course what turned most students off (who weren't science oriented naturally) was the failure to explain what the practical significance of this stuff was.

For example, one could look up the square root of a number in a table, but what if the number you wanted wasn't in the table? Could you actually calculate the number rather than look it up? (I could once, long, long ago. I could even do cube roots, which was way more involved. Both now long forgotten).

I had a good algebra teacher, but a poor trig teacher. I never really did understand sines, cosine, tangents, etc., other than how to look them up. They were explained as to what they were (the relationships of angles) but never how they were derived.

I can still do basic algebra fairly well if necessary, but that's about it. I'd certainly have to look up some formulas that have been lost to memory depending what I was solving for.

It's sad so many students aren't given a better appreciation of mathematics. It is, after all, the language of the structure of the universe. Understanding that can be handy.

[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)

[anomster.livejournal.com]

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

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!)

[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)