If you have a little time, try this. Find someplace with a little space to it. Maybe Custer National Forest in South Dakota, or the Bonneville Salt Flats in Utah or maybe the football field down at the high school, or your living room, or even right there at your computer desk. You could even make this one of them there “Thought Experiments” if you want, but I don’t recommend that. Now, walk in a big circle. The bigger the better. It’ll give you a little time to yourself and if anyone pesters you, you can snap “It’s for Science dammit!” at them. Serve them right too, interrupting Science. After you’ve walked in your circle, where are you? Right where you started. (Of course. It’s a circle. Duh.) Only you traveled through 360 degrees. Which is what a circle is. Everyone knows that. A circle is 360º. (182.2º Celsius.) (Ha ha ha ha ha ha!) (Ha!)
Now, head off on another little walk. Hum to yourself if you want. This is just “you time”. Only this time, it’s not a circle. This time, it’s a square. Head off a little way and then turn… left! You have to turn left. I should have mentioned this earlier so you could plan your route accordingly. Why, you might wind up in a river in South Dakota if you don’t plan ahead. After you turn left, you walk and turn left again. Then some more walking and another Louie. More walking, a last left turn. Congratulations! You’re ready to walk the Indianapolis 500! Only they use cars, so don’t try it on Race Day. If you counted your steps right, you’re back where you started. If you didn’t, I don’t know where you are. But you turned left, left, left and finally left. Four 90 degree turns. That’s another 360º. Just like the circle.
OK, now it gets tricky. Go for another walk. It’s good for your heart. Go a little ways and make a 60º turn. Now walk twice as far and make another 60º turn in the same direction you picked last time. (I’m leaving the choice up to you this time since you fell into the river last time.) Walk as far again as you did after the first turn and make yet another 60º turn. Walk as far again as you did before your first turn. You know what? You’re back where you started. Only it was 60º + 60º + 60º which is 180º. Where did the other 180º go?
Er, I didn’t walk it, but I did sketch it, and you know what? You’re not back where you started at all!
I think you are confusing the internal and external angles of the triangle. If you made three 60deg turns, you’d have traced out half of a hexagon (60deg x 6 would make the full 360 degrees).
However, assuming you meant tracing out a triangle and coming back to where you started, you are actually making 120deg turns. You are doubling back on yourself, so although the internal angle is 60 degrees, it’s a 120 degree turn.
The third walk was a triangle. It was only 180 degrees. That’s how many degrees are in a triangle. Which is not to say that’s nothing. It is, in fact, scorching, even compared to here. Of course in a triangle you don’t have the humidity. Which is the killer.
**You’d Think You’d Be Facing the Other Way ** :smack: Ignore me…I need coffee. I just realized what you were refering to. I think I am going back to bed now.
Yes, and no - you’re turning through 360 degrees. Imagine, at each corner, your original path continuing on in a straight line. This forms a 180 degree “angle”, right. Now, to make the 60-degree internal angle of the triangle, you have to alter your heading by 180 - 60 = 120 degrees:
\ new path
\
\
60º \ 120º
------ - - - - - - continuation of original path
You are turning through more than 90 degrees, not less - your turn is sharper in making a triangle than it is in making a square. In the case of the square, both the internal and external angles are 90 degrees, but you picked the wrong one to compare in the case of the triangle.
Psst! Colophon! You’re in a Rue DeDay start-the-week thread. You’re not supposed to be all correct and everything. You’re supposed to be all kind of rambling-like. I guess you could try to ramble in the right general direction, and leave some actual true facts out where people would run into them and accidentally learn stuff, but you’d have to cover them up with something so people wouldn’t just walk around them. Like you could say, “I tried the third walk, and I didn’t fall in the river. Which is a good thing, because I don’t think I would have been able to swim very well after walking into the STOP sign. I was really glad I walked into that STOP sign, though, because it had the answer to the missing 180 degrees. No, the answer isn’t STOP, although some of you would really like that to be the answer, wouldn’t you, ‘cause you never liked geometry in the first place. Actually, the answer is in the angles of the hexagon…” and on like that for a while. See, you could sneak in stuff about supplementary angles right there. Go on, give it a try.
The point isn’t how many degrees are on the inside or outside of the triangular walk, the real point is that it’s ‘Centigrade’, not this new-fangled ‘Celsius’.
and I concur, Maths is hard… are hard… am hard. Ayiyiyiyi!.
urm… Unca Rue, where IS everyone? Where’s the MMP? Is this the MMP?
Of course, the great thing about that example is that a STOP sign is an OCTOGON, for crying out loud, which will give people a chance to show how much more alert they are than you about traffic signs. On second thought, maybe you should try something else for an example.
You know where we are? We’re huddled in the corner, weeping over the math in this thread.
(Yeah, I got through Calculus, and I loved math, but hey, you don’t use it and you lose it. What? I’m an accountant? You’d be surprised how little math that involves.)
That’s all I got right now. Still trying to get back into “work mode” after the 3 day weekend. Surfing the SDMB is probably not helping that endeavor.
I tried your little stunt and ended up in the Womens Restroom here at the plant. Womens Restroom is in all caps because I have a great deal of respect for what goes on in there. More like a perverted curiosity, really.
Anyway, since my ‘science’ study was rudely interrupted by a scream and a verbal lashing by some uppity suit from HR, I think I’ll have to resort to leasing some space on the Bonneville Salt Flats for next weekend. Anyone want to go in? I’m a little short on funds this week. Plus, I live about 10,570,000 feet from the place. Can I borrow a compass or a protractor from someone, or both?
So it’s not the math, it’s the humidity? Well then, I feel much better about the whole thing.
Yesterday was a holiday around here dangergene. That means I had the day off. Most precisely the Little Woman had the day off. Which means the MMP comes out today which is Tuesday. If you look at it one way it should be the TMP, but the MMP isn’t about the M (or the M) so much as about the P. So this is the MMP even though it’s not M any more. Note to Self Next time I go on a walk with Colophon, push 'em in the river.
Hey! That reminds me! Anyone intersted in a Fall Hike this year? It’ll be fun!
Hmmmm, according to Bill Bryson in his book, *A Short History Of Nearly Everything, if you tried to beeline it to the edge of the universe (assuming you could travel faster than the speed of light and were immortal) you would actually end up back where you started…without intentionally turning any angles at all. At least that’s what I think he said. Math hurts my widdle buffler brain cells, don’tcha know. Anyhoo, the book is really good. That’s what I been reading when I haven’t been watching oak trees in my yard bend 60 degrees (or 120, take your pick).
