21/7/2006

180/360

Filed under: — Bravus @ 9:35 am

If we drive home from Brisbane via the freeway, there’s one point on our journey home where we approach a roundabout (traffic circle), go around it and come back, going the opposite direction on the same road we came in on.

Sue said this meant we were ‘doing a 360’, and I said ‘no, it’s a 180’. Significant discussion ensued…

My argument was that you go in one way, and come out facing in exactly the opposite direction, having rotated through 180o. As a good physicist, I argued that the circle you drive around on the roundabout is irrelevant – what’s important is the initial and final states. I said that to do a 360 you’d have to keep on going around the roundabout until you were going the same way you’d been going initially.

Sue said ‘No, if you took the left turnoff you’d have turned 90o from your initial direction, if you went straight ahead that’s 180, taking your initial position as 0, if you went around and turned right you’d have gone through 270 and going right around to come back the way you came is a 360. (I’ve helpfully illustrated the situation and her system below.)

180

I think her system of descriptions has a lot to recommend it as a way of explaining directions to people… but it seems to me as though under that system, when you’re driving along a straight stretch of road you’re continually doing 180s, and that doesn’t seem right. So I still reckon we do a 180 at the roundabout. What do you think?

3 responses to “180/360”

  1. Sirdar says:

    You are both right…in a way. Sue is correct in that you did do a 360° in the traffic circle. David is right because you change direction 180°. But you can’t take the traffic circle into play when it comes to direction of travel. One is travelling on a straight line. The other is a circle. You changed directions on the straight line. Look at it this way…no matter “how” you changed directions, you changed directions, and those directions were 180° difference.

    Maybe if you drove on the right side of the road you might have a different perspective on the whole thing 🙂

  2. Zaakistan says:

    First of all, I don’t see a circle in the diagram, more of a perimeter around a rugged mountain.

    It depends on if you look at it as rays or not. If you’re car had a big stick poking out of the muffler, then it would be easy to track the angle change – 180°. Use the traffic rugged mountain as a pivot point. Sue should consider a left turn as 90°, a right turn as -90° (or 270°), going straight as 0°.

    It’s not good math to track points along a circle with out the rays connected to the center of the circle. I would have a hard time acknowledging a 360° turn as the end of your muffler stick doesn’t trace an entire circle.

    What would happen if you used radians?

  3. Bravus says:

    Heh – not sure radians help that much – different numbers, same conceptual problem… And hey, ‘rugged mountain’? You dissin’ my trackpad circle-drawing skillz? 😉 I take some comfort in the factoid that being able to draw a perfect circle freehand is supposed to be evidence of psychosis…

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