I, too, came upon the idea of using moving coordinate frames
fairly soon, perhaps based on a mental picture.*
Not having thought about relative motion for a decade prior,
I'm sure it's because I'm currently reading the
recent biography of Einstein (by Walter Isaacson).
(Has anyone else read that book? I've had at least one
interesting matematical idea as a result of reading it.)
--Dan
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* What I posted was what I wrote on paper (including no pictures).
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Bill T. wrote:
<<
On Aug 6, 2007, at 7:57 AM, gale(a)Math.Berkeley.EDU wrote:
> I'M AFRAID I didn't express myself clearly.I wasn't asking for
a
> solution
> but rather about the mechanics of finding it. Did either of you
> use pen
> or pencil or paper at any point? I had to draw two pictures before
> I could
> see what the equations had to be. Maybe you were able to do all these
> things in your head in which case my speculations are off base.
>
. . .
. . .
In my case, I worked it out in my head. I had a mental picture of
the two people running in opposite directions around a circle, and
then I thought of using moving coordinates as in high school physics
class so that one of the runners moved at the sum of speeds, which I
said to myself was one lap per minute. The same picture said the
difference of speeds was 1 lap per hour. Then I thought of a picture
of an interval of length 60, with two points (the two speeds)
averaging at the halfway mark but being 1/60th apart: from the
picture you see the ratio as 61:59.
. . .
. . .
>>
