Re: Average Distance to Circumference


<HWayne@xxxxxxxxx> wrote in message
news:1172541926.687785.166090@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hi,

First, I'd like to begin by saying this isn't a homework problem. I'm
a high school student, and this isn't exactly the kind of problem they
teach in geometry. It's something I came up with recently. I also
apologize if this is the wrong group.

So, assume we have a circle with a radius of ten meters. An insect is
placed on a random point in the circle and immediately begins crawling
in a random direction. On average, how far will it have to travel to
get to the edge of the circle? Assume it follows a straight line.
Also, what field of mathematics is this covered in?

The only answer I've come up with is ten meters. If the insect was
placed in the center it would be ten and at any other place the
different distances are "cancelled out" by the different distances on
the point's reflection. This answer feels too intuitive, though, and I
was hoping for a more concrete (and accurate) answer.


This is true if the insect crawls along one of the radials. If it starts
off-centre and crawls in an arbitrary direction the sums are harder.




.

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