The angle in radians = arctan of the slope. Maybe it's easier if you draw the line to the center of the circle and see that the slope is about 1/10 or 1/100 or so on, so the arctan is about 1/10 or 1/100 radians, and of course there are pi radians in a semicircle. --Joshua On Wed, Nov 24, 2010 at 9:08 PM, Gary Antonick <gantonick@post.harvard.edu> wrote:
Thanks, Joshua. But I still don't get it. Why does a line of slope -10 carve out exactly 31 arcs and not, say, 30?
I'll try to think about some more.
On Wed, Nov 24, 2010 at 2:01 AM, Joshua Zucker <joshua.zucker@gmail.com> wrote:
tan theta = theta for small theta.
--Joshua
On Tue, Nov 23, 2010 at 9:55 PM, Gary Antonick <gantonick@post.harvard.edu> wrote:
Just noticed this yesterday and can't figure out why it works.
Draw a circle with radius 1 around 0,0. Draw a line with slope -10 that hits the circle at 1,0. This line will also hit the circle again and make a little arc. The length of the arc will be about 1/31 the perimeter of the circle.
Now try again with a line of slope -100. The line will create an arc 1/314 of the circle.
Starting to look a bit like pi. Am wondering why this is.
In case I made a mistake here's what I'm trying to describe.. if the circle were a clock the first line would cut an arc from 15 minutes (3:00) to almost the 13 minute mark.
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