Re: OT: White Goddess

> Date:         Wed, 11 Apr 2001 14:13:56 -0400
> From: Andreas Johansson <and_yo@...>
> Eh, seeing that I supposed to be good at math, I should probably know this
> myself, but what's the difference between a circle and a regular polygon
> with an infinite number of sides? I definitely recall being told by my math
> teacher tellin' me they're the same ...
I'll avoid the thorny subject of infinite numbers of sides, and
whether such a polygon can be said to exist.

But, taking polygons as curves, if you fix the center and the distance
from center to vertices, the limit of the curves as the number of
sides tend to infinity is certainly a circle.

If you take the polygons as closed regions in the plane, and take the
intersection of all polygons with a vertex on a specific line through
the center, you get an interesting set that only includes the
'rational' points of its boundary.

Lars Mathiesen (U of Copenhagen CS Dep) <thorinn@...> (Humour NOT marked)