How does small angle theorem prove that as the no. of sides of polygon goes up, it eventually becomes circle?

Question

What is small angle theorem?
what is a radian? how does it differ from degrees?
what is the significance of radians?
how can I use small angle theorem and radians to prove that as the number of sides of a polygon increases to an infiite level it becomes a circle?

Answer 1

On radians:
http://en.wikipedia.org/wiki/Radian

Never heard of the small angle theorem, but here is a page on the small angle approximations which rely on the use of radians:
http://en.wikipedia.org/wiki/Small_angle_approximation\

As for approximating a circle with polygons of increasing number of sides to compute the area or circumference:
http://www.math.hmc.edu/funfacts/ffiles/20009.2-3.shtml

Note the use of the small angle approximation when computing the sides and heights of the triangles.

Answer 2

Small Angle Theorem