I was just curious about something:
Say you had a normal polygon with sides. As approaches infinity, your polygon begins to look more and more like a circle.
We could define a straight line to be 180 degrees.
We know that the equation of the sum of the interior angles of a polygon is:
We know that the measure of a single interior angle is:
When we take the limit of n as n approaches zero:
By L'Hopitals rule
It's weird to me, because it seems like the curve of a circle is flat, but also curved. What if you visualized this in three dimensions? Does that mean that the surface of a sphere is 2 dimensional?