as a regular polygon increases in sides, it becomes rounder. As you increase the number of sides, the polygon will tend towards a perfect circle but never quite make it. you can only make the circle with an infinite number of sides - stopping at any other number but infinity you will only get a very very very round but noncircle shape. but you know all this... IS IT APPROPRIATE TO CONSIDER A CIRCLE A REGULAR POLYGON WITH INFINITE SIDES? ARE THERE ANY DISCREPANCIES IN CONSIDERING A CIRCLE A REGULAR POLYGON? also I am wondering... technically a circle must have vertices of 180 degrees, right? is this a discrepancy?