Can a computer really draw a cirlce?
Posted on 2005-04-22
I'm interested in answers on this one. Way back when I was in highschool I argued with my geometry teacher about a circle being a polygon and I still think I am right on this, but it brings up a potential limit of a logical device like a computer.
The definition of a line any 2 connected points, and the definition of a circle is all points (infinite in number) equidistant from a center point, so I say that a circle is just a special polygon. I say it's an equalateral polygon of infinate sides where each side is exactly 2 points long and the angle between one side and the next is infintesimally smaller than 180 degrees. Thus a true circle is really an abstract concept that I don't believe can be programmed into a computer.
That said, can a computer draw a circle? I say no because a computer has a finite number of points it can display/print/whatever and if it tried to draw a circle and had the accuracy to do so, it would never finish since it would be drawing an infinate number of points.
Thoughts? Feel free to comment on both the theoretical capability of a computer to draw a circle as well as a circle just being an infinately and equally sided polygon.