1. ## Circles and Computers

Hey all,

While this is connected with C, I put it here, since it's technically a computer quiestion. So on we go.

When you tell the computer to draw a circle with a diameter x on the screen, it won't draw a perfect circle. Why? Well, let's skip the "Pi is irrational part" for a second. The screen is made of pixels. Pixels are squares. So, ultimately, the shape we see is lots of tiny squares put together so as to form something resembling a circle. But it's not a circle. It's squares. Now here's what I need; how does a computer know, based on the diameter of the circle that we want it to draw, how many squares to draw, and what shape to make? I'm writing a program where I need to be able to say "Okay, the diameter is two (in pixels), so that means that we're going to have 5 squares, and it will look like a plus sign.". So I took a squared paper, and tried to draw the shapes up myself, and to be honest, I'm pretty sure I got 'circles' with diameters three and four (in squares) right, but anything higher than that, and I don't have a clue how it's supposed to look.

Could anybody here tell me, given a radius x, how many pixels, or "squares" the computer needs to draw to form the shape we perceive to be a circle? And how that shape looks? Or at least tell me how to draw up the shapes myself, I can calculate the formula from there.

Cheers,

Gabe

EDIT: I've been doing some drawings, based on intuition, and here's what I got: