why we cannot get a smooth circle? just now i zoomed in Autocad still cannot have jagged edges. it is fucking with my mind. why Pi cannot be rounded up? math noob here.

circle cant be smooth cuz of screen resolution and pixels..
printing of perfect circle needs a plotter..
pi = 3.141592654 ... irregular number, never repeats..

Because pixel is square thus you are only looking at a representation of a circle not the actual ring in material.

True.. circles appeared tp be circle as it is built from endless / lines that linked together... It is like a metal that you spend hours polised it. From naked eye and tactile sense, it is smooth, but closer look with microscope, it is still rough.. same thing here

i still dont understand. does that mean we human will never be able to observe true circles because our eyes always understand lights in pixel???

No, its the LCD technology, but what is a true circle? A needle point mechanical pen drawn with a circular stencil on smooth paper are not perfect either, try use a magnifying glass to view the line and double that compare to the width you see on LCD monitor, now how can it be smooth?

Or, you think glass surface is smooth but try look at it with electro microscope, nothing is perfect even light bends by gavitaty. So what is the point?

Because 'a perfect circle' is an abstract object, an idea that exists in our minds. It's very much like numbers, can you tell me what is a number, physically? They're all abstract ideas.

We perceive perfect circles just fine, even if the circle in front of us is slightly less than perfect.

For one thing, the cones and rods (the light sensitive elements) on our retina are not laid out in a perfect grid like that you see on a digital cameras CCD sensor.

For another, we don't actually "see" pixels in that sense. The "signal" has been processed to some degree before it reaches your conscious mind. You perceive lines, curves, areas, etc. When you see a circle, you see "a circle". You don't see 3,423 pixels laid out in a pattern approximating a circle.

As for autocad, render the circle at a higher resolution, or use anti-aliasing.

Numbers can be represent physically by number of physical items. Better analogy would be the longitude and latitude lines. Even if you know where these lines are on the earth, you still wont be able to dig them up.

This post has been edited by DarkNite: Oct 8 2010, 08:06 AM

Try to use paint brush to draw a circle and you will see....

The answer you seek depends on you definition of 'perfect circle'.
If you mean a circle with no perceivable deformities you can see, then we can see these almost everyday.

I guess the answer lies within the programming language it self. As when I see technical drawing printed out from CAD, it is perfect cricle alright(from naket eye)

It's less of being the programming language than the resolution of the screen.
Using any programming language, I can tell the computer to draw a circle. But how smooth you perceive the edges of the circle is determined by the resolution of the screen you're looking at. A high resolution will produce what our eyes perceive to be a perfect circle. A low resolution (Should I decide to set your monitor to only 64 pixels), will probably look as if I cellotaped 4 squares together.