A circle is a simple shape of Euclidean geometry consisting of those points in a plane which are equidistant from a given point called the center. The common distance of the points of a circle from its center is called its radius.

But Circles can not, and do not exist in reality, anything that seems to be a Circle is actually a polygon with a very high number of sides... the closes to a Circle that we can get is to have each side of the polygon the size of quantum distance.

Just try and draw a Circle in TheGimp:

http://s3.amazonaws.com/readers/2009/09/23/1253646512_1.png

Now zoom 1600% in to it. You will see it is actually a polygon, composed of thousands of little pixels, the same is true for "circles" in reality, they are composed of thousands of little quantum pixels.

http://s3.amazonaws.com/readers/2009/09/23/1253646570_1.png

So, Circles do not exist, they are just a math abstraction. And that is why we end up needing unattainable numbers like Pi to deal with the area inside of a circle... because there is no such thing as the area inside of a circle (because there are no circles). 

The area inside of anything in reality, that looks like a circle, can be calculated by dividing it in "quantum pixel areas", and the adding those areas to get the total area inside of the supposed circle. Now, that would require a lot of effort, that is the reason we believe in circles, because  they are a very useful abstraction (even if it is an abstraction that fails and produces Pi as a result of its failure) PiIsTheAbstractionLeakOfCircles
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''What, no anti-aliasing?''
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See PhysicsAndMathematicsAsAbstractionOrReality, ValueOfPi
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CategoryAbstraction CategoryMath