Among Archimedes mathematical accomplishments is the computation of pi, he used the method of exhaustion as a way to compute the area inside a circle by filling the circle with a polygon of a greater and greater number of sides. The quotient formed by the area of this polygon divided by the square of the circle radius can be made arbitrarily close to Pi as the number of polygon sides becomes large, proving that the area inside the circle of radius r is Pi * (r*r),Pi being defined as the ratio of the circumference to the diameter. 

When a circle's diameter is 1 unit, its circumference is Pi units. Why Pi is such simple concept but such a strange "number"? because Circles do not exist, Pi is an example of a Mathematics (Geometry?) abstraction leak.

You can see in this image, how, as we increase the number of sides, we approximate more, and more to the circle, but we can never really have a circle. This is why we can never know the complete value of Pi, because there is no way to have a circle in a discrete quantum based reality, "circles" are a good model for this things with too many sides to count easily, but circles are just a model, not a reality

http://upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Archimedes_pi.svg/500px-Archimedes_pi.svg.png

See FindMeaCircle for context
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This also applies to ''any'' geometric artifact. We merely find UsefulLie''''''s.
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CategoryAbstraction CategoryMath