Find Mea Circle

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:

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.

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

What, no anti-aliasing?

See PhysicsAndMathematicsAsAbstractionOrReality, ValueOfPi

CategoryAbstraction CategoryMath