Well no matter how many corners you cut, it'll never be the exact shape of a circle. Even if it is really miniscule, they'll add up to 4 while the actual circle still has a pi value of 3.14.
If they are so small that the smallest dimensions are at plank length then nothing smaller makes any physical sense, and for that matter is impossible. Since our universe has a minimum distance that means it is actually pixelated, and thus is a raster system. A perfect circle is impossible in a raster system, only in a vector system. That means for all logical purposes, π = 4
If they are so small that the smallest dimensions are at plank length then nothing smaller makes any physical sense, and for that matter is impossible. Since our universe has a minimum distance that means it is actually pixelated, and thus is a raster system. A perfect circle is impossible in a raster system, only in a vector system. That means for all logical purposes, π = 4
Math deals with abstract concepts that are beyond the physical realm. You are injecting physical properties into mathematical concepts, but I am talking about pure math. A pixelated figure that resembles a circle at a distance is not a circle, but rather a polygon. Saying that this polygon has a π value of 4 is correct. Saying that the circle it approximates has π = 4 is not.
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Math deals with abstract concepts that are beyond the physical realm. You are injecting physical properties into mathematical concepts, but I am talking about pure math. A pixelated figure that resembles a circle at a distance is not a circle, but rather a polygon. Saying that this polygon has a π value of 4 is correct. Saying that the circle it approximates has π = 4 is not.
Also, it's 'Planck,' not 'plank.'
A similar case would be pythagoras' theorem. if the hypotenuse was just a whole bunch of perpendicular steps, it would still have the same problem.
Also, good to see some threads in MS again!