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But here the pieces aren't infinitesimal. They're fractals, but still measurable.
by nmilo 5y ago
But here the pieces aren't infinitesimal. They're fractals, but still measurable.
- mrob 5y agoFractals are still cheating IMO, because fractals have infinitely small features. Whenever you use infinity you can get all kinds of crazy results. It's like the geometric proof that pi=4: Draw a circle of diameter 1 Draw a square touching it on all sides, perimeter 4 Cutting at right angles to the existing edges, cut smaller squares out of all the corners so they touch the circle Perimeter remains 4 Repeat this corner cutting infinity times Perimeter of the cut square (4) matches the circumference of the circle (pi) pi = 4 Unlike traditional geometry, it's just abstract symbol manipulation with no relevance to real shapes.
- mb7733 5y agoThat proof is just plain incorrect, though. It will break down when trying to prove this statement: >Perimeter of the cut square (4) matches the circumference of the circle (pi) Calculus will show that the area of the fractal approaches the area of the circle. But it will not show that the perimeter of the fractal approaches the circumference of the circle. It remains 4 at every step in the iteration, so the limit is still 4.