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Sierpinski Triangle

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

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A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

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How Many Elements Are There in the Cantor Set?

This article gives a proof of the uncountability of the Cantor set.

Von Koch Curve

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
It helps to consider the area added to ONE edge first. You have to sum an infinite geometrical series.