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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.

Von Koch Curve

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

How Many Elements Are There in the Cantor Set?

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

Sierpinski Triangle

Age 16 to 18 Challenge Level:
The fractal consists of the red triangles that remain if the process of removing the central 'quarter' of each red triangle is repeated indefinitely. Consider the first few stages, how many red triangles are there? How many triangles have been removed?