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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.

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.


Age 16 to 18
Challenge Level
Try some drawings for yourself. What happens to the area at each stage? What happens to the perimeter at each stage?