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Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Fractal

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Where Art and Maths Combine

Age 11 to 18

In this article, Rachel Melrose describes what happens when she mixed mathematics with art.

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Paper Curves

Age 7 to 11 Challenge Level:

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

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How Many Elements Are There in the Cantor Set?

Age 14 to 18

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

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How Long Is the Cantor Set?

Age 11 to 14 Challenge Level:

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?

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The Cantor Set

Age 11 to 14 Challenge Level:

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?

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Von Koch Curve

Age 16 to 18 Challenge Level:

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.

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Squareflake

Age 16 to 18 Challenge Level:

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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Sierpinski Triangle

Age 16 to 18 Challenge Level:

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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Smaller and Smaller

Age 7 to 14 Challenge Level:

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?