Ratio and Proportion - February 2006, Stage 4&5

Problems

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A Change in Code

Stage: 4 Challenge Level: Challenge Level:1

There are two sets of numbers. The second is the result of the first after an increase by a constant percentage. How can you find that percentage if one set of numbers is in code?

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Tin Tight

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What's the most efficient proportion for a 1 litre tin of paint?

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Orbiting Billiard Balls

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

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Squareflake

Stage: 5 Challenge Level: Challenge Level:1

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

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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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Von Koch Curve

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.