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Saturday, June 07, 2008

Eleven Plus Ratios

The Ancient Greeks still have an influence over Eleven Plus mathematics today.

There is a legend that the Athenians sent a deputation to the oracle at Delos to inquire how they might save themselves from a plague that was ravaging the city. They were instructed to double the size of the altar of Apollo.

The altar, as you will recall from your studies of the Ancient Greeks at school, was cubical in shape. (A cube!)

So the Athenians built a new altar twice as large in each direction. The new altar was eight times the volume of the original.

The gods were un-amused. The plague continued.

Some good Eleven Plus candidates will be able to solve this problem.

A different sort of question could be put to an equally able Eleven Plus child:

“Which fits better, a round peg in a square hole or a square peg in a round hole?

Your bright Eleven Plus child will look forward to the `hard’ questions towards the end of the paper. You will have covered ratio, area of a circle, and possibly used the word `circumscribed’ at some stage.

Your bright and highly motivated child may be able to work out that the problem is actually asking the question:

Which is larger, the ratio of the area of a circle to a circumscribed square, or the area of a square to a circumscribed circle?

If you are working in two dimensions the ratio is π/4 and 2/ π.

Thus a round peg fits better into a square hole than a square peg fits into round hole.

I am not sure if questions on ratio will be expressed in terms of altars or round pegs – but surely it is better to be safe than sorry.

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