Thursday, 1 April 2010

Mathematical Problem 3: a metric/imperial curiosity

You can drive under an ancient archway across a cobbled street that runs alongside Norwich Cathedral. As I went through it the other day (on my bicycle, of course) I noticed a sign indicating the clearance under the archway, given in both metric and imperial measurements:

10 feet 3 inches 3m 10cm

What a happy coincidence that you can convert this length from imperial to metric (approximately) by swapping over the two numbers! It reminded me of how 82 degrees fahrenheit converts to about 28 degrees celsius, and 61 degrees fahrenheit to about 16 degrees celsius.

I wondered, therefore, whether there are any other lengths that can convert approximately from feet and inches to metres and centimetres by swapping over the two numbers in this way. Are there?

As in the given example, assume that the metric length is rounded down to the nearest 5 cm.

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