Birthday box

Created 27th August, 2009 04:27 (UTC), last edited 27th August, 2009 04:46 (UTC)

Cuboids have three pairs of faces the same size. The first pair of sides have an area equal to your birth year, i.e. for me the first pair have an area of 1970 units. The next largest has a size of your birth year with birth month. I was born in September, so the next area is 197009 units. The largest have an area the size of your full birthday, i.e. for me it will be 19700903 units.

Work out a way to determine the lengths of the sides of the cuboid formed from any birthday.

One of the interesting things about computers is that they don't deal at all well with continuous functions* [*Digital computers anyway, analogue computers deal with them just fine, but they have their own set of problems.] — there's always some quantisation involved.

Write a program that will calculate the cuboid lengths from a birthday where the lengths must be integral. Calculate these lengths so that they have the smallest error.

There are many ways of measuring the total error. How do different ways of measuring the error affect the result?