## Thursday, April 5, 2007

### Renard Numbers

I don't yet quite understand the logic behind this (why is the error minimized, exactly?), but I really like seeing the reasoning behind the standard:

"Renard's system of preferred numbers divides the interval from 1 to 10 into 5, 10, 20, or 40 steps. The factor between two consecutive numbers in a Renard series is constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10.

The most basic R5 series consists of these five rounded numbers:

R5: 1.00 1.60 2.50 4.00 6.30

Example: If our design constraints tell us that the two screws in our gadget can be spaced anywhere between 32 mm and 55 mm apart, we make it 40 mm, because 4 is in the R5 series of preferred numbers.

Example: If you want to produce a set of nails with lengths between roughly 15 and 300 mm, then the application of the R5 series would lead to a product repertoire of 16 mm, 25 mm, 40 mm, 63 mm, 100 mm, 160 mm, and 250 mm long nails."

From this wikipedia entry.