Audio Banter - View Single Post - Super discussion about negative numbers on the BBC

**Eiron** · March 10th 06, 06:07 PM posted to rec.audio.tubes,uk.rec.audio

wrote:
why would "equations for getting the maximum use of a given width and length of corrugated cardboard (roll) sheeting..." need to involve "i"?

Well, one is subtracting from a given area, and the numbers subtracted
are therefore 'negative'. As the numbers are _areas_, then we have a
negative number that often needs to have its square root taken.
Mathematically, this does not work. as -1 x -1 = 1. So. " i " is
introduced to make the calculations work.

This was a lecture mind... so here is the issue: feedstock is
expensive, and there are thousands of sizes of boxes. These were
corrugate boxes, with varying dimensions. This plant did not 'stock',
but made to order, to size. The knives were capable of cutting in
either horizontally or vertically and as finenly placed as necessary,
as well as partial cuts. Set-up and roll changing were the costliest
operations (as both involved machine shut-down), waste being the third
largest cost. Several sizes of boxes could be run at once. He
calculated how to run the orders to avoid waste and slivering, and to
minimize the number of different widths of feedstock required. He chose
to use the 'imaginary number i' in his process. It seemed to work as
their scrap-pile was rather tiny to his great pride and joy.

Can you give any more details? Still can't quite see where i or j is required.

--
Eiron

There's something scary about stupidity made coherent - Tom Stoppard.