OK... how would you come up with the square root of -4? Practical
application, you are starting with so many square feet of feedstock,
you are making 22 boxes each requiring two 4 square foot faces, two
feet on a side and other sides may vary within certain parameters, and
12 boxes each requiring two 1 square foot faces. But the dimensions of
the first box must be calculated to have the correct volume as a
function of dimensions and not preclude the similar values for the
second box. So, you are SUBTRACTING dimensions as square roots of total
areas required for square cuts. As sq.rt. -4 does not calculate, but
sq.rt. 4 x i does... that is how it comes in. Keep in mind that one
*could* reverse the signs in one's head the reality is that all the
areas calculated are *real*, but as there are many sign-changes in the
calculation apart from negative number roots, the chance of error
increases greatly. The elegant part of all this is that the " i " drops
out at the end of the calculations, but it allows the rule of 8 (8
basic axioms of 'real' numbers) to apply during. As others have
suggested, we have computers do this these days. The need for practical
math has been relegated mostly to calculating tips in a restaurant. And
few do even this, it seems.

The history of Negative Numbers, remember?

Peter Wieck
Wyncote, PA