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•78 The 100 Greatest Business Ideas of All Time

we get:

X = 1.5
2

X = 1.417
3

X4 = 1.414

so that with only three steps we have reached a very good approximation. It would
have taken many more iterations if our original guess had been much wider of the
mark. If, for example, we had started with X1 = 50 it would have taken nine itera-
tions to get to the same point. The iterative process is continued until any desired
accuracy, tested for by the computer, is reached.

This is a very simple example. There are many extremely useful and sometimes
sophisticated iterative processes for solving various types of equation. Iteration is
also used in routines that are closer to business needs, such as sorting tables of data.
It is unlikely that all equations can be solved by iterative methods, but the computer
has certainly extended vastly the number that can be tackled in this way.

But it comes down in the end to a combination of man and machine. The better
the guess, from a better feel for the problem, the fewer steps it takes.

Idea 46 – When it’s critical to be on time and within
budget

There are many instances where computer power has enabled a mathematical proc-
ess to be used where, with only brain and pencil power, the number of calculations
required to do something useful make it quite impossible. Perhaps a good example
of this came early in the development of computers when they were programmed to
work out critical paths for projects.

To carry out critical path analysis, each separate event and activity of a project
is assembled into a network. The resources required and the time to complete is