I program a Coordinate Measuring Machine. This is a machine that uses a 3D Cartesian coordinate system to measure things with a ruby stylus. I understand very much about how it works, using XYZ coordinates and vectors, IJK.

One thing I don't understand is that when probing circles, either inside diameters or outside diameters it uses the Least Squares Method to calculate the size of the circle. Can anyone explain to me, in layman's terms, just what Least Squares Method is?

The machine is trying to find the best average circle for the points meaured. The best average would have the smallest set of errors.
Some of the points are inside this average circle some are on the outside. If we use the the absolute error the + and - net out to zero. If we square the error it's 2 fold advantage we eliminate the negative numbers and the errors get big really quickly. The machine is programmed to systematically make a circle minimizes the squared errors.

But why are the errors squared in the first place?

quote:

Originally posted by Kendor:
But why are the errors squared in the first place?

If they were not squared the numbers would be positive in one direction and negative in the opposite direction, adding to zero. No error means no correction. Squaring numbers make bigger, all positive - numbers, exaggerate the error, therefore call for correction more emphatically. No?