Need help with method of least squares

Hello, I've been writing some program for calculating the principal
radii of curvature for a triangular mesh. I've been following this
thesis :

http://www.cs.princeton.edu/gfx/pubs/_2004_ECA/curvpaper.pdf

I got stuck up in page number 3, section 3.1 "Per face curvature
Computation"

He calculates a matrix lets call it A :

A00 = (del n / del u) dot u
A01 = (del n / del v) dot u
A10 = (del n / del u) dot v
A11 = (del n / del v) dot v


Now it seems he wants to calculate del n / del u and del n / del v
which give the principal radii of curvature.
There are three matrix equations given in the same page with a
triangle diagram. What I don't understand is why we want to solve
three equations when only two variables (del n / del u and del n / del
v) are needed. Further in the same page he says that they use method
of least squares to solve the equations. What is this method of least
squares in this context ?
.

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