Documentation autogenerated by HWEB

This is a fourth test of the HWEB system of documentation. This test focuses on mathematical formatting. Consider the parametrization of a cylinder as "all points at radius A from the three-dimensional line p = (0, B, C)+t(1, D, E)." Okay, that's bogus, but let's go on. We have

p		= (0, B, C)+(1, D, E)
	ideal

p		= (X		, Y		, Z		)
	actual, i		i		i		i

So we have differences (X′, Y′, Z′) in X, Y, Z as follows:

X′		: = 0
	i

Y′		: = Y		−(B+DX		)
	i		i		i

Z′		: = Z		−(C+EX		)
	i		i		i

We want to minimize the sum of squared errors

∑	X′	2	+Y′	2	+Z′	2
		i		i		i
i

(that is, ∑_i∈Pn X′_i²+Y′_i²+Z′_i² where P_n is the number of points involved). So we have

∑		X′	2	+Y′	2	+Z′	2
			i		i		i
i∈P
	n