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Let's consider the simplest case of two parallel segments placed on distance 2*x_0 from each other. The cross-section of the considered picture is shown on fig.5a. On this picture the position of the approximating segment axial line is determined by parameter x. In this case

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**

**Where k - number
of points in each segment.**

**Extrema of such
measure are determined by zero values of its derivative:**

**
**

**The denominator
of resulting expression is positive at any values of entering variables.
The numerator can be transformed to the view**

**
**

**This equation
has five solutions, one of which is x_1 = 0, and four others : **

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**

**Two solutions
which are determined by a difference of the expressions placed under
sign of exterior square root, have imaginary values at any values of
entering variables (as x_0> 0, under the initial agreement - see fig.5a).
Others two have real values, when **

**
**

**Simplifying
this expression, we shall obtain that at D < sqrt(3)*x_0 investigated
conformity function has three extremums: one central and two symmetric side
ones. It is easy to show, that: **

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**

**It is obvious,
if D < sqrt(3)*x_0, then S"(x)|_0 > 0, i.e. the central extremum
is a local minimum of considered conformity function of and, hence,
adjacent side exremums are local maximums of this function (see fig.5b).
At D > sqrt(3)*x_0, these maximums merge in one (see fig.5c). Positions
of maximums depending on a value of parameter D are shown on fig.5d
(see the formula for an evaluation of x_2... x_5). **