Tip 74. Two operators of input and solution of a system of the algebraic equations
Fig. 74.
Nautilus I
The attempts of solving the problem about the sizes of the submarine
“Nautilus” from the famous roman of Jule Vern “Twenty thousand league[1]
under water” and “Mysterious island” are made in the fig. 74.
If we take description of the submarine without assumtions and reservations[2]
(see the beginning of the fig. 74) then the
problem is reduced to solution of two nonlinear algebraic equations with three
unknowns. The solution of such (“underdetermined”[3])
problem will be not simply three number (dimension of the submarine: diameter of
the cylinder d, length of the
submarine L and length of
its crown Lc),
but the dependence of two parameters of the submarine – for example the
dependence of its length and diameter from its third parameter. Three points of
such dependence are obtained in the fig. 74.
Main point of the tip: when you solve the system of the
algebraic equations numerically then the values of all variables are
given. At that one part of the variables is constants, the other part is
unknowns of the system, which values are selected by the function Find such way that the equations would
become the identities. It is worth to write this feature by corresponding not
before the key word Given: the values of the constants are given by the operator “º”, but the values of the variables – by the
operator “:=”. This way was dome in the fig. 74
in three attempts (methods) of calculation of the sizes of the “Nautilus”. When the constant that is given by user by
turns becomes one of the variables: d (diameter of the submarine – the first solution), L (its length – the second solution)
and Lc (length of its bit core – the third
solution).
Our three solutions in the fig. 74 are closed in the limits of the areas
(area), that are ready for protection from editing (Lock) and/or for slam
(Collapse) – see tip 62. Owing to it the solutions
in the fig. 74 can be overlooked not all at
once but only by turns on a display.