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 L_{c}),
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 L_{c} (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.

[1]
From “Popular illustrated dictionary of history and
geography” published in
France last century in the article about league (*une lieue*) it is possible to know that in X century one league equaled 1 500 “Roman
steps” (2 222 m). In
XVIII century “post
league” was 3 894
m, but “general league” was
4 445 m. The length of league changes “in time and space”. In the same XVIII century the league was 3 898 m in Turin, in Bern the league was 4 278 m, in Burgundy it was 5 169 m, in Provence and Gascon the league was 5 847
m and etc. In the second part of XIX century
(when J. Vern had been writing its roman)
the sea league equaled 5592
ì in France and England,
the astronomical one equaled 6418
m, but the metrical league (“simple average of all league”)
equaled 4 km. That’ why
followed the fuzzy-set theory the title of this roman we should read the
following way: “Very
many leagues under water”. But this note could be
considered as the continuation of the sketch “Mathcad and some secrets of literature”
(http://twt.mpei.ac.ru/ochkov/Gerasim/Gerasim.htm).

It is possible to dispute not only about the length of the league but
also about *gender* of
this noun. In French *the
league *is female – une
lieue. In our note
Russian word *the league* is neuter but the author is not sure in it. It is said that widely officer rank “lieutenant” comes from this word “the league” – “kept a place” (“span (league) of own
ground”).

[2] But assumtions and reservations may be the following: the submarine is not round straight cylinder with two round right cones along the edges, but it is only something reminiscent this composite solid; the section of the submarine does not have to be round necessarily; it is not said exactly what area is meant: surface area of the submarine or, one might say, “living” area, area of inside rooms and etc.

[3] “Underdetermined” problem we have in the sketch “Mathcad and some secrets of literature” (http://twt.mpei.ac.ru/ochkov/Gerasim/Gerasim.htm): when we calculated rubles price it was possible to use not seven but three algebraic equations. In “underdetermined” problem about the size of “Nautilus” we have two equations but we need three ones as since there are three unknowns.