sborník

Gunter Weiss
“industrial reality”, and the languages spoken by engineers and
mathematicians are very different and aggravate communication between
them.
In Germany politicians want to establish the Bachelor qualification as an
academic degree qualifying for a profession. So the ‘Pure Mathematics’
point of view is surely wrong!
One parameter for gaining financial bonuses for a department or an
institute is the number of articles published by the members of that unit.
Sometimes also their impact factor and citation index counts. This causes a
so called ‘publish or perish’-mentality among scientists. Here the single
fields in Mathematics have to compete with each other and classical
Geometry has not a good hand in that game, as Geometry journals
undeservedly are ranked absolutely not at the top. There is no lobby for
declaring classical Geometry for being a “mainstream science”.
Authors of papers with classical geometric content often emphasise the
‘many possible applications’ of their results and algorithms in industry. But
it is a fact that of hundreds of articles e.g. on CAGD only a handful reaches
to have influence on industrial software. The reasons for not being accepted
of industry are
- lack of communication abilities on both sides, the engineers and the
mathematicians, as already mentioned above, and
- incomplete description of the transfer of the result to a final industrial
product or algorithm,
- resistance in industry to give up well approved and maybe patented
solutions, which perhaps have cost much money.
Some examples will be shown in the next chapters.
4 Why still ‘Constructive Geometry’ in
engineering and teachers’ education
This subject flourished at the begin of the 20 th century but now it has rather
low scientific reputation. In fact, there are still no modern textbooks on the
theory of geometric mappings besides the three famous volumes “Lehrbücher
zur Darstellenden Geometrie” of E. MÜLLER (~ 1923), which link
Geometry as a tool for engineers with its scientific background. Resent
research results on geometric mappings exist of course and can be found in
mathematical journals, but they have little or no impact to the classical
Descriptive Geometry teacher, who is, in most cases, an architect or
engineer. Recent research on Constructive Geometry mostly deals with
differential geometric problems, too. But even the results are indeed
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