  We present some notes on the definition of mathematical design as well as on
the methods of mathematical modeling which are used in the process of the
artistic design of the environment and its components. For the first time in
the field of geometric modeling, we perform an aesthetic analysis of planar
Bernstein-Bezier curves from the standpoint of the laws of technical
aesthetics. The shape features of the curve segments' geometry were evaluated
using the following criteria: conciseness-integrity, expressiveness,
proportional consistency, compositional balance, structural organization,
imagery, rationality, dynamism, scale, flexibility and harmony. In the
non-Russian literature, Bernstein-Bezier curves using a monotonic curvature
function (i.e., a class A Bezier curve) are considered to be fair (i.e.,
beautiful) curves, but their aesthetic analysis has never been performed. The
aesthetic analysis performed by the authors of this work means that this is no
longer the case. To confirm the conclusions of the authors' research, a survey
of the "aesthetic appropriateness" of certain Bernstein-Bezier curve segments
was conducted among 240 children, aged 14-17. The results of this survey have
shown themselves to be in full accordance with the authors' results.
