**Prof. Sergey Larin, DSc.**

*School of Mathematics, Physics and Computer Technology*

*Krasnoyarsk, Russia*

**Abstract.** As a generalization of the well-known concept of Pascal’s snail for
two circles a geometric notion of Pascal’s snail of order n is introduced in the paper
for n circles. It is solved the problem of its algebraic description in the form of
a polynomial with complex coefficients under the condition that the module of
the complex variable is equal to 1. The role and importance of the information
component is demonstrated by an example of animation drawings in GeoGebra
environment, which have been used during the experiments. Some of the
accompanying proofs turn out to be obvious in verbal sense and the realibility of
the assertions is confirmed by animation drawing models.

*Keywords:* animated drawings; GeoGebra environment; Pascal’s snail; complex plane; transformation; polynomial

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