Introduction. The use of geometry in the description of nature, beginning with the Platonic solids, has gone a long way up to modern string theory. It seems, it is no accident that geometry has always been a reliable tool for modeling complex phenomena. The aim of the article is to find such universal geometric images that would allow to visually illustrate the well-known techniques of the theory of solving inventive problems.
Materials and Methods. Based on the principle of minimum complexity, a combination of four identical figures is obtained as the basis for the method of creating geometric images. And by way of an elementary figure is chosen such a simple geometric object that contains asymmetry and curvature as a minimum of requirements for it as an elementary object. This choice of combination allowed to cover practically all methods of solving problems. In the work, only some examples of techniques are given, namely: the principles of crushing, asymmetry, unification, taking, spheroidality, local quality.
Results. Heuristic methods of the theory of solving inventive problems (TRIZ), replenished and developed in the world, need a compact representation. The inventive experience of man has led to the fact that the most effective cognitive tools of practice have become geometric forms. The article proposes a technique for constructing visual images for methods known from TRIZ and is illustrated by several examples of these techniques. To assess the power of geometric images in solving complex problems in various areas of creative activity, examples are given from the field of mechanics and architecture. An example of the use of a chain line for the design of temple vaults is based on the same fundamental principle of a minimum of the functional (potential energy) as an effective use of the same principle with respect to kinetic energy in solving the problem of describing a turbulent flow where the geometrically formed images are organized circles .
Conclusions. It is concluded that the correlation of the appropriate geometric images at the very beginning of the scientific investigation seems to be underestimated when constructing effective mathematical models.