Galileo"s geometry

Planimetry is the science of the properties of figures of a plane invariant regarding the movements of the plane. Figures that can be combined with movements, geometry considers it equal and does not distinguish. Everyone knows the movements of Euclidean planimetry: parallel transfer, turn, axial symmetry. If you change the group of movements, for example, add transformations of likeness, then geometry will also change. In a certain sense, any group of transformations gives rise to its geometry.
The brochure tells about geometry, which is generated by the transformations of inertial reference systems familiar from the school physics course. Such geometry is called Galileo"s geometry. In some ways, this strange geometry differs from Euclidean, and in some way it looks like it.
The text of the brochure is a processing of a lecture recording read by the author on March 30, 2002 at a small mechmate of Moscow State University for schoolchildren in grades 9 - 11.
The brochure is designed for a wide range of readers interested in mathematics