Paved circles (Topic n°3) - Lycée Val de Durance (Pertuis)

The problem describes a recursive geometric construction. Initially, two circles are placed with centers at (0, ½) and (1, ½) and radius 0.5. The new circles added in each step are the largest possible that are tangent to the Ox axis and also to the existing circles. In each stage, the newly introduced circles continue filling gaps while maintaining tangency, leading to a diminishing sequence of radii and structured center positions.
In our research work we have managed to tackle recursivity and functions for our problem, the Apollonian gasket, Descartes' theorem, Ford circles, and the
Farey sequence. We have created a Python code to ease visualisation, and a wooden puzzle to be able to grasp the perhaps more dicult mathematical concepts. There are plenty of things left to discover, and many more ideas to explore.