Two problems on touching circles - ISISS M. Casagrande (Pieve di Soligo)

Sangaku are traditional Japanese wood paintings representing geometric problems. In this work, the authors consider series of circles tangent to each other and to a same given line, or to each other and to a same other circle. In the first case, they determine the radii of the generated circles and relate their structure to the Stern-Brocot tree, a binary tree whose vertices correspond to all positive rational numbers. In the second case, using the inversion transformation it is shown that the first Sangaku can be mapped to the second one, so that they are actually equivalent.