The three circles of radii 1, 2 and 3 tangent to each other contemplated last week will have their centers at the vertices of a triangle with sides 3, 4 and 5. The key lines of Soddy's poem, as far as the statement of Descartes' theorem is concerned, are those that say "it is the addition of its squares/half a square of the sum" The value of the fourth radius based on the other three can be deduced from a simple formula.

Descarte's rival, Pierre de Fermat, tried to discredit the “competent lawyer” by calling his methods lax, but given the good results he obtained, it was a losing battle, says Annoyed. The two heavyweights of French mathematics faced each other in the ring of… Cartesian coordinates? It was a battle that was won by the Frenchman, Annoying says, and it is only now that we can talk about Fermat's greater prestige.