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We study analytic surfaces in 3-dimensional Euclidean space containing twocircular arcs through each point. The problem of finding such surfaces tracesback to the works of Darboux from XIXth century. We reduce finding all suchsurfaces to the algebraic problem of finding all Pythagorean 6-tuples ofpolynomials. The reduction is based on the Schicho parametrization of surfacescontaining two conics through each point and a new approach using quaternionicrational parametrization.

Surfaces containing two circles through each point and Pythagorean 6-tuples