Problems 5 and 12 of the recent Arnold list concern the continued fractions of irrational roots of quadratic equations. These continued fractions are periodic, and the periods may have some symmetry, like palindromicity. I show that these symmetries are related to the symmetries of the classes of quadratic forms associated to the quadratic equations. I give moreover a geometrical description of the quadratic fields theory. The mathematical seminar organised by V.I. Arnold is devoted to several subjects of mathematics. It will take place on FRIDAYS (not on Wednesdays as previously announced), at 14:30 hours, in the Seminar Room of the ICTP Main Building.