Fernando Galván, José FranciscoRuiz Sancho, Jesús María2023-06-202023-06-2020050037-9484https://hdl.handle.net/20.500.14352/49907We Show that (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ is contained in a real analytic surface germ with the same Pythagoras number (or Pythagoras number 2 if the curve is Pythagorean). This gives new examples and counterexamples concerning sums of squares and positive semidefinite analytic function germs.engjournal articlehttp://smf.emath.fr/en/Publications/Bulletin/http://smf.emath.fr/open access512.7Pythagoras numbersum of squaresM. Artin’s approximation.Geometria algebraica1201.01 Geometría Algebraica