Ruiz Sancho, Jesús María2023-06-212023-06-2119840035-759610.1216/RMJ-1984-14-4-899https://hdl.handle.net/20.500.14352/64761In this note we deal with the pythagoras number p of certain 1-dimensional rings, i.e., real irreducible algebroid curves over a real closed ground field k. The problem we are concerned with is to characterize those real irreducible algebroid curves which are pythagorean (i.e., p = 1). We obtain two theorems involving the value-semigroup. Then we apply them to solve the cases of: (a) Gorenstein curves, (b) planar curves, (c) monomial curves, and (d) curves of multiplicity <= 5. Finally, two conjectures are stated.engjournal articlehttp://projecteuclid.org/euclid.rmjm/1250127369http://projecteuclid.orgopen access512.7Real irreducible algebroid curvePythagoras numbersum of squareslow multiplicityGeometria algebraica1201.01 Geometría Algebraica