C. PELLEGRINO and C. FIORI
Piani formalmente euclidei
In memoria di Francesco Speranza
Received: 28 Novembre 1999
Mathematics Subject Classification: 51A30 - 51E15
Lavoro eseguito nell'ambito delle attivitą finanziate dal MURST
Abstract: In this paper we fix geometrical conditions that allow todefine and algebraically characterize the notions of congruence, orthogonality, similitude and isometry on a Pappo's affine plane (finite or not). So we state that the class of the affine planes in which the representation of the affine transformations, of the similitudes and of the isometries coincides with those of the ordinary plane is exactly that of the planes by von Staudt. This shows that in order to characterize the ordinary plane it is not necessary to start from the field of real numbers.