C. PELLEGRINO and C. FIORI

Piani formalmente euclidei

In memoria di Francesco Speranza

Pages: 199-213
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.