Showing papers on "Euclidean geometry published in 1972"

The Effects of Teaching Euclidean Geometry via Transformations on Student Achievement and Attitudes in Tenth-Grade Geometry.

Abstract: Prominent mathematics educators (eg, Adler, 1968; and Allendoerfer, 1969) have suggested that the study of geometric transformations be one of the major goals of tenth-grade Euclidean geometry and have offered rationales for the insertion of this content Geometry texts in which transformations are given strong attention have recently appeared (eg, Kelly & Ladd, 1965; Fitzgerald, Lindblom, Zetterberg, & Dalton, 1970) Yet there has been little, if any, research that sheds light on the possible effects of studying transformations on student achievement or attitudes There exist three rather different aspects to the problem of using transformations as a fundamental idea in tenth-grade geometry First, can one create a geometry course using transformations in the framework of standard courses, including a systematic development of basic theorems of Euclidean geometry from postulates? Second, can students learn anything more from such a course than they might otherwise learn? Third, can teachers teach such a course without a large amount of retraining? The first aspect of the problem-the question of materials creationwas necessarily attacked first This aspect is briefly summarized in this

On the geometrical interpretation of the harmonic analysis of the scattering amplitude

Abstract: In this paper we intend to analyze the geometry underlying the various representations of the relativistic scattering amplitudes. More precisely we consider the direct-channel expansion, its euclidean contraction and the crossed-channel representation. In all these representations one can distinguish the factors which express the dynamics from those which reflect the symmetry; starting from the latter, one can try a geometrical interpretation of the harmonic analysis of the scattering amplitude on the Poincare group.