Projective Duality and the Rise of Modern Logic

Abstract

The symmetries between points and lines in planar projective geometry and between points and planes in solid projective geometry are striking features of these geometries that were extensively discussed during the nineteenth century under the labels "duality" or "reciprocity". The aims of this article are, irst, to provide a systematic analysis of duality from a modern point of view, and, second, based on this, to give a historical overview of how discussions about duality evolved during the nineteenth century. Speci ically, we want to see in which ways geometer's preoccupation with duality was shaped by developments that lead to modern logic towards the end of the nineteenth century, and how these developments in turn might have been in luenced by re lections on duality. This is a ``preproof'' accepted article for The Bulletin of Symbolic Logic. This version may be subject to change during the production process.

Curriculum Setting Method for Special Education Specialty Integrating Projective Geometry

“…Eder proposed that there is an obvious symmetry relationship between points and lines in projective geometry. To this end, he systematically analyzed the duality of point and line from the perspective of three-dimensional, and proposed new thinking about duality [9]. Santos et al studied the laws of projective geometry in the context of quantum mechanics.…”