Projective Space: Tetrads and Harmonicity
P.L. Robinson
TL;DR
This paper investigates the properties of three-dimensional projective space using lines alone, focusing on the Fano axiom of harmonicity and the behavior of diagonal lines in a complete quadrilateral.
Contribution
It provides an axiomatic framework for projective space emphasizing the harmonicity axiom and analyzes the concurrency of diagonal lines in quadrilaterals.
Findings
Diagonal lines of a complete quadrilateral are not concurrent under the Fano harmonicity axiom.
The axiomatic framework clarifies the role of harmonicity in projective geometry.
Insights into the structure of three-dimensional projective space based on line configurations.
Abstract
Within an axiomatic framework for three-dimensional projective space based on lines alone, we explore the Fano axiom of harmonicity according to which the diagonal lines of a complete quadrilateral are not concurrent.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics