H.S.M. Coxeter’s Theory of Accessibility: A Narrative in the Language of Synthetic Projective Geometry (Elena Marchisotto, Cal State Northridge)

The relation of accessible points in a projective incidence plane defined by Coxeter in the 1960s is the focus of my narrative. It reveals historical pathways bookending the 19th and 20th centuries that bring G.K.C. von Staudt, Mario Pieri, Marvin Greenberg and others into the conversation. The published references to Coxeter’s theory, including his own, are few. Were it not for his letter to me in the 1980s, the myriad of interesting mathematical and historical connections emanating from it might have remained in the shadows. My narrative will address how accessible points behave in different types of projective planes partitioned in terms interior/exterior points of conics. Its language pays homage to the invention of geometry, and shows what can be gained from the power of synthetic methods.

References:

Pambuccian, V. and Schacht, C.: The case for the irreducibility of geometry to algebra. Philos. Math. (III) 30, 1–31 (2022). https://academic.oup.com/philmat/article-abstract/30/1/1/6371269?redirectedFrom=fulltext

Marchisotto, E.A. C.: H.S.M. Coxeter’s Theory of Accessibility: From Mario Pieri to Marvin Greenberg. Results in Mathematics 77(5), 1-61 (July 2022). DOI: 10.1007/s00025-022-01690-9