Unifying Ancient and Modern Geometries Through Octonions

Authors

Sultan Catto, CUNY Graduate CenterFollow
Yasemin Gürcan, CUNY Borough of Manhattan Community CollegeFollow
Amish Khalfan, CUNY La Guardia Community CollegeFollow
Levent Kurt, CUNY Borough of Manhattan Community CollegeFollow

Document Type

Article

Publication Date

2016

Abstract

We show the first unified description of some of the oldest known geometries such as the Pappus’ theorem with more modern ones like Desargues’ theorem, Monge’s theorem and Ceva’s theorem, through octonions, the highest normed division algebra in eight dimensions. We also show important applications in hadronic physics, giving a full description of the algebra of color applicable to quark physics, and comment on further applications.

Comments

This article was originally published in the Journal of Physics: Conference Series 766 (2016) 012001. doi:10.1088/1742-6596/670/1/012016.