A Historical Perspective on the Topology and Physics of Hyperspace

Abstract

This paper examines the history of the development of dimensional analysis, from Euclidean geometry to hyperspace. This is largely a secondary source work intended to summarize, as briefly as possible, with enough mathematical rigor, the mathematical developments in dimensional analysis over the past 2550 years. It is intended to stimulate further research and interest in the topic while also presenting a few original thoughts on certain aspects of the subject. In particular, the paper focuses on the development of Euclidean geometry, the intense study of the parallel axiom in the 1800's, the development of time as a dimension leading to Kaluza-Klein theory, and finally the explosion of work in the combined areas of string theory, M-theory, and F-theory in the past 30 years.