2000/11/18 by Ian T. Durham, Durham, Ian T.
Arts and Humanities · Computer Science · Engineering · Mathematics · Physics and Astronomy · #Architecture and Computational Design #Art, Technology, and Culture #FOS: Mathematics #FOS: Physical sciences #History and Overview (math.HO) #History and Philosophy of Physics (physics.hist-ph) #Topological and Geometric Data Analysis #math.HO #physics.hist-ph
paper · pdf · doi:10.48550/arxiv.physics/0011042
25 pages, 4 figures, research performed under the auspices of the Graduate Program in Applied Physics, Johns Hopkins University, Baltimore, Maryland
arxiv created 2000/11/18 · openalex publication_date 2000/11/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.