{
  "annotation_id": "dbb0d66d-6448-48eb-af79-8d712f61fa60",
  "date_created": "2026-03-02T18:00:32.249000Z",
  "date_modified": "2026-03-02T18:00:32.249000Z",
  "file_hash": "bac8d6d18a8724ceb45dae893c3aa7521081c6aa9b35506e705025fa2d637ec6",
  "private": false,
  "record": {
    "abstract": "This paper examines the history of the development of dimensional analysis,\nfrom Euclidean geometry to hyperspace. This is largely a secondary source work\nintended to summarize, as briefly as possible, with enough mathematical rigor,\nthe mathematical developments in dimensional analysis over the past 2550 years.\nIt is intended to stimulate further research and interest in the topic while\nalso presenting a few original thoughts on certain aspects of the subject. In\nparticular, the paper focuses on the development of Euclidean geometry, the\nintense study of the parallel axiom in the 1800\u0027s, the development of time as a\ndimension leading to Kaluza-Klein theory, and finally the explosion of work in\nthe combined areas of string theory, M-theory, and F-theory in the past 30\nyears.",
    "arxiv_id": "physics/0011042",
    "authors": [
      "Ian T. Durham"
    ],
    "categories": [
      "physics.hist-ph",
      "math.HO"
    ],
    "title": "A Historical Perspective on the Topology and Physics of Hyperspace",
    "url": "https://arxiv.org/abs/physics/0011042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9399f45f-bf48-4d4f-b7a7-1be87143d6a1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}