{
  "annotation_id": "798d3acc-d246-4604-92df-e5563aed8be1",
  "date_created": "2026-03-02T18:01:00.587000Z",
  "date_modified": "2026-03-02T18:01:00.587000Z",
  "file_hash": "9b9da245325eb0f447b7800e0dd142acb2e6dda383b0c7330c7efc9d52aa11eb",
  "private": false,
  "record": {
    "abstract": "The formal structure of the early Einstein\u0027s Special Relativity follows the\naxiomatic deductive method of Euclidean geometry. In this paper we show the\ndeep-rooted relation between Euclidean and space-time geometries that are both\nlinked to a two-dimensional number system: the complex and hyperbolic numbers,\nrespectively. By studying the properties of these numbers together,\npseudo-Euclidean trigonometry has been formalized with an axiomatic deductive\nmethod and this allows us to give a complete quantitative formalization of the\ntwin paradox in a familiar \"Euclidean\" way for uniform motions as well as for\naccelerated ones.",
    "arxiv_id": "physics/0509161",
    "authors": [
      "Dino Boccaletti",
      "Francesco Catoni",
      "Vincenzo Catoni"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "title": "Space-time trigonometry and formalization of the \"Twin Paradox\" for   uniform and accelerated motions",
    "url": "https://arxiv.org/abs/physics/0509161"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "35741a0a-cf4a-424c-ba4e-79526b3c4bf1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}