{
  "annotation_id": "e21fe5f6-ec28-423c-8031-a5606a29f6fc",
  "date_created": "2026-03-02T18:01:27.798000Z",
  "date_modified": "2026-03-02T18:01:27.798000Z",
  "file_hash": "c0b00d42642c54fc5100b683733b54cd222916024f90971f49b9e00411ff203d",
  "private": false,
  "record": {
    "abstract": "This paper introduces the concept of a Fourier knot. A Fourier knot is a knot\nthat is represented by a parametrized curve in three dimensional space such\nthat the coordinate functions are finite Fourier series in the parameter. The\npreviously studied Lissajous knots constitute a case of Fourier knots with\nsingle frequencies in each coordinate direction. Not all knots are Lissajous.\nIn fact the trefoil knot and the figure eight knot are the first examples of\nnon- Lissajous knots. This paper gives robust and simple Fourier\nrepresentations for these and other examples. This new version of the paper\ncontains a crucial reference to the beautiful work of Aaron Trautwein on\nHarmonic Knots. See \u003chttp://www.carthage.edu/~trautwn\u003e. See also\n\u003chttp://math.uic.edu/~kauffman/\u003e.",
    "arxiv_id": "q-alg/9711013",
    "authors": [
      "Louis H. Kauffman"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Fourier Knots",
    "url": "https://arxiv.org/abs/q-alg/9711013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9950f0e2-3495-4fe8-9dac-169563a0586e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}