"turning number" meaning in English

{
  "forms": [
    {
      "form": "turning numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "turning number (plural turning numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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        },
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Topology",
          "orig": "en:Topology",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1989, Wayne Sewell, Weaving a Program: Literate Programming in WEB, page 516:",
          "text": "This program illustrates the Whitney-Graustein theorem, that two closed curves (immersions of the circle) in the plane can be deformed into one another without letting go of the immersion property if and only if their turning numbers are the same.",
          "type": "quote"
        },
        {
          "ref": "1998, Karsten Groβe-Brauckmann, Robert B. Kusner, John M. Sullivan, “Constant Mean Curvature Surfaces with Cylindrical Ends”, in Hans-Christian Hege, Konrad Polthier, editors, Mathematical Visualization: Algorithms, Applications and Numerics, Springer, page 114:",
          "text": "Moreover, l gives the turning number of the k-gon one sees in the horizontal symmetry plane when the axes of the ends are deleted.[…]Moreover, every even k ≥ 30 except for 32, 36, 40, 44, 48 52 an 56 gives an example, while for every even k > 102 there is more than one example since different turning numbers are possible.",
          "type": "quote"
        },
        {
          "text": "2002, Journal of Physics: Mathematical and general, page 6187,\nFor any oriented curve β(τ),τ∈I,I=[0,Λ] of class C¹ (τ is the arclength parametrization) lying in an oriented Euclidean plane E, the turning number 𝒯_(n_β) may be defined as\n𝒯_(n_β)=1/(2π)∫₀^Λκ_β(τ)dτ\nwhere κ_β(τ) is the signed curvature of β."
        }
      ],
      "glosses": [
        "A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point."
      ],
      "id": "en-turning_number-en-noun-v2EoXVtR",
      "links": [
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          "geometry",
          "geometry"
        ],
        [
          "topology",
          "topology"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "winding number",
          "winding number"
        ],
        [
          "rotation",
          "rotation"
        ],
        [
          "tangent",
          "tangent"
        ],
        [
          "curve",
          "curve"
        ]
      ],
      "raw_glosses": [
        "(geometry, topology, mathematical analysis) A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point."
      ],
      "topics": [
        "geometry",
        "mathematical-analysis",
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "turning number"
}

{
  "forms": [
    {
      "form": "turning numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "turning number (plural turning numbers)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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        "en:Geometry",
        "en:Mathematical analysis",
        "en:Topology"
      ],
      "examples": [
        {
          "ref": "1989, Wayne Sewell, Weaving a Program: Literate Programming in WEB, page 516:",
          "text": "This program illustrates the Whitney-Graustein theorem, that two closed curves (immersions of the circle) in the plane can be deformed into one another without letting go of the immersion property if and only if their turning numbers are the same.",
          "type": "quote"
        },
        {
          "ref": "1998, Karsten Groβe-Brauckmann, Robert B. Kusner, John M. Sullivan, “Constant Mean Curvature Surfaces with Cylindrical Ends”, in Hans-Christian Hege, Konrad Polthier, editors, Mathematical Visualization: Algorithms, Applications and Numerics, Springer, page 114:",
          "text": "Moreover, l gives the turning number of the k-gon one sees in the horizontal symmetry plane when the axes of the ends are deleted.[…]Moreover, every even k ≥ 30 except for 32, 36, 40, 44, 48 52 an 56 gives an example, while for every even k > 102 there is more than one example since different turning numbers are possible.",
          "type": "quote"
        },
        {
          "text": "2002, Journal of Physics: Mathematical and general, page 6187,\nFor any oriented curve β(τ),τ∈I,I=[0,Λ] of class C¹ (τ is the arclength parametrization) lying in an oriented Euclidean plane E, the turning number 𝒯_(n_β) may be defined as\n𝒯_(n_β)=1/(2π)∫₀^Λκ_β(τ)dτ\nwhere κ_β(τ) is the signed curvature of β."
        }
      ],
      "glosses": [
        "A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "topology",
          "topology"
        ],
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "winding number",
          "winding number"
        ],
        [
          "rotation",
          "rotation"
        ],
        [
          "tangent",
          "tangent"
        ],
        [
          "curve",
          "curve"
        ]
      ],
      "raw_glosses": [
        "(geometry, topology, mathematical analysis) A version of winding number in which the number of rotations is counted with respect to the tangent of the curve rather than a fixed point."
      ],
      "topics": [
        "geometry",
        "mathematical-analysis",
        "mathematics",
        "sciences",
        "topology"
      ]
    }
  ],
  "word": "turning number"
}