"Gauss-Bonnet theorem" meaning in All languages combined

{
  "etymology_text": "Named after Carl Friedrich Gauss, who was aware of a version of the theorem but never published it, and Pierre Ossian Bonnet, who published a special case in 1848.",
  "forms": [
    {
      "form": "the Gauss-Bonnet theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
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      },
      "expansion": "the Gauss-Bonnet theorem",
      "name": "en-proper noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
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        {
          "kind": "other",
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "An important statement about surfaces in differential geometry, connecting their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic)."
      ],
      "id": "en-Gauss-Bonnet_theorem-en-name-Yjy55xRs",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "surface",
          "surface"
        ],
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "curvature",
          "curvature"
        ],
        [
          "topology",
          "topology"
        ],
        [
          "Euler characteristic",
          "Euler characteristic"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An important statement about surfaces in differential geometry, connecting their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic)."
      ],
      "synonyms": [
        {
          "word": "Gauss-Bonnet formula"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Gauss-Bonnet theorem"
      ]
    }
  ],
  "word": "Gauss-Bonnet theorem"
}

{
  "etymology_text": "Named after Carl Friedrich Gauss, who was aware of a version of the theorem but never published it, and Pierre Ossian Bonnet, who published a special case in 1848.",
  "forms": [
    {
      "form": "the Gauss-Bonnet theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
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      "expansion": "the Gauss-Bonnet theorem",
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
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        "English proper nouns",
        "English uncountable nouns",
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        "Pages with entries",
        "en:Mathematics"
      ],
      "glosses": [
        "An important statement about surfaces in differential geometry, connecting their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic)."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "surface",
          "surface"
        ],
        [
          "differential geometry",
          "differential geometry"
        ],
        [
          "geometry",
          "geometry"
        ],
        [
          "curvature",
          "curvature"
        ],
        [
          "topology",
          "topology"
        ],
        [
          "Euler characteristic",
          "Euler characteristic"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An important statement about surfaces in differential geometry, connecting their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic)."
      ],
      "synonyms": [
        {
          "word": "Gauss-Bonnet formula"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Gauss-Bonnet theorem"
      ]
    }
  ],
  "word": "Gauss-Bonnet theorem"
}