"Japanese theorem" meaning in English

See Japanese theorem in All languages combined, or Wiktionary

Proper name

Forms: the Japanese theorem [canonical]
Head templates: {{en-prop|def=1}} the Japanese theorem
  1. A theorem stating that, no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant. Conversely, if the sum of inradii is independent of the triangulation, then the polygon is cyclic.
    Sense id: en-Japanese_theorem-en-name-UmKNlA6r
  2. A theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. Categories (topical): Geometry
    Sense id: en-Japanese_theorem-en-name-2KXHkBPE Disambiguation of Geometry: 29 71 Categories (other): English entries with incorrect language header Disambiguation of English entries with incorrect language header: 35 65

Download JSON data for Japanese theorem meaning in English (1.4kB)

{
  "forms": [
    {
      "form": "the Japanese theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "def": "1"
      },
      "expansion": "the Japanese theorem",
      "name": "en-prop"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "glosses": [
        "A theorem stating that, no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant. Conversely, if the sum of inradii is independent of the triangulation, then the polygon is cyclic."
      ],
      "id": "en-Japanese_theorem-en-name-UmKNlA6r",
      "links": [
        [
          "triangulate",
          "triangulate"
        ],
        [
          "cyclic",
          "cyclic"
        ],
        [
          "polygon",
          "polygon"
        ],
        [
          "inradii",
          "inradius"
        ],
        [
          "triangle",
          "triangle"
        ],
        [
          "constant",
          "constant"
        ]
      ]
    },
    {
      "categories": [
        {
          "_dis": "35 65",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "29 71",
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "A theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle."
      ],
      "id": "en-Japanese_theorem-en-name-2KXHkBPE",
      "links": [
        [
          "center",
          "center"
        ],
        [
          "incircle",
          "incircle"
        ],
        [
          "quadrilateral",
          "quadrilateral"
        ],
        [
          "vertices",
          "vertex"
        ],
        [
          "rectangle",
          "rectangle"
        ]
      ]
    }
  ],
  "word": "Japanese theorem"
}

{
  "categories": [
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English proper nouns",
    "English uncountable nouns",
    "en:Geometry"
  ],
  "forms": [
    {
      "form": "the Japanese theorem",
      "tags": [
        "canonical"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "def": "1"
      },
      "expansion": "the Japanese theorem",
      "name": "en-prop"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "glosses": [
        "A theorem stating that, no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant. Conversely, if the sum of inradii is independent of the triangulation, then the polygon is cyclic."
      ],
      "links": [
        [
          "triangulate",
          "triangulate"
        ],
        [
          "cyclic",
          "cyclic"
        ],
        [
          "polygon",
          "polygon"
        ],
        [
          "inradii",
          "inradius"
        ],
        [
          "triangle",
          "triangle"
        ],
        [
          "constant",
          "constant"
        ]
      ]
    },
    {
      "glosses": [
        "A theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle."
      ],
      "links": [
        [
          "center",
          "center"
        ],
        [
          "incircle",
          "incircle"
        ],
        [
          "quadrilateral",
          "quadrilateral"
        ],
        [
          "vertices",
          "vertex"
        ],
        [
          "rectangle",
          "rectangle"
        ]
      ]
    }
  ],
  "word": "Japanese theorem"
}

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.