"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, {{tlb|en|geometry}} (geometry)
  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 Topics: geometry, mathematics, sciences
  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: 45 55 Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 36 64 Disambiguation of Pages with 1 entry: 35 65 Disambiguation of Pages with entries: 30 70 Topics: geometry, mathematics, sciences
     
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      "tags": [
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    {
      "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"
        ]
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        {
          "_dis": "36 64",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w+disamb"
        },
        {
          "_dis": "35 65",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w+disamb"
        },
        {
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        },
        {
          "_dis": "45 55",
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
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        }
      ],
      "glosses": [
        "A theorem stating that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle."
      ],
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      "links": [
        [
          "center",
          "center"
        ],
        [
          "incircle",
          "incircle"
        ],
        [
          "quadrilateral",
          "quadrilateral"
        ],
        [
          "vertices",
          "vertex"
        ],
        [
          "rectangle",
          "rectangle"
        ]
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Japanese theorem"
}

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    "English lemmas",
    "English multiword terms",
    "English proper nouns",
    "English uncountable nouns",
    "Pages with 1 entry",
    "Pages with entries",
    "en:Geometry"
  ],
  "forms": [
    {
      "form": "the Japanese theorem",
      "tags": [
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    }
  ],
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      "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"
        ]
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    },
    {
      "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"
        ]
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "Japanese theorem"
}

Download raw JSONL data for Japanese theorem meaning in English (1.3kB)

This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2025-01-18 from the enwiktionary dump dated 2025-01-01 using wiktextract (e4a2c88 and 4230888). 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.