"spherical triangle" meaning in English

{
  "forms": [
    {
      "form": "spherical triangles",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "args": {},
      "expansion": "spherical triangle (plural spherical triangles)",
      "name": "en-noun"
    }
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  "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"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Geometry",
          "orig": "en:Geometry",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1830, Pierce Morton, Geometry, Plane, Solid, and Spherical, in Six Books, Baldwin and Craddock, page 189",
          "text": "If the three sides of a spherical triangle be each of them equal to a quadrant, the polar triangle will coincide with it; for each of the angular points will be the pole of the side opposite to it.",
          "type": "quotation"
        },
        {
          "ref": "1876, Edward Olney, A Treatise on Special Or Elementary Geometry, Sheldon & Company, page 220",
          "text": "570. Theorem. The sum of the sides of a spherical triangle may be anything between 0 and a circumference.",
          "type": "quotation"
        },
        {
          "text": "1893, Crossley William Crosby Barlow, George Hartley Bryan, Elementary Mathematical Astronomy, W. B. Clive, page v,\nA spherical triangle, like a plane triangle, has six parts, viz., its three sides and its three angles. The sides are generally measured by the angles they subtend, so that the six parts are all expressed as angles.\nAny three parts suffice to determine a spherical triangle, but there are certain \"ambiguous cases\" when the problem admits of more than one solution. The formulæ required in solving spherical triangles form the subject of Spherical Trigonometry, and are in every case different from the analogous formulæ in Plane Trigonometry. There is this further difference, that a spherical triangle is completely determined if its three angles are given."
        },
        {
          "ref": "2012, Daniel Zwillinger, CRC Standard Mathematical Tables and Formulae, 32nd edition, Taylor & Francis (CRC Press / Chapman & Hall), page 218",
          "text": "The angles in a spherical triangle do not have to add up to 180 degrees. It is possible for a spherical triangle to have 3 right angles.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A triangle, described on the surface of the sphere, whose each side is an arc of some great circle."
      ],
      "hypernyms": [
        {
          "word": "spherical polygon"
        }
      ],
      "hyponyms": [
        {
          "word": "polar triangle"
        }
      ],
      "id": "en-spherical_triangle-en-noun-~uhMkROn",
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "triangle",
          "triangle"
        ],
        [
          "arc",
          "arc"
        ],
        [
          "great circle",
          "great circle"
        ]
      ],
      "qualifier": "spherical geometry",
      "raw_glosses": [
        "(geometry, spherical geometry) A triangle, described on the surface of the sphere, whose each side is an arc of some great circle."
      ],
      "related": [
        {
          "word": "spherical geometry"
        },
        {
          "word": "spherical trigonometry"
        }
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "Triangle on the surface of a sphere, whose sides are arcs of great circles",
          "tags": [
            "neuter"
          ],
          "word": "Kugeldreieck"
        }
      ]
    }
  ],
  "word": "spherical triangle"
}

{
  "forms": [
    {
      "form": "spherical triangles",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "spherical triangle (plural spherical triangles)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "spherical polygon"
    }
  ],
  "hyponyms": [
    {
      "word": "polar triangle"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "spherical geometry"
    },
    {
      "word": "spherical trigonometry"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Geometry"
      ],
      "examples": [
        {
          "ref": "1830, Pierce Morton, Geometry, Plane, Solid, and Spherical, in Six Books, Baldwin and Craddock, page 189",
          "text": "If the three sides of a spherical triangle be each of them equal to a quadrant, the polar triangle will coincide with it; for each of the angular points will be the pole of the side opposite to it.",
          "type": "quotation"
        },
        {
          "ref": "1876, Edward Olney, A Treatise on Special Or Elementary Geometry, Sheldon & Company, page 220",
          "text": "570. Theorem. The sum of the sides of a spherical triangle may be anything between 0 and a circumference.",
          "type": "quotation"
        },
        {
          "text": "1893, Crossley William Crosby Barlow, George Hartley Bryan, Elementary Mathematical Astronomy, W. B. Clive, page v,\nA spherical triangle, like a plane triangle, has six parts, viz., its three sides and its three angles. The sides are generally measured by the angles they subtend, so that the six parts are all expressed as angles.\nAny three parts suffice to determine a spherical triangle, but there are certain \"ambiguous cases\" when the problem admits of more than one solution. The formulæ required in solving spherical triangles form the subject of Spherical Trigonometry, and are in every case different from the analogous formulæ in Plane Trigonometry. There is this further difference, that a spherical triangle is completely determined if its three angles are given."
        },
        {
          "ref": "2012, Daniel Zwillinger, CRC Standard Mathematical Tables and Formulae, 32nd edition, Taylor & Francis (CRC Press / Chapman & Hall), page 218",
          "text": "The angles in a spherical triangle do not have to add up to 180 degrees. It is possible for a spherical triangle to have 3 right angles.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A triangle, described on the surface of the sphere, whose each side is an arc of some great circle."
      ],
      "links": [
        [
          "geometry",
          "geometry"
        ],
        [
          "triangle",
          "triangle"
        ],
        [
          "arc",
          "arc"
        ],
        [
          "great circle",
          "great circle"
        ]
      ],
      "qualifier": "spherical geometry",
      "raw_glosses": [
        "(geometry, spherical geometry) A triangle, described on the surface of the sphere, whose each side is an arc of some great circle."
      ],
      "topics": [
        "geometry",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Triangle on the surface of a sphere, whose sides are arcs of great circles",
      "tags": [
        "neuter"
      ],
      "word": "Kugeldreieck"
    }
  ],
  "word": "spherical triangle"
}