"inversive geometry" meaning in English

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  "lang_code": "en",
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          "text": "1983, John Willard Milnor, On the Geometry of the Kepler Problem, The American Mathematical Monthly, Volume 90, reprinted in 1994, John Milnor, Collected Papers, I: Geometry, page 261,\nIn particular, the non-Euclidean geometry of Lobachevsky and Bolyai, and the inversive geometry of Steiner play an important role."
        },
        {
          "ref": "1999, David A. Brannan, Matthew F. Esplen, Jeremy J. Gray, Geometry, page 2",
          "text": "The study of properties of such families of circles gave rise to a new geometry, called inversive geometry, which was able to provide particularly striking proofs of previously known results in Euclidean geometry as well as new results.",
          "type": "quotation"
        },
        {
          "ref": "2007, Elena Anne Marchisotto, James T. Smith, The Legacy of Mario Pieri in Geometry and Arithmetic, page 143",
          "roman": "David Hilbert's school at Göttingen spawned an axiomatization of inversive geometry by B. L. van der Waerden and Lucas J. Smid in 1935.",
          "text": "Even after that, despite the need identified by Klein, Kasner, and J. W. Young, foundations of inversive geometry did not receive much research attention.",
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      "glosses": [
        "The branch of geometry concerned with inversion transformations, specifically circle inversions in the Euclidean plane, but also as generalised in non-Euclidean and higher-dimensional spaces."
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      "id": "en-inversive_geometry-en-noun-nj6fjlCV",
      "links": [
        [
          "geometry",
          "geometry"
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        [
          "inversion",
          "inversion"
        ],
        [
          "circle inversion",
          "circle inversion"
        ]
      ],
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        "(geometry) The branch of geometry concerned with inversion transformations, specifically circle inversions in the Euclidean plane, but also as generalised in non-Euclidean and higher-dimensional spaces."
      ],
      "related": [
        {
          "word": "circle inversion"
        },
        {
          "word": "inversion"
        },
        {
          "word": "plane inversion"
        },
        {
          "word": "sphere inversion"
        }
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        "geometry",
        "mathematics",
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      "wikipedia": [
        "inversive geometry"
      ]
    }
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  "word": "inversive geometry"
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      "word": "circle inversion"
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    {
      "word": "plane inversion"
    },
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      "word": "sphere inversion"
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      "examples": [
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          "text": "1983, John Willard Milnor, On the Geometry of the Kepler Problem, The American Mathematical Monthly, Volume 90, reprinted in 1994, John Milnor, Collected Papers, I: Geometry, page 261,\nIn particular, the non-Euclidean geometry of Lobachevsky and Bolyai, and the inversive geometry of Steiner play an important role."
        },
        {
          "ref": "1999, David A. Brannan, Matthew F. Esplen, Jeremy J. Gray, Geometry, page 2",
          "text": "The study of properties of such families of circles gave rise to a new geometry, called inversive geometry, which was able to provide particularly striking proofs of previously known results in Euclidean geometry as well as new results.",
          "type": "quotation"
        },
        {
          "ref": "2007, Elena Anne Marchisotto, James T. Smith, The Legacy of Mario Pieri in Geometry and Arithmetic, page 143",
          "roman": "David Hilbert's school at Göttingen spawned an axiomatization of inversive geometry by B. L. van der Waerden and Lucas J. Smid in 1935.",
          "text": "Even after that, despite the need identified by Klein, Kasner, and J. W. Young, foundations of inversive geometry did not receive much research attention.",
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        "The branch of geometry concerned with inversion transformations, specifically circle inversions in the Euclidean plane, but also as generalised in non-Euclidean and higher-dimensional spaces."
      ],
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          "geometry",
          "geometry"
        ],
        [
          "inversion",
          "inversion"
        ],
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          "circle inversion",
          "circle inversion"
        ]
      ],
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        "(geometry) The branch of geometry concerned with inversion transformations, specifically circle inversions in the Euclidean plane, but also as generalised in non-Euclidean and higher-dimensional spaces."
      ],
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