"circle inversion" meaning in English

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  "lang_code": "en",
  "pos": "noun",
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Circle",
          "orig": "en:Circle",
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        {
          "ref": "1875, A. B. Kempe, On Some New Limkages: Messenger of Mathematics, volume 4, page 121:",
          "text": "The first of these is obtained by the method of circle inversion first discovered by Peaucellier.",
          "type": "quote"
        },
        {
          "ref": "1997, Mathematical Association of America, MAA Notes, numbers 41-42, page 169:",
          "text": "Nikolai Joukowski (1847-1921) was a Russian mathematician who did research in aerodynamics (James and James, 1992). He used circle inversion in the complex number plane to study airfoil shapes.",
          "type": "quote"
        },
        {
          "ref": "2011, David Salomon, The Computer Graphics Manual, page 88:",
          "text": "As is common with nonlinear projections, it is possible to come up with many variants of circle inversions.[…]An obvious (but perhaps not very useful) extension of circle inversion is sphere inversion, where the spaces inside and outside a sphere are swapped.",
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      "glosses": [
        "A transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the point at infinity."
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      "qualifier": "inversive geometry",
      "raw_glosses": [
        "(geometry, inversive geometry, for a given circle with centre O and radius r) A transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the point at infinity."
      ],
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        "for a given circle with centre O and radius r"
      ],
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        {
          "word": "sphere inversion"
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            "inversion"
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          "word": "transformation"
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      "topics": [
        "geometry",
        "mathematics",
        "sciences"
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      "wikipedia": [
        "Inversive geometry"
      ]
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  "word": "circle inversion"
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  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "sphere inversion"
    }
  ],
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        "en:Circle",
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        },
        {
          "ref": "1997, Mathematical Association of America, MAA Notes, numbers 41-42, page 169:",
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        {
          "ref": "2011, David Salomon, The Computer Graphics Manual, page 88:",
          "text": "As is common with nonlinear projections, it is possible to come up with many variants of circle inversions.[…]An obvious (but perhaps not very useful) extension of circle inversion is sphere inversion, where the spaces inside and outside a sphere are swapped.",
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        "A transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the point at infinity."
      ],
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      "qualifier": "inversive geometry",
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        "(geometry, inversive geometry, for a given circle with centre O and radius r) A transformation that maps any point P ≠ O to the point P’ on the ray from O through P for which OP × OP’ = r², and which maps O to the point at infinity."
      ],
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        "for a given circle with centre O and radius r"
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  "synonyms": [
    {
      "tags": [
        "inversion"
      ],
      "word": "transformation"
    }
  ],
  "word": "circle inversion"
}