"stereographic projection" meaning in English

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  "pos": "noun",
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      "examples": [
        {
          "text": "1974 [Prentice-Hall], Richard A. Silverman, Complex Analysis with Applications, Dover, 1984, Unaltered republication, page 19,\nThus we see that stereographic projection establishes a one-to-one correspondence between the extended complex plane and the Riemann sphere."
        },
        {
          "text": "1991, E. J. F. Primrose (translator), Simeon Ivanov (editor of translation), A. T. Fomenko, A. A. Tuzhilin, Elements of the Geometry and Topology of Minimal Surfaces in Three-Dimensional Space, American Mathematical Society, page 67,\nProposition 2. The stereographic projection π_N:S²→Oxy of the sphere S² onto the xy-plane from the North Pole N preserves the angles between tangent vectors. Thus, the coordinates specified on S²⧵N by the stereographic projection π_N are isothermal."
        },
        {
          "ref": "2004, Richard J. Lisle, Peter R. Leyshon, Stereographic Projection Techniques for Geologists and Civil Engineers, 2nd edition, Cambridge University Press, page 40:",
          "text": "Before we can recognize such patterns confidently, we need to know whether the stereographic projection faithfully represents the true clustering of directions in space.",
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        "A function that maps a sphere onto a plane; especially, the map generated by projecting each point of the sphere from the sphere's (designated) north pole to a point on the plane tangent to the south pole."
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      "qualifier": "projective geometry",
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        "(projective geometry, complex analysis, cartography) A function that maps a sphere onto a plane; especially, the map generated by projecting each point of the sphere from the sphere's (designated) north pole to a point on the plane tangent to the south pole."
      ],
      "related": [
        {
          "word": "inversive geometry"
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        {
          "word": "Riemann sphere"
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          "text": "1974 [Prentice-Hall], Richard A. Silverman, Complex Analysis with Applications, Dover, 1984, Unaltered republication, page 19,\nThus we see that stereographic projection establishes a one-to-one correspondence between the extended complex plane and the Riemann sphere."
        },
        {
          "text": "1991, E. J. F. Primrose (translator), Simeon Ivanov (editor of translation), A. T. Fomenko, A. A. Tuzhilin, Elements of the Geometry and Topology of Minimal Surfaces in Three-Dimensional Space, American Mathematical Society, page 67,\nProposition 2. The stereographic projection π_N:S²→Oxy of the sphere S² onto the xy-plane from the North Pole N preserves the angles between tangent vectors. Thus, the coordinates specified on S²⧵N by the stereographic projection π_N are isothermal."
        },
        {
          "ref": "2004, Richard J. Lisle, Peter R. Leyshon, Stereographic Projection Techniques for Geologists and Civil Engineers, 2nd edition, Cambridge University Press, page 40:",
          "text": "Before we can recognize such patterns confidently, we need to know whether the stereographic projection faithfully represents the true clustering of directions in space.",
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        "A function that maps a sphere onto a plane; especially, the map generated by projecting each point of the sphere from the sphere's (designated) north pole to a point on the plane tangent to the south pole."
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        "(projective geometry, complex analysis, cartography) A function that maps a sphere onto a plane; especially, the map generated by projecting each point of the sphere from the sphere's (designated) north pole to a point on the plane tangent to the south pole."
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