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  "body": "\n## Summary\n\nStereographic projection maps the unit sphere minus one point, its north pole, bijectively onto a plane, see the [[definition|RN8RBM2A8A]].\nSending the north pole to a point at infinity makes the sphere a model of the [[Riemann sphere|0J78KBPFZB]] $\\C \\cup \\set{\\infty}$.\nThe map preserves angles and sends circles on the sphere to circles or lines in the plane.\nIt is the bridge between the geometry of the sphere and complex analysis on the extended plane.\n\n## Explanations\n\n### L1 human\n\nPut a ball on a flat floor so that it touches the floor at its south pole.\nShine a light from the north pole: each other point of the ball casts a shadow on the floor.\nThe map from a point to its shadow is the stereographic projection.\nThe south pole goes to itself, the equator goes to a circle, and points near the north pole go far away.\nSo the whole floor, together with one extra point at infinity, is a copy of the sphere.\n",
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