{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "4695YA7F87"
    },
    {
      "field": "uses",
      "target": "NPNNXWMVCC"
    },
    {
      "field": "defines",
      "target": "EMWW6PKFSG"
    },
    {
      "field": "about",
      "target": "NPNNXWMVCC"
    }
  ],
  "body": "\n## Summary\n\nProjective geometry studies the properties of figures that survive projection, such as incidence and the [[cross-ratio|09ASMRMD67]].\nLength and angle are not among them.\nIts spaces are [[projective spaces|ZT9A6JK8QF]], where any two lines of a plane meet.\nIt can be built either from linear algebra or from incidence axioms.\nIn it, points and hyperplanes play symmetric roles, which gives the principle of [[duality|DCMP1A0138]].\nIt underlies perspective drawing, algebraic geometry and computer vision.\n\n## Explanations\n\n### L1 human\n\nWhen a lamp casts the shadow of a shape on a wall, lengths and angles change, but straight lines stay straight.\nProjective geometry studies exactly what such shadows and perspective views keep.\nIn this geometry parallel lines are said to meet at a point at infinity, so any two lines in a plane meet.\nFor example, all ellipses, parabolas and hyperbolas become the same kind of curve, a conic seen from different viewpoints.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "51A05",
      "51N15"
    ],
    "name": "Projective geometry",
    "same_as": {
      "wikidata": "Q177409",
      "wikipedia": "Projective geometry"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Projective_geometry"
      }
    ],
    "tag": "N32Z68F0D3"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/N32Z68F0D3/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/N32Z68F0D3.md",
  "msc": [
    "51A05",
    "51N15"
  ],
  "name": "Projective geometry",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/N32/N32Z68F0D3.md",
  "status": null,
  "tag": "N32Z68F0D3",
  "uri": "m2://N32Z68F0D3",
  "url": "https://tamnd.github.io/math2/wiki/projective-geometry/",
  "writing": {
    "tag": "N32Z68F0D3",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}