{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "8NCGCJ2YBH"
    },
    {
      "field": "specializes",
      "target": "DED008EJVH"
    },
    {
      "field": "specializes",
      "target": "F0JQ1TGKB0"
    },
    {
      "field": "specializes",
      "target": "VB2D03PD9Y"
    }
  ],
  "body": "\n## Summary\n\nBenz plane is the common name for three kinds of circle geometry: Möbius planes, Laguerre planes and Minkowski planes.\nEach kind is an incidence structure of points and circles in which three suitable points lie on exactly one circle and circles can touch.\nThe classical examples are the plane sections of a sphere, of a circular cylinder and of a hyperboloid of one sheet.\nThe name honours Walter Benz, who developed their common theory.\n\n## Explanations\n\n### L1 human\n\nCut a sphere, a cylinder or a hyperboloid with planes and call the curves you get circles.\nIn each case three points that are not in some special position lie on exactly one circle.\nThe three resulting geometries share many features, and the word Benz plane names all three at once.\nThey differ in their parallel points: none on a sphere, one family of lines on a cylinder, two families on a hyperboloid.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "51B05",
      "51B10"
    ],
    "name": "Benz plane",
    "same_as": {
      "wikidata": "Q3210599",
      "wikipedia": "Benz plane"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Benz_plane"
      }
    ],
    "tag": "BG5A4CB6NB"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/BG5A4CB6NB/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/BG5A4CB6NB.md",
  "msc": [
    "51B05",
    "51B10"
  ],
  "name": "Benz plane",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/BG5/BG5A4CB6NB.md",
  "status": null,
  "tag": "BG5A4CB6NB",
  "uri": "m2://BG5A4CB6NB",
  "url": "https://tamnd.github.io/math2/wiki/benz-plane/",
  "writing": {
    "tag": "BG5A4CB6NB",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}