{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "CW1TJDGCKA"
    },
    {
      "field": "uses",
      "target": "HA63ZVJFVZ"
    }
  ],
  "body": "\n## Summary\n\nThe circumsphere of a [[simplex|YX1DJK2QAG]] is the unique [[sphere|P9CM4GQ2T0]] in its affine span that passes through all its vertices.\nIts centre is the circumcentre and its radius the circumradius.\nFor a triangle it is the [[circumcircle|03VZJE6C8C]], and for a [[tetrahedron|JFX8ASQS3E]] it is a sphere through the four vertices.\nThe word is also used for a sphere through all vertices of a polyhedron, which exists only for some polyhedra.\n\n## Explanations\n\n### L1 human\n\nThrough any three points that are not on a line there is exactly one circle.\nIn space, through any four points not in a plane there is exactly one sphere.\nThat sphere is the circumsphere of the tetrahedron with these four corners.\nFor the cube with corners $(\\pm 1, \\pm 1, \\pm 1)$, the sphere of radius $\\sqrt{3}$ about the origin passes through all eight corners.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "51M04",
      "51M20"
    ],
    "name": "Circumsphere",
    "same_as": {
      "wikidata": "Q1414689",
      "wikipedia": "Circumscribed sphere"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Circumscribed_sphere"
      }
    ],
    "tag": "MRC4WMVTAH"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/MRC4WMVTAH/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/MRC4WMVTAH.md",
  "msc": [
    "51M04",
    "51M20"
  ],
  "name": "Circumsphere",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/MRC/MRC4WMVTAH.md",
  "status": null,
  "tag": "MRC4WMVTAH",
  "uri": "m2://MRC4WMVTAH",
  "url": "https://tamnd.github.io/math2/wiki/circumsphere/",
  "writing": {
    "tag": "MRC4WMVTAH",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}