{
  "aliases": [
    "manhattan-metric",
    "l1-metric"
  ],
  "backlinks": null,
  "body": "\n## Example\n\nLet $n \\ge 1$ be an integer.\nFor $x = (x_1, \\ldots, x_n)$ and $y = (y_1, \\ldots, y_n)$ in $\\mathbb{R}^n$, let\n$$d_1(x, y) = \\sum_{i=1}^{n} |x_i - y_i|.$$\nThen $d_1$ is a [[metric|063W5JMY85]] on $\\mathbb{R}^n$, the taxicab metric.\n\n## Remarks\n\nThe triangle inequality for $d_1$ follows from the [[triangle inequality|03HF5PMY5T]] for real numbers in each coordinate.\nIn $\\mathbb{R}^2$, the distance from $(0, 0)$ to $(3, 4)$ is $7$, but the [[Euclidean distance|0E1MMCAY5B]] is $5$.\nIt is the case $p = 1$ of the [[p-metric|0TFDZN6AXP]].\n\n## Explanations\n\n### L1 human\n\nA taxi in a city with a grid of streets cannot drive through the blocks.\nIt must go along the streets, so it travels the sum of the east-west and the north-south distances.\n",
  "commit": "f591989ed15704e9d8755a7a5a6426d73de7a3ae",
  "front": {
    "aliases": [
      "manhattan-metric",
      "l1-metric"
    ],
    "instance_of": [
      "0VKD1TP7F3"
    ],
    "kind": "example",
    "msc": [
      "51F99"
    ],
    "name": "Taxicab metric",
    "same_as": {
      "wikidata": "Q573509",
      "wikipedia": "Taxicab geometry"
    },
    "sources": [
      {
        "locator": "Formal definition",
        "url": "https://en.wikipedia.org/wiki/Taxicab_geometry"
      }
    ],
    "tag": "07CJNE6ZAQ"
  },
  "kind": "example",
  "link": "https://math2.tamnd.com/node/07CJNE6ZAQ/",
  "links": [
    {
      "field": "instance_of",
      "target": "0VKD1TP7F3"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/07CJNE6ZAQ.md",
  "msc": [
    "51F99"
  ],
  "name": "Taxicab metric",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/07C/07CJNE6ZAQ.md",
  "status": null,
  "tag": "07CJNE6ZAQ",
  "uri": "m2://07CJNE6ZAQ",
  "url": "https://math2.tamnd.com/wiki/taxicab-metric/",
  "writing": {
    "tag": "07CJNE6ZAQ",
    "kind": "example",
    "level": "W2",
    "next": [
      {
        "what": "a person confirmed each agent-written section",
        "note": "rule P04",
        "have": 0,
        "want": 1
      }
    ]
  }
}