"hexagonal number" meaning in English

{
  "forms": [
    {
      "form": "hexagonal numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "hexagonal number (plural hexagonal numbers)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "_dis1": "50 50",
      "word": "figurate number"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "_dis": "59 41",
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
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          "source": "w+disamb"
        },
        {
          "_dis": "75 25",
          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "57 43",
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
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        },
        {
          "_dis": "62 38",
          "kind": "other",
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          "parents": [],
          "source": "w+disamb"
        },
        {
          "_dis": "70 30",
          "kind": "other",
          "name": "Terms with German translations",
          "parents": [],
          "source": "w+disamb"
        }
      ],
      "glosses": [
        "The number of dots in a figure made up of partially overlapping dotted regular hexagons (6k dots arranged into a regular hexagon) of perimeter 6k for k = 1 ... n which grow out of a common vertex (and two shared or partially shared sides); a.k.a. “cornered hexagonal number”; H_n+1=6Δₙ-n²+1 where Δₙ denotes the nᵗʰ triangular number."
      ],
      "id": "en-hexagonal_number-en-noun-OAuulEdl",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "hexagon",
          "hexagon"
        ],
        [
          "perimeter",
          "perimeter"
        ],
        [
          "triangular number",
          "triangular number"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The number of dots in a figure made up of partially overlapping dotted regular hexagons (6k dots arranged into a regular hexagon) of perimeter 6k for k = 1 ... n which grow out of a common vertex (and two shared or partially shared sides); a.k.a. “cornered hexagonal number”; H_n+1=6Δₙ-n²+1 where Δₙ denotes the nᵗʰ triangular number."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "_dis1": "69 31",
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "Sechseckszahl"
        }
      ]
    },
    {
      "categories": [
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The number of dots in a figure made up of regular dotted hexagons (of perimeter 6k for k = 1 ... n) arranged concentrically around an extra dot at their common center; a.k.a. “centered hexagonal number”; H_n+1=1+6Δₙ."
      ],
      "id": "en-hexagonal_number-en-noun-fa9I8mLh",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "concentrically",
          "concentrically"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The number of dots in a figure made up of regular dotted hexagons (of perimeter 6k for k = 1 ... n) arranged concentrically around an extra dot at their common center; a.k.a. “centered hexagonal number”; H_n+1=1+6Δₙ."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "hexagonal number"
}

{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English multiword terms",
    "English nouns",
    "Entries with translation boxes",
    "Pages with 1 entry",
    "Pages with entries",
    "Terms with German translations",
    "Translation table header lacks gloss"
  ],
  "forms": [
    {
      "form": "hexagonal numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "hexagonal number (plural hexagonal numbers)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "figurate number"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "The number of dots in a figure made up of partially overlapping dotted regular hexagons (6k dots arranged into a regular hexagon) of perimeter 6k for k = 1 ... n which grow out of a common vertex (and two shared or partially shared sides); a.k.a. “cornered hexagonal number”; H_n+1=6Δₙ-n²+1 where Δₙ denotes the nᵗʰ triangular number."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "hexagon",
          "hexagon"
        ],
        [
          "perimeter",
          "perimeter"
        ],
        [
          "triangular number",
          "triangular number"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The number of dots in a figure made up of partially overlapping dotted regular hexagons (6k dots arranged into a regular hexagon) of perimeter 6k for k = 1 ... n which grow out of a common vertex (and two shared or partially shared sides); a.k.a. “cornered hexagonal number”; H_n+1=6Δₙ-n²+1 where Δₙ denotes the nᵗʰ triangular number."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Mathematics"
      ],
      "glosses": [
        "The number of dots in a figure made up of regular dotted hexagons (of perimeter 6k for k = 1 ... n) arranged concentrically around an extra dot at their common center; a.k.a. “centered hexagonal number”; H_n+1=1+6Δₙ."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "concentrically",
          "concentrically"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The number of dots in a figure made up of regular dotted hexagons (of perimeter 6k for k = 1 ... n) arranged concentrically around an extra dot at their common center; a.k.a. “centered hexagonal number”; H_n+1=1+6Δₙ."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "Sechseckszahl"
    }
  ],
  "word": "hexagonal number"
}