"figurate number" meaning in English

{
  "forms": [
    {
      "form": "figurate numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "figurate number (plural figurate numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
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          "kind": "other",
          "name": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
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          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A number equal to the number of dots in a geometric figure formed of dots. The series begins with unity and is formed so that subtracting each from the following, and treating the series so formed in the same way, by a continuation of the process, yields equal differences."
      ],
      "id": "en-figurate_number-en-noun-FyRik3zJ",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "number theory",
          "number theory"
        ],
        [
          "number",
          "number#Noun"
        ],
        [
          "equal",
          "equal#Adjective"
        ],
        [
          "dots",
          "dot#Noun"
        ],
        [
          "geometric",
          "geometric"
        ],
        [
          "figure",
          "figure#Noun"
        ],
        [
          "formed",
          "form#Verb"
        ],
        [
          "unity",
          "unity"
        ]
      ],
      "raw_glosses": [
        "(mathematics, number theory) A number equal to the number of dots in a geometric figure formed of dots. The series begins with unity and is formed so that subtracting each from the following, and treating the series so formed in the same way, by a continuation of the process, yields equal differences."
      ],
      "related": [
        {
          "word": "gnomon"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ]
    }
  ],
  "word": "figurate number"
}

{
  "forms": [
    {
      "form": "figurate numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "figurate number (plural figurate numbers)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "gnomon"
    }
  ],
  "senses": [
    {
      "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",
        "en:Mathematics",
        "en:Number theory"
      ],
      "glosses": [
        "A number equal to the number of dots in a geometric figure formed of dots. The series begins with unity and is formed so that subtracting each from the following, and treating the series so formed in the same way, by a continuation of the process, yields equal differences."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "number theory",
          "number theory"
        ],
        [
          "number",
          "number#Noun"
        ],
        [
          "equal",
          "equal#Adjective"
        ],
        [
          "dots",
          "dot#Noun"
        ],
        [
          "geometric",
          "geometric"
        ],
        [
          "figure",
          "figure#Noun"
        ],
        [
          "formed",
          "form#Verb"
        ],
        [
          "unity",
          "unity"
        ]
      ],
      "raw_glosses": [
        "(mathematics, number theory) A number equal to the number of dots in a geometric figure formed of dots. The series begins with unity and is formed so that subtracting each from the following, and treating the series so formed in the same way, by a continuation of the process, yields equal differences."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ]
    }
  ],
  "word": "figurate number"
}