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  2. Figurate number - Wikipedia

    en.wikipedia.org/wiki/Figurate_number

    a number represented as a discrete r-dimensional regular geometric pattern of r-dimensional balls such as a polygonal number (for r = 2) or a polyhedral number (for r = 3). a member of the subset of the sets above containing only triangular numbers, pyramidal numbers , and their analogs in other dimensions.

  3. Category:Figurate numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Figurate_numbers

    Pages in category "Figurate numbers" The following 51 pages are in this category, out of 51 total. This list may not reflect recent changes. ...

  4. Hexagonal number - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_number

    Proof without words that a hexagonal number (middle column) can be rearranged as rectangular and odd-sided triangular numbers. A hexagonal number is a figurate number.The nth hexagonal number h n is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.

  5. Polygonal number - Wikipedia

    en.wikipedia.org/wiki/Polygonal_number

    In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon [1]: 2-3 . These are one type of 2-dimensional figurate numbers . Polygonal numbers were first studied during the 6th century BC by the Ancient Greeks, who investigated and discussed properties of oblong , triangular , and square numbers ...

  6. Triangular number - Wikipedia

    en.wikipedia.org/wiki/Triangular_number

    Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers, starting with the 0th triangular number, is

  7. Nonagonal number - Wikipedia

    en.wikipedia.org/wiki/Nonagonal_number

    A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided polygon). [1] However, unlike the triangular and square numbers, the patterns involved in the construction of nonagonal numbers are not rotationally symmetrical.

  8. Tetrahedral number - Wikipedia

    en.wikipedia.org/wiki/Tetrahedral_number

    Number of gifts of each type and number received each day and their relationship to figurate numbers. Te 12 = 364 is the total number of gifts "my true love sent to me" during the course of all 12 verses of the carol, "The Twelve Days of Christmas". [3] The cumulative total number of gifts after each verse is also Te n for verse n.

  9. Decagonal number - Wikipedia

    en.wikipedia.org/wiki/Decagonal_number

    In mathematics, a decagonal number is a figurate number that extends the concept of triangular and square numbers to the decagon (a ten-sided polygon). However, unlike the triangular and square numbers, the patterns involved in the construction of decagonal numbers are not rotationally symmetrical.