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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. The first four hexagonal numbers. The formula for the nth hexagonal number = = = (). The ...
Centered hexagonal numbers appearing in the Catan board game: 19 land tiles, 37 total tiles. In mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, [1] [2] is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice.
Polygonal numbers: These are numbers that can be represented as dots that are arranged in the shape of a regular polygon, including Triangular numbers, Square numbers, Pentagonal numbers, Hexagonal numbers, Heptagonal numbers, Octagonal numbers, Nonagonal numbers, Decagonal numbers, Hendecagonal numbers, and Dodecagonal numbers.
Figurate numbers were a concern of the Pythagorean worldview. It was well understood that some numbers could have many figurations, e.g. 36 is a both a square and a triangle and also various rectangles. The modern study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem.
Hexadecimal (also known as base-16 or simply hex) is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9 and "A"–"F" to represent values from ten to fifteen.
The nth pentagonal number p n is the number of distinct dots in a pattern of dots consisting of the outlines of regular pentagons with sides up to n dots, when the pentagons are overlaid so that they share one vertex. For instance, the third one is formed from outlines comprising 1, 5 and 10 dots, but the 1, and 3 of the 5, coincide with 3 of ...
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 ...
In mathematics, a heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The n -th heptagonal number is given by the formula H n = 5 n 2 − 3 n 2 {\displaystyle H_{n}={\frac {5n^{2}-3n}{2}}} .