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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.
This is the minimum number of characters needed to encode a 32 bit number into 5 printable characters in a process similar to MIME-64 encoding, since 85 5 is only slightly bigger than 2 32. Such method is 6.7% more efficient than MIME-64 which encodes a 24 bit number into 4 printable characters. 89
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.
The number x is pentagonal if and only if n is a natural number. In that case x is the nth pentagonal number. For generalized pentagonal numbers, it is sufficient to just check if 24x + 1 is a perfect square. For non-generalized pentagonal numbers, in addition to the perfect square test, it is also required to check if
A computer search for pentagonal square triangular numbers has yielded only the trivial value of 1, though a proof that there are no other such numbers has yet to be found. [5] The number 1225 is hecatonicositetragonal (s = 124), hexacontagonal (s = 60), icosienneagonal (s = 29), hexagonal, square, and triangular.
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.
Alternating triangular numbers (1, 6, 15, 28, ...) are also hexagonal numbers. Every even perfect number is triangular (as well as hexagonal), given by the formula = (+) = where M p is a Mersenne prime. No odd perfect numbers are known; hence, all known perfect numbers are triangular.