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Encyclopedia > Centered hexagonal number
It has been suggested that this article or section be merged into Centered polygonal number. (Discuss)

A centered hexagonal number, or hex number, 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. Wikipedia does not have an article with this exact name. ... The centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers with a constant number of sides. ... The centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers with a constant number of sides. ... A figurate number is a number that can be represented as a regular and discrete geometric pattern (e. ... A regular hexagon. ... Triangular tiling. ...

1 7 19 37
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The nth centered hexagonal number is given by the formula Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links GrayDotX.svg Summary Light gray circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ... Image File history File links RedDotX.svg‎ Red circle. ...

1+3n(n-1).,

Expressing the formula as

1+6left({1over 2}n(n-1)right)

shows that the centered hexagonal number for n is 1 more than 6 times the (nāˆ’1)th triangular number. A triangular number (so called because it can be arranged into a triangle) is the sum of the n natural numbers from 1 to n. ...


The first few centered hexagonal numbers are

1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919

In base 10 one can notice that the hexagonal numbers' ones' digits follow the pattern 1-7-9-7-1. Look up one in Wiktionary, the free dictionary. ... Seven Days of Creation - 1765 book, title page 7 (seven) is the natural number following 6 and preceding 8. ... 19 (nineteen) is the natural number following 18 and preceding 20. ... 37 (thirty-seven) is the natural number following 36 and preceding 38. ... 61 (sixty-one) is the natural number following 60 and preceding 62. ... 91 (ninety-one) is the natural number following 90 and preceding 92. ... 127 is the natural number following 126 and preceding 128. ... 169 is the natural number following one hundred sixty-eight and preceding one hundred seventy. ...


Centered hexagonal numbers have practical applications in materials logistics management, for example, in packing round items into larger round containers, such as Vienna sausages into round cans. Packing problems are one area where mathematics meets puzzles (recreational mathematics). ... Opened can of Vienna sausage Vienna sausage is a variety of canned sausage. ...


The sum of the first n centered hexagonal numbers happens to be n3. That is, centered hexagonal pyramidal numbers and cubes are the same numbers, but they represent different shapes. Viewed from the opposite perspective, centered hexagonal numbers are differences of two consecutive cubes, so that the centered hexagonal numbers are the gnomon of the cubes. In particular, prime centered hexagonal numbers are cuban primes. In arithmetic and algebra, the cube of a number n is its third power — the result of multiplying it by itself two times: n3 = n × n × n. ... A figurate number is a number that can be represented as a regular and discrete geometric pattern (e. ... In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. ... A cuban prime is a prime number that is a solution to one of two different specific equations involving third powers of x and y. ...


The difference between (2n)2 and the nth centered hexagonal number is a number of the form n2 + 3n āˆ’ 1, while the difference between (2n āˆ’ 1)2 and the nth centered hexagonal number is a pronic number. A pronic number, or oblong number or heteromecic number, is a number which is the product of two consecutive nonnegative integers, that is, n(n + 1). ...


See also


  Results from FactBites:
 
Centered hexagonal number (334 words)
A centered hexagonal number, or hex number is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot equidistantly.
To find centered hexagonal numbers besides 1 that are also triangular numbers or squares, it is necessary to solve Diophantine equations.
Viewed from the opposite perspective, centered hexagonal numbers are differences of two consecutive cubes, so that the centered hexagonal numbers are the gnomon of the cubes.
  More results at FactBites »


 

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