Decagonal number
Encyclopedia
A decagonal number is a figurate number
that represents a decagon
. The n-th decagonal number is given by the formula
The first few decagonal numbers are:
The n-th decagonal number can also be calculated by adding the square of n to thrice the (n—1)-th pronic number
or, to put it algebraically, as
Figurate number
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes and different dimensions...
that represents a decagon
Decagon
In geometry, a decagon is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and each internal angle equal to 144°...
. The n-th decagonal number is given by the formula
The first few decagonal numbers are:
- 00 (number)0 is both a numberand the numerical digit used to represent that number in numerals.It fulfills a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures. As a digit, 0 is used as a placeholder in place value systems...
, 1, 1010 (number)10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...
, 2727 (number)27 is the natural number following 26 and preceding 28.- In mathematics :Twenty-seven is a perfect cube, being 33 = 3 × 3 × 3. 27 is also 23 . There are exactly 27 straight lines on a smooth cubic surface, which give a basis of the fundamental representation of the E6 Lie algebra...
, 5252 (number)52 is the natural number following 51 and preceding 53.-In mathematics:Fifty-two is the 6th Bell number and a decagonal number...
, 8585 (number)85 is the natural number following 84 and preceding 86.-In mathematics:85 is an octahedral number, a centered triangular number, a centered square number, a decagonal number, and a Smith number....
, 126126 (number)126 is the natural number following 125 and preceding 127.-In mathematics:One hundred [and] twenty-six is a pentagonal pyramidal number, and a decagonal number as well as a pentatope number....
, 175175 (number)175 is the natural number following 174 and preceding 176.-In mathematics:* 175 is an odd number* 175 is a composite number* 175 is a decagonal number, a figurate number that represents a decagon* 175 is a deficient number, as 73 is less than 175...
, 232, 297, 370, 451, 540, 637, 742, 855, 976, 1105, 1242, 1387, 1540, 1701, 1870, 2047, 2232, 2425, 2626, 2835, 3052, 3277, 3510, 3751, 40004000 (number)4000 is the natural number following 3999 and preceding 4001. It is a decagonal number.- Selected numbers in the range 4001–4999 :* 4005 – triangular number* 4007 – safe prime...
, 4257, 4522, 4795, 5076, 5365, 5662, 5967, 6280, 6601, 6930, 7267, 7612, 7965, 8326
The n-th decagonal number can also be calculated by adding the square of n to thrice the (n—1)-th pronic number
Pronic number
A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n . The n-th pronic number is twice the n-th triangular number and n more than the n-th square number...
or, to put it algebraically, as
Properties
- Decagonal numbers consistently alternate parity.