81 (eighty-one) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 80and preceding 82.

In mathematics

81 is: * the

square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...

of 9 and the second fourth-power of a prime; 3⁴. * with an

aliquot sum In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself. That is, s(n)=\sum_ d \, . It can be used to characterize the prime numbers, perfect numbers, sociabl ...

of 40; within an

aliquot sequence In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0. Def ...

of three composite numbers (81, 40, 50, 43, 1,0) to the Prime in the 43-aliquot tree. * a perfect totient number like all powers of three. * a heptagonal number. * an icosioctagonal number. * a

centered octagonal number A centered octagonal number is a centered number, centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers.. The centered octagonal numbers are th ...

. * a tribonacci number. * an open meandric number. * the ninth member of the Mian-Chowla sequence. * a

palindromic number A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis. The term ''palin ...

in bases 8 (121₈) and 26 (33₂₆). * a

Harshad number In mathematics, a harshad number (or Niven number) in a given radix, number base is an integer that is divisible by the digit sum, sum of its digits when written in that base. Harshad numbers in base are also known as -harshad (or -Niven) numbers ...

in bases 2, 3, 4, 7, 9, 10 and 13. * one of three non-trivial numbers (the other two are

1458 Year 1458 ( MCDLVIII) was a common year starting on Sunday of the Julian calendar, the 1458th year of the Common Era (CE) and Anno Domini (AD) designations, the 458th year of the 2nd millennium, the 58th year of the 15th century, and the 9th year ...

and

1729 Events January–March * January 8 – Frederick, the eldest son of King George II of Great Britain is made Prince of Wales at the age of 21, a few months after he comes to Britain for the first time after growing up in Hanover ...

) which, when its digits (in decimal) are added together, produces a sum which, when multiplied by its reversed self, yields the original number: : 8 + 1 = 9 : 9 × 9 = 81 (although this case is somewhat degenerate, as the sum has only a single digit). The inverse of 81 is 0. recurring, missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base ''b'', :

\frac = 0.\overline,

omitting only the digit ''b''−2.

In other fields

Eighty-one is also: *The number of chapters in the

Tao Te Ching The ''Tao Te Ching'' () or ''Laozi'' is a Chinese classic text and foundational work of Taoism traditionally credited to the sage Laozi, though the text's authorship and date of composition and compilation are debated. The oldest excavated por ...

, the foundational text of

Taoism Taoism or Daoism (, ) is a diverse philosophical and religious tradition indigenous to China, emphasizing harmony with the Tao ( zh, p=dào, w=tao4). With a range of meaning in Chinese philosophy, translations of Tao include 'way', 'road', ' ...

. *The symbolic number of the

Hells Angels The Hells Angels Motorcycle Club (HAMC) is an international outlaw motorcycle club founded in California whose members typically ride Harley-Davidson motorcycles. In the United States and Canada, the Hells Angels are incorporated as the Hells ...

Motorcycle Club. 'H' and 'A' are the 8th and 1st letter of the alphabet, respectively.. *81 (八一) is referenced in flags and symbols of the

People's Liberation Army The People's Liberation Army (PLA) is the military of the Chinese Communist Party (CCP) and the People's Republic of China (PRC). It consists of four Military branch, services—People's Liberation Army Ground Force, Ground Force, People's ...

as it was founded on August 1 (8/1). *The career high of points scored in a single game by

Kobe Bryant Kobe Bean Bryant ( ; August 23, 1978 – January 26, 2020) was an American professional basketball player. A shooting guard, he List of NBA players who have spent their entire career with one franchise, spent his entire 20-year career with t ...

on January 22, 2006 against the

Toronto Raptors The Toronto Raptors are a Canadian professional basketball team based in Toronto. The Raptors compete in the National Basketball Association (NBA) as a member of the Atlantic Division (NBA), Atlantic Division of the Eastern Conference (NBA), E ...

. 81 is the second most points scored in an American professional basketball game, behind Wilt Chamberlain's 100. * The international calling code for

Japan Japan is an island country in East Asia. Located in the Pacific Ocean off the northeast coast of the Asia, Asian mainland, it is bordered on the west by the Sea of Japan and extends from the Sea of Okhotsk in the north to the East China Sea ...

References

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