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27 (number) : ウィキペディア英語版
27 (number)

27 (twenty-seven) 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 (see tetration). There are exactly 27 straight lines on a smooth cubic surface, which give a basis of the fundamental representation of the E6 Lie algebra. 27 is also a decagonal number.
* In base 10, it is the first composite number not evenly divisible by any of its digits.
* It is the radix (base) of the septemvigesimal positional numeral system.
* 27 is the only positive integer that is 3 times the sum of its digits.
* In a prime reciprocal magic square of the multiples of 1/7, the magic constant is 27.
* In the Collatz conjecture (aka the "3''n'' + 1 conjecture") a starting value of 27 requires 112 steps to reach 1, many more than any lower number.
* The unique simple formally real Jordan algebra, the exceptional Jordan algebra of self-adjoint 3 by 3 matrices of quaternions, is 27-dimensional.〔V. G. Kac, "Classification of Simple Z-Graded Lie Superalgebras and Simple Jordan Superalgebras" ''Communications in Algebra'' 5 13 (1977): 1380〕
* In base 10, it is a Smith number and a Harshad number.
* It is the twenty-eighth (and twenty-ninth) digit in π. (3.141592653589793238462643383279...). ''If you start counting with 0 it is considered one of few (Self-Locating strings in pi ).''
* 27 contains the decimal digits 2 and 7, and is the result of adding together the integers from 2 to 7 (2+3+4+5+6+7=27)
* There are 27 sporadic groups, if the Tits group is included.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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