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.
- 27 has an aliquot sum of 13 and is the first composite member of the 13-aliquot tree with the aliquot sequence (27,13,1,0). Twenty-seven is the aliquot sum of the two odd discrete semiprimes 69 and 133.
- 273 = 19,683 and 1+9+6+8+3=27.
- 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 "3n + 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.
- 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.
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