27 (number) - in Mathematics

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.