Difference between revisions of "Talk:Twenty-four"
(Created page with "I would like to edit this page to add some additional interesting information about the number <math>24</math>. <math>24</math> is, in fact, the difference of squares in two...") |
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Also, the fact that <math>24 = 4!</math> is noteworthy, since for example <math>4!</math> is the order of <math>S_4</math>, the group of permutations of four objects or of orientation-preserving symmetries of a cube or an octahedron. | Also, the fact that <math>24 = 4!</math> is noteworthy, since for example <math>4!</math> is the order of <math>S_4</math>, the group of permutations of four objects or of orientation-preserving symmetries of a cube or an octahedron. | ||
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+ | Another interesting, if advanced, piece of information is that the definition of Ramanujan's tau function includes a conspicuous power of <math>24</math>. <math>\tau(n)</math> is the coefficient of the degree-<math>n</math> term of the power series <cmath>q \left( (1-q)(1-q^2)(1-q^3) \dots \right)^{24}.</cmath> Notably, <math>\tau</math> is multiplicative, that is, if <math>m</math> and <math>n</math> are relatively prime, then <math>\tau(m)\tau(n) = mn</math>. [[User:Orange quail 9|Orange quail 9]] ([[User talk:Orange quail 9|talk]]) 12:34, 18 May 2022 (EDT) |
Revision as of 12:34, 18 May 2022
I would like to edit this page to add some additional interesting information about the number .
is, in fact, the difference of squares in two ways:
. In fact, it is the common difference of the smallest nontrivial arithmetic progression among the perfect squares:
.
is not the sum of any two squares, however.
Also, the fact that is noteworthy, since for example
is the order of
, the group of permutations of four objects or of orientation-preserving symmetries of a cube or an octahedron.
Another interesting, if advanced, piece of information is that the definition of Ramanujan's tau function includes a conspicuous power of .
is the coefficient of the degree-
term of the power series
Notably,
is multiplicative, that is, if
and
are relatively prime, then
. Orange quail 9 (talk) 12:34, 18 May 2022 (EDT)