Happy New Year 2008! CORREC TION!
Henry Gould
gould at math.wvu.edu
Tue Jan 1 05:42:01 CET 2008
Jonathan Post wrote:
> Around this time of the year, for many many years, my father would ask
> me for a numerical or numerological fact about the coming year.
>
> So, channeling my late father, I do so now.
>
> 2008 = 2^3 × 251
>
> 2^3 is 2 cubed.
>
> 251 is the smallest number that can be written as the sum of 3
> positive cubes in 2 ways. Specifically (he said, 4-banger calculator
> in hand):
> 251 = 5^3 + 5^3 + 1^3 = 125 + 125 + 1
> 251 = 6^3 + 3^3 + 2^3 = 216 + 27 + 8
>
> And, rather surprisingly, 2008 also can be written as the sum of 3
> positive cubes in 2 ways.
>
> 2008 = 10^3 + 10^3 + 2^3 = 1000 + 1000 + 8
> 2008 = 12^3 + 6^3 + 4^3 = 1728 + 216 + 64
>
> The previous time this was true was in 1945, a year when my father was
> engaged in World War II, a very important year of his life.
>
> 1945 = 12^3 + 6^3 + 1^3 = 1728 + 216 + 1
> 1945 = 10^3 + 9^3 + 6^3 = 1000 + 729 + 216
>
$$$$ $$$$ Of course this has a connection with Hardy and Ramanujan;
because your 1945 is 216 more than the Taxi number 1729 that Hardy
thought was uninteresting, but which Ramanujan immediately noticed was
the smallest number that is the sum of two cubes in two different ways,
i.e. 1729 = 1728 + 1 = 1000 + 729.
From the Hardy-Ramanujan we can of course find other fascinating
results. - - - Henry Gould
$$$$
> Isaac Asimov wrote that this year was a singularity in History, as I'd
> discussed with my dad, with Hiroshima making a total break between
> past and future, in a novel and significant way.
>
> So 2008 will be a curiously cubical year.
>
> Which means what? That I should hit the Craps table at Vegas casinos?
> That I shall have a job in a cubicle? That World War will break out?
>
> Be that as it may, as Samuel Herbert Post used to say,
>
> Happy New Year
>
> -- Jonathan Vos Post
>
> References:
>
> A025396 Numbers that are the sum of 3 positive cubes in exactly 2 ways.
>
>
>
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