Sum of first odd numbers

[José Carlos Santos]

Hi all,

Consider the statement: "The sum of the first _n_ odd numbers is n^2".
I saw it ascribed to Pythagoras, but I very much doubt that this is
true. Does anyone here know where did this statement appeared for the
first time?

Best regards,

Jose Carlos Santos

[José Carlos Santos]

On 03-01-2011 12:37, José Carlos Santos wrote:

> Consider the statement: "The sum of the first _n_ odd numbers is n^2".
> I saw it ascribed to Pythagoras, but I very much doubt that this is
> true. Does anyone here know where did this statement appeared for the
> first time?

Forget it. The statement was, at least, _known_ by the Pythagoreans. I
got this information from Sir Thomas Heath's A History of Greek
Mathematics.

[Han de Bruijn]

1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25

In general:
1 + 3 + 5 + .. + 2*n-1 = s
2*n-1 + 2*n-3 + 2*n-5 + .. + 1 = s

2*s = 2*n*n ==> s = n^2 . Thus true, not?

Han de Bruijn

[Jesse F. Hughes]

He was asking whether it was true that the Pythagoreans proved it. I'm
sure he agrees that it is a true mathematical claim.

(In any case, he later discovered an authority that the Pythagoreans
knew the theorem.)

--
Jesse F. Hughes
"And hey, if you're moping and miserable because mathematics tests you,
then maybe, if you think you're a mathematician, you might want to try
a different field." -- Another James S. Harris self-diagnosis.