Mathematical fact about sums of cubes (Kelsey)

[Kelsey]

Sorry I didn't post a fact earlier. I don't know how well known this
is, but I thought it was cool.

If you sum the first N perfect cubes, the result is the sum of the
first N integers, squared, or

1^3 + 2^3 + ... + N^3 = (1+2+...+N)^2.

[Abe Rabin]

Oh, this reminds me. For people who have taken calculus, you know how there is integration by parts? There is also something similar called summation by parts(which I don't think is surprising because integration is summation) which is here http://en.wikipedia.org/wiki/Summation_by_parts

Sorry for that Kelsey, it just reminded me of something cool.

[James Crook]

Kelsey, that is so cool!

I can see how to prove it, but not a nice geometrically way to make it evident why it is so.

Abe,

Can you talk a little more about summation by parts, why Kelsey's fact reminded you of it?

This is really really useful, because we want to look not only at how to solve problems, but how we make connections.  

--James

[Shri R Ganeshram]

As far as my earlier statement concerning elementary row operations; I messed up. It's actually just the first elementary row operation which is multiplying one row by a constant c and adding it to another row. I didn't realize that switching rows and multiplying a row by a constant c were considered elementary row operations as well.
:)
-Shri
________________________________________
From: l2lea...@googlegroups.com [l2lea...@googlegroups.com] On Behalf Of James Crook [james....@gmail.com]
Sent: Friday, June 17, 2011 3:04 PM
To: l2lea...@googlegroups.com
Subject: Re: Mathematical fact about sums of cubes (Kelsey)

Kelsey, that is so cool!

I can see how to prove it, but not a nice geometrically way to make it evident why it is so.

Abe,

Can you talk a little more about summation by parts, why Kelsey's fact reminded you of it?
This is really really useful, because we want to look not only at how to solve problems, but how we make connections.

--James

On 17 June 2011 19:15, Abe Rabin <honest....@gmail.com<mailto:honest....@gmail.com>> wrote:
Oh, this reminds me. For people who have taken calculus, you know how there is integration by parts? There is also something similar called summation by parts(which I don't think is surprising because integration is summation) which is here http://en.wikipedia.org/wiki/Summation_by_parts

Sorry for that Kelsey, it just reminded me of something cool.