Does anyone know if there''s currently someone trying to solve the Basel Problem for the third power? (ex: the sum of the reciprocals of all cubic numbers: 1+1/8+1/27+1/64...) The Basel Problem is one of the more famous problems Euler solved - is anyone trying to solve the cubic version?

Heh, I just wrote a little program and got:
1.202056903150316103

Firebird Entertainment

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Heh, I just wrote a little program and got:
1.202056903150316103

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My God!!! how did you do it???+
you like solved a math problem thats like a gazillion years old!!!111 skillzz

[edited by - uncutno on February 17, 2003 6:28:41 PM]

yeah AP, calm down, he only got an approximation.

integer division makes the program print 1 as an answer

but as it''s obviously pseudo-code i''ll forgive you!

I love my Calculus book. Regarding the Basel Problem:

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The exact sum of this series was found by the Swiss mathematician Leonhard Euler (1707-1783) to be PI²/6, but the proof of this fact is beyond the scope of this book.

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Well thank you, Calculus book, you suck. I hate you

As a matter if fact, Euler solved the Basel problem for all even powers. Squared, to-the-fourth, to-the-sixth, etc. Well technically, he found the method for solving them, but you get the point

[edited by - Zipster on February 17, 2003 7:13:36 PM]

Yeah, Euler''s answer to the Basel Problem for even powers is actually pretty simple to anyone who''s familiar with the series expansion of sin(x). I found the proof originally in the book "Journey Through Genius: The Great Theorems of Mathematics" by William Dunham. It''s actually a pretty good book and most of the chapters can be read without a calculus background. I recommend it to anyone who''s interested in this kind of thing.

Anyway-I was just wondering because it''s an unsolved problem that has been around for centuries, sort of like Fermat''s Last Theorem was before it was proved. If someone found the answer they would make the news if not become famous-especially since Euler couldn''t solve it. Plus, you can''t use a computer to solve it-it''s purely human logic!

If you have done research, than you know the connection between this and the Riemann Zeta function. Here is a link at mathworld:
http://mathworld.wolfram.com/RiemannZetaFunction.html

If you scroll down, you see that Zeta(3) is not given in an exact form, so my guess is that no, it hasn''t been solved exactly yet. Maybe this would be an interesting problem to solve. Read up on it at mathworld and see what you find.

Brendan