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PhytoExtractum Shop: Maeng Da Thai Kratom Leaf Powder

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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 13 years, 2 days
Every number is the sum of four squares (check it out!).
    #9358025 - 12/03/08 01:11 PM (15 years, 2 months ago)

Formula: 0

This works all of the time and is known as Lagrange's four-square theorem. God has an awesome sense of humor.


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Edited by isaacein (12/03/08 01:13 PM)


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OfflinefreeDOOM
Stranger then you
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Registered: 07/28/08
Posts: 1,536
Loc: New York, USA
Last seen: 2 years, 1 month
Re: Every number is the sum of four squares (check it out!). [Re: isaacein]
    #9358092 - 12/03/08 01:18 PM (15 years, 2 months ago)

Aaaahhhhhh. . .


















Math  :wow:


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OfflineIrdamage
Autobot


Registered: 11/19/05
Posts: 1,491
Loc: Canada
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Re: Every number is the sum of four squares (check it out!). [Re: freeDOOM]
    #9358104 - 12/03/08 01:19 PM (15 years, 2 months ago)

Is correct sir. Reminds me for some reason of first learning to count in binary. Just because of the limitation of digits and having to include zero spacing into your counts.


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InvisibleFerris
PsychedelicJourneyman
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Folding@home Statistics
Registered: 03/12/06
Posts: 11,529
Re: Every number is the sum of four squares (check it out!). [Re: isaacein]
    #9358126 - 12/03/08 01:22 PM (15 years, 2 months ago)

Quote:

isaacein said:
Formula: 0

This works all of the time and is known as Lagrange's four-square theorem. God has an awesome sense of humor.




That doesn't seem all that impressive considering that one can use 1^2 more than once.


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OfflineTangerines
 User Gallery


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Registered: 04/17/05
Posts: 17,918
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Re: Every number is the sum of four squares (check it out!). [Re: Ferris]
    #9358141 - 12/03/08 01:24 PM (15 years, 2 months ago)

It's impressive. Try it with large numbers. The ones won't make much difference.


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Offlineimagine
Psychic
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Registered: 09/24/05
Posts: 758
Loc: CA
Last seen: 12 years, 3 months
Re: Every number is the sum of four squares (check it out!). [Re: Tangerines]
    #9358148 - 12/03/08 01:25 PM (15 years, 2 months ago)

There should be a math forum for all you....freaks? :eek:


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Offlineisaacein
exp(ix) = cosx + isinx


Registered: 05/21/08
Posts: 1,141
Last seen: 13 years, 2 days
Re: Every number is the sum of four squares (check it out!). [Re: Ferris]
    #9358360 - 12/03/08 01:51 PM (15 years, 2 months ago)

Quote:

Ferris said:
Quote:

isaacein said:
Formula: 0

This works all of the time and is known as Lagrange's four-square theorem. God has an awesome sense of humor.




That doesn't seem all that impressive considering that one can use 1^2 more than once.




Well three squares don't always suffice (and we know exactly when they do). Four squares is the minimum number of squares which works for all numbers.

Moreover, the number of ways in which a number can be written as the sum of four squares is quite large for most large numbers.

If n is odd, then the number of ways in which n can be written as the sum of four squares is 8 times the sum of the positive divisors of n;

if n is even, 24 times the sum of the positive odd divisors of n.

Note that here we consider different arrangements of the same squares as different ways.


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