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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
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34661

"What is the square root of 2? 1.4141592653589793238" Seriously, I thought it was that. Too round?

3.141592653589793238...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

80^2 + 102^2 + 134^2 = 34760

**In mathematics, you don't understand things. You just get used to them.**

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,895
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34869

"What is the square root of 2? 1.4141592653589793238" Seriously, I thought it was that. Too round?

3.141592653589793238...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

92^2 + 98^2 + 130^2 = 34968

**In mathematics, you don't understand things. You just get used to them.**

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,895
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35067

"What is the square root of 2? 1.4141592653589793238" Seriously, I thought it was that. Too round?

3.141592653589793238...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

94^2 + 101^2 + 127^2 = 35166

**In mathematics, you don't understand things. You just get used to them.**

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,895
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35265

3.141592653589793238...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

92^2 + 100^2 + 130^2 = 35364

**In mathematics, you don't understand things. You just get used to them.**

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,895
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35463

3.141592653589793238...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

92^2 + 97^2 + 133^2 = 35562

**In mathematics, you don't understand things. You just get used to them.**

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35661

How are you getting those expansions?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

By a program that does them for me.

52^2 + 116^2 + 140^2 = 35760

**In mathematics, you don't understand things. You just get used to them.**

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35859

Mathematica?

Do you have a proof that this can be done as for all numbers?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

Mathematica yes.

Sum of squares? Yes there is a proof.

74^2 + 91^2 + 149^2 = 35958

**In mathematics, you don't understand things. You just get used to them.**

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36057

Will you please post it?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

91^2 + 93^2 + 95^2 + 101^2 = 36156

```
PowersRepresentations[36156, 4, 2]//Last
yields:{91,93,95,101}
```

**In mathematics, you don't understand things. You just get used to them.**

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36255

But ..... The proof?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

The proof? What proof are we talking about?

2 x 107^2 + 116^2 = 36354

**In mathematics, you don't understand things. You just get used to them.**

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36453

bobbym wrote:

Sum of squares? Yes there is a proof

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

I think it was Legendre who proved that 4 squares were enough for any number. The proof requires quarternions.

94^2 + 104^2 + 130^2 = 36552

**In mathematics, you don't understand things. You just get used to them.**

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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,895
- Website

36651

3.141592653589793238...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

109^2 + 110^2 + 113^2 = 36750

**In mathematics, you don't understand things. You just get used to them.**

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36849

Is it like a complex hyperspace where both the axes are complex?

If ij =k then how can ji = -k, that makes sense?

*Last edited by Agnishom (2013-04-07 14:16:17)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,663

Hi;

That I do not know because I know nothing about complex hyperspace.

92^2 + 110^2 + 128^2 = 36948

**In mathematics, you don't understand things. You just get used to them.**

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37047

What about the proof, then?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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