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Randall wrote:

Also, I hear the 4th root of (9^2 + 19^2/22) is pi.

Verification follows

```
In[1]:= N[E^\[Pi] - \[Pi]]
Out[1]= 19.9991
In[3]:= N[Solve[x^4 == 9^2 + 19^2/22]]
Out[3]= {{x -> -3.14159}, {x -> 0. - 3.14159 I}, {x ->
0. + 3.14159 I}, {x -> 3.14159}}
```

My question is: How did Randall (or Cueball) know that?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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In one of the comics there is a whole table of those.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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Link please?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

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

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**anonimnystefy****Real Member**- From: The Foundation
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Comic 1047.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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Do you understand tip 2 in the alt text?

Can we explain how these estimations were done?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'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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**anonimnystefy****Real Member**- From: The Foundation
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Well, I really would get scared if I got pi-th root of something as an answer to anything.

And, as to how he finds those, probably just playing with numbers. You try different stuff, and sometimes the number comes out to be close to some known constant.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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Suppose I have some strange looking number and I want it as an approximation in terms of pi and e. How do I do that?

'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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**anonimnystefy****Real Member**- From: The Foundation
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There is no algorithm. You just try. You might have a bit luck with PLSQ, but with a bit of luck.

*Last edited by anonimnystefy (2014-04-22 14:11:04)*

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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What is PSLQ?

'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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**anonimnystefy****Real Member**- From: The Foundation
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It's and algorithm for finding integer relations.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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Can you teach me that?

'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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**anonimnystefy****Real Member**- From: The Foundation
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There is a thread (I think by me) called "PLSQ and LLL". You should be able to find it.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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Thanks. I will look for 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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**anonimnystefy****Real Member**- From: The Foundation
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No problemo.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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There is a definite algorithm for it. Mine uses a lattice reduce. It is easily programmable in M.

Do you know it has been called the most important algorithm of the 20th century and it is not taught in school.

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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Can you teach me?

'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
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I can instruct M to do them. Have you not read DZ?

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

**Online**

What is DZ?

How does M do them?

'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
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It is almost entirely done using the lattice reduce command.

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

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

**Online**

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,796

DZ is Doron Zeilberger.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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I have not read DZ. Teach me the Lattice if that is the way to go.

'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
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There is nothing really to teach that has not been said in the 2 threads devoted to this but I have the code.

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I'd rather have Lettuce than Lattice.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 91,574

Me too but it does not work as well.

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

**Online**

Can you tell me how randall does all that?

'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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