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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?

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

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Link please?

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

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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'

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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.

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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?

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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)*

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What is PSLQ?

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

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Can you teach me that?

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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.

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Thanks. I will look for it.

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**anonimnystefy****Real Member**- From: The Foundation
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No problemo.

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**bobbym****Administrator**- From: Bumpkinland
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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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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Can you teach me?

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**bobbym****Administrator**- From: Bumpkinland
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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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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What is DZ?

How does M do them?

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**bobbym****Administrator**- From: Bumpkinland
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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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
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DZ is Doron Zeilberger.

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

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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.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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

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**bobbym****Administrator**- From: Bumpkinland
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Me too but it does not work as well.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Can you tell me how randall does all that?

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