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#1 2014-04-22 13:16:09

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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How does Randall do these?

e_to_the_pi_minus_pi.png

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

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#2 2014-04-22 13:23:52

anonimnystefy
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Registered: 2011-05-23
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Re: How does Randall do these?

In one of the comics there is a whole table of those.


“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

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#3 2014-04-22 13:36:43

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: How does Randall do these?

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

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#4 2014-04-22 13:41:20

anonimnystefy
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Re: How does Randall do these?

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

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#5 2014-04-22 13:46:59

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: How does Randall do these?

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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#6 2014-04-22 13:51:07

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: How does Randall do these?

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

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#7 2014-04-22 13:57:29

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: How does Randall do these?

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?


'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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#8 2014-04-22 13:59:48

anonimnystefy
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From: The Foundation
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Posts: 15,673

Re: How does Randall do these?

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)


“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

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#9 2014-04-22 14:03:03

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: How does Randall do these?

What is PSLQ?


'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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#10 2014-04-22 14:06:22

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: How does Randall do these?

It's and algorithm for finding integer relations.


“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

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#11 2014-04-22 14:08:26

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: How does Randall do these?

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

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#12 2014-04-22 14:10:39

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: How does Randall do these?

There is a thread (I think by me) called "PLSQ and LLL". You should be able to find it.


“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

Online

#13 2014-04-22 14:15:14

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
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Re: How does Randall do these?

Thanks. I will look for it.


'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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#14 2014-04-22 14:16:41

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: How does Randall do these?

No problemo.


“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

Online

#15 2014-04-22 19:55:51

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: How does Randall do these?

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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#16 2014-04-22 20:36:10

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
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Re: How does Randall do these?

Can you teach me?


'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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#17 2014-04-22 20:43:07

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: How does Randall do these?

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.

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#18 2014-04-22 23:36:09

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: How does Randall do these?

What is DZ?

How does M do them?


'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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#19 2014-04-22 23:37:14

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: How does Randall do these?

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.

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#20 2014-04-22 23:37:27

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: How does Randall do these?

DZ is Doron Zeilberger.


“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

Online

#21 2014-04-22 23:40:54

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: How does Randall do these?

okaytemplate.PNG

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


'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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#22 2014-04-22 23:42:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: How does Randall do these?

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.

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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#23 2014-04-22 23:42:22

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: How does Randall do these?

I'd rather have Lettuce than Lattice.


“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

Online

#24 2014-04-22 23:42:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,791

Re: How does Randall do these?

Me too but it does not work as well.


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.

Offline

#25 2014-04-22 23:45:26

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,897
Website

Re: How does Randall do these?

Can you tell me how randall does all 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'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

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