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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
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How does Randall do these?

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'
I'm not crazy, my mother had me tested.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: How does Randall do these?

'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'
I'm not crazy, my mother had me tested.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

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'
I'm not crazy, my mother had me tested.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

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'
I'm not crazy, my mother had me tested.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

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'
I'm not crazy, my mother had me tested.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

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'
I'm not crazy, my mother had me tested.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

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'
I'm not crazy, my mother had me tested.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

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'
I'm not crazy, my mother had me tested.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
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'
I'm not crazy, my mother had me tested.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
Website

Re: How does Randall do these?

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'
I'm not crazy, my mother had me tested.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

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

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,838
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'
I'm not crazy, my mother had me tested.

Offline