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#1 2014-11-16 12:36:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

How to do it.

This sum appears in another thread.

There it is solved well by bob bundy. The question always remains how would an EM guy do it? Supposing he were armed only with his trusty CAS. Supposing he needs an answer to save the world?

He has these options:

1) Cry for his Mommy.

2) Just let the world explode.

3) Pull out his hair and violently bash his head into the ground cursing all creation for his ill luck.

4) Use EM.

Now, clearly options 1,2 and 3 are the correct ones but we will ignore them and try 4.

We follow Agnishom's analysis.

If we vary k = 1 ... 13 in

we get:

We try the best ability a human brain has other then savageness, its ability to play STP. Not too difficult to see that k =2,4,6... are all rational and easy but 1947 is odd so we isolate the k =1,3,5... terms and have a look.

Hmmm, we notice that 1,3,5 and 7 and make an ansatz that those ones in the numerators between them are the results of some cancellations in the denominator.

We hopefully guess that the numerators are 1,2,3,4,5,6,7..., the simplest possible answer. Actually, we have some justification for this. We are either lucky ( which happens often ) or God loves EM because we immediately find:

Now B matches A term for term so we have the ansatz that

this can be simplified to the very pleasing

So,


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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#2 2014-11-16 19:41:10

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
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Re: How to do it.

Ah! smile

That is how I did it when they asked me to do in the test.

Last edited by Agnishom (2014-11-16 19:59:26)


'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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#3 2014-11-16 21:04:02

bob bundy
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Registered: 2010-06-20
Posts: 7,763

Re: How to do it.

EM is an essential part of mathematics but the following example shows why you should beware.

Hypthesis:  the formula

is a prime number generator.

Investigate by trying n = 1, 2, 3 etc

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2014-11-17 00:31:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

Hi;

All the following is my own personal opinion on how EM should be done. For the exact meaning as understood by smarter people than I, I can direct you to the books and videos of Doron Zeilberger and others for all the points that I do not understand well enough to explain.


An EM would never be interested in making such a sweeping statement as that polynomial generates all the primes based on a mere 40 examples and would have quickly found the first counterexample. They work in limited ranges where of course they already have the answered bounded as I did before I started.

There is a well know sum that generates a billion correct digits of pi and fails afterwards. One of the purposes in EM is to find conjectures and counterexamples for real life problems. School problems and contest problems are not the same as real life problems. The additional information that there is a solution makes them much easier. A technique we call, Attacking the problem itself.


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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#5 2014-11-17 00:38:23

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

ade27c3.jpg


'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 2014-11-17 00:39:56

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

Hmmm, you broke the first rule of presenting any bit of EM.


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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#7 2014-11-17 00:41:40

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

What first rule?


'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 2014-11-17 00:47:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

All presented data must be in a form where the other can just copy and paste. Pictures are not good because too many mistakes are made translating them into text or code. Accuracy, accuracy and accuracy - Joseph Pulitzer.


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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#9 2014-11-17 00:48:25

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

Let me blame Michael Mendrin for 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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#10 2014-11-17 00:51:05

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

Is he an EM guy?


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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#11 2014-11-17 00:52:12

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

I do not know.


'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 2014-11-17 00:55:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

Is that his work or yours?


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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#13 2014-11-17 00:56:55

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

His work. Probably he didn't provide the code in text because he did not want us to get hold of 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 2014-11-17 01:00:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

That is conjecture, I am unable and unwilling to examine his motives. The use of m does not make an EM as I understand it. It is a mindset.

What we can examine are your motives because you are right here to explain them. What is your point?


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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#15 2014-11-17 01:02:15

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

I do not have any.


'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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#16 2014-11-17 01:05:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

What were your reasons to post #5? You must have been trying to tell me something. What was it?


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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#17 2014-11-17 01:06:38

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

I wanted to post some crazy looking prime generating formula


'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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#18 2014-11-17 01:12:18

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

There are formulas that generate lots of primes. One that books say generates all of them.


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.

Offline

#19 2014-11-17 01:39:40

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

Yes, they are there


'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

#20 2014-11-17 01:46:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

What did you think of the EM method for this problem?


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.

Offline

#21 2014-11-17 01:48:10

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

Look at post 2


'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

#22 2014-11-17 01:50:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

Yes, I saw that. But did you like the idea?


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 2014-11-17 01:52:24

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

Yes, it is very good.


'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

#24 2014-11-17 02:00:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 107,765

Re: How to do it.

Supposing you used the EM method you would get the answer in a different form. How would you go about solving your problem then?


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.

Offline

#25 2014-11-17 02:06:58

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,577
Website

Re: How to do it.

another form? What could be wrong with 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

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