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#1 2013-03-30 22:40:52

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
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Non Intersecting chords

<<Problem Attached>>

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

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#2 2013-03-31 03:54:12

stapel
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Registered: 2006-07-22
Posts: 15

Re: Non Intersecting chords

For other users: The text of the tiny image is as follows:


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#3 2013-03-31 05:01:57

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
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Re: Non Intersecting chords

Thank You -_-"


'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 2013-04-02 00:00:58

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

Hi Agnishom;

I am getting 17.


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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#5 2013-04-02 04:41:40

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
Website

Re: Non Intersecting chords

I do not know the answer.

But please do tell about how you did this


'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 2013-04-02 04:45:44

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

Hi;

The probability is 2 / 15 , so a + b = 17.


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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#7 2013-04-02 04:59:36

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
Website

Re: Non Intersecting chords

Yes, I agree

How did you know that it is 2/15?


'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 2013-04-02 05:11:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

Hi;

where r is the number of chords. Plug in 4 and you get 2 / 15.


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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#9 2013-04-02 08:13:20

zetafunc.
Guest

Re: Non Intersecting chords

Where did you get that formula from?

#10 2013-04-02 08:15:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

Hi;

It was got from some combinatorial reasoning and some experimental mathematics. I am also working on another method.


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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#11 2013-04-02 08:26:37

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
Website

Re: Non Intersecting chords

So, what is the reasoning behind 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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#12 2013-04-02 08:31:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

As you know any probability can expressed as success / ( success + failure).

That allows us to break the problem down into 2 sub problems.


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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#13 2013-04-02 08:52:48

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Non Intersecting chords

Hm, how'd you get that formula?


“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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#14 2013-04-02 08:57:07

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

Post #12 outlines the method I used. Did you understand what I meant?


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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#15 2013-04-02 08:59:07

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Non Intersecting chords

Yes. But, I still do not know how you got that...


“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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#16 2013-04-02 09:05:04

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
Website

Re: Non Intersecting chords

Maybe you are using something like a case study? Or a recurrence relation?


'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 2013-04-02 09:06:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

The job is done if it is correct in two steps. The denominator is done first.


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 2013-04-02 13:21:11

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Non Intersecting chords

How'd you get the denominator?


“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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#19 2013-04-02 14:27:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

If you call the first point A there are n-1 lines that can drawn from that point. From the second point there are n-3 lines from the third point there are n-5 lines etc.


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

#20 2013-04-02 14:36:01

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,657

Re: Non Intersecting chords

How does that give you (n+1)! ?


“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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#21 2013-04-02 14:39:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

There are cancellations with the the numerator.

The numerator is the world famous Catalan Numbers!


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

#22 2013-04-02 16:36:06

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
Website

Re: Non Intersecting chords

I really didn't understand


'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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#23 2013-04-02 20:12:33

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

I am working on something simpler than the first idea. It should be clearer.


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

#24 2013-04-03 01:40:25

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 18,872
Website

Re: Non Intersecting chords

But I like the Idea, please make it clearer


'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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#25 2013-04-03 02:13:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,615

Re: Non Intersecting chords

The denominators are easy, the numerators are the Catalan numbers. The author of this idea noticed that the solution is the same as the bracket matching problem. So, I used that.


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

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