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#26 2013-04-03 02:19:35

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
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Re: Non Intersecting chords

I am still not getting you? Whats n?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#27 2013-04-03 02:22:33

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

I am still not getting you? Whats n?

He meant r. r is the number of chords.

I know it is difficult to understand that is why I am trying to come
up with another solution.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#28 2013-04-03 02:25:33

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
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Re: Non Intersecting chords

Okay

Last edited by Agnishom (2013-04-03 02:26:25)


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#29 2013-04-03 23:36:08

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

Hi;

Sorry, I am unable to improve on this solution as posted earlier.

where r is the number of chords.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#30 2013-04-04 00:03:26

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

But please, explain its derivation


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#31 2013-04-04 00:05:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

First, do you understand how the denominator was derived.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#32 2013-04-04 00:08:52

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

No, nothing at all


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#33 2013-04-04 00:13:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

Okay, I will make a drawing but you have posted another problem. Which do want first?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#34 2013-04-04 00:14:57

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

As you wish

I would prefer this one


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#35 2013-04-04 00:33:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

Let's start with 6 points that will determine 3 chords. WLOG we start with A and see that A can choose 5 points. Once it chooses B, then C can only choose 3 points. When C and D are joined then E can only choose 1 point.

View Image: 2013-04-04_052242.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#36 2013-04-04 00:34:52

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

Yes


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#37 2013-04-04 00:36:06

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

So for 6 points we 5 * 3 * 1 choices of chords.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#38 2013-04-04 00:39:13

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

Yes


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#39 2013-04-04 00:42:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

For 8 points (4 chords ) there are 7 * 5 * 3 * 1 choices.

For r points and r / 2 chords there will be

choices.

You might notice that we are describing the !! operator but we will leave that out for now. We have solved for the denominator.

Ready?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#40 2013-04-04 01:03:30

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

Yes!


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#41 2013-04-04 01:04:40

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

Okay, know what a bijection is?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#42 2013-04-04 01:07:53

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

No, I am googling 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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#43 2013-04-04 01:18:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

We will not need the Set theory definition. I will describe the idea very loosely as taking the set of one problem and changing it to another set with the same number of elements. But the new set is easier to count.

This is a very, very loose definition but it will suffice for our purposes with this problem.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#44 2013-04-04 01:39:08

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

It is pairing something with something. like you pair two points to make a segment


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#45 2013-04-04 01:44:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

There is a problem that already has been solved many times called the bracket matching problem.

Given pairs of parentheses consisting of  one left and one right how many legal expressions can we make:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#46 2013-04-04 01:46:55

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

For example?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#47 2013-04-04 01:50:13

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

2 parentheses () form one pair ()

4 parentheses (()) form two pair ()(), (())

6 parentheses ((())) for 5 pairs ()()(), ()(()), (())(), (()()), ((()))


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#48 2013-04-04 01:56:37

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

I see.

So the puzzle is two find out a 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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#49 2013-04-04 02:01:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,597

Re: Non Intersecting chords

No not yet. We know the formula, the numbers

1, 2, 5, 14, 42, 132, 429, 1430, 4862... are called Catalan numbers.

What we need is the observation that each parentheses () represents a chord. with the brackets being the endpoints.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#50 2013-04-04 02:04:22

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 14,296
Website

Re: Non Intersecting chords

They are Catalan numbers?!

I don't see how it helps if we compare them with chords


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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