Math Is Fun Forum
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#26 2013-04-03 02:19:35
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'
I'm not crazy, my mother had me tested.
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#27 2013-04-03 02:22:33
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#28 2013-04-03 02:25:33
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'
I'm not crazy, my mother had me tested.
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#29 2013-04-03 23:36:08
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#30 2013-04-04 00:03:26
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'
I'm not crazy, my mother had me tested.
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#31 2013-04-04 00:05:42
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#32 2013-04-04 00:08:52
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'
I'm not crazy, my mother had me tested.
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#33 2013-04-04 00:13:28
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#34 2013-04-04 00:14:57
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'
I'm not crazy, my mother had me tested.
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#35 2013-04-04 00:33:40
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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
#36 2013-04-04 00:34:52
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'
I'm not crazy, my mother had me tested.
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#37 2013-04-04 00:36:06
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#38 2013-04-04 00:39:13
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'
I'm not crazy, my mother had me tested.
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#39 2013-04-04 00:42:36
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#40 2013-04-04 01:03:30
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'
I'm not crazy, my mother had me tested.
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#41 2013-04-04 01:04:40
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Non Intersecting chords
Okay, know what a bijection is?
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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#42 2013-04-04 01:07:53
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'
I'm not crazy, my mother had me tested.
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#43 2013-04-04 01:18:09
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#44 2013-04-04 01:39:08
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'
I'm not crazy, my mother had me tested.
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#45 2013-04-04 01:44:50
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#46 2013-04-04 01:46:55
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'
I'm not crazy, my mother had me tested.
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#47 2013-04-04 01:50:13
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#48 2013-04-04 01:56:37
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'
I'm not crazy, my mother had me tested.
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#49 2013-04-04 02:01:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
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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#50 2013-04-04 02:04:22
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'
I'm not crazy, my mother had me tested.
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