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#51 2014-09-13 08:11:52
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
The page you got your equations from 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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#52 2014-09-13 08:20:53
- NakulG
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- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
wolfram alpha page ...
http://mathworld.wolfram.com/PappusChain.html
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#53 2014-09-13 08:24:27
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
Do you have the first 3 circles drawn?
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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#54 2014-09-13 08:25:09
- NakulG
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- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
first 2 are not drawn, the third circle is the p for n=1, that is drawn...
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#55 2014-09-13 08:27:24
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
Then you do not have AB and AC?
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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#56 2014-09-13 08:28:22
- NakulG
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- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
AB and AC,
AB=1 and AC=2
for r = 0.5
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#57 2014-09-13 08:30:06
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
Looking at their diagram I do not think that AB is half of AC.
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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#58 2014-09-13 08:32:17
- NakulG
- Member
- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
As i understood, r is a ratio, AB/ AC = 1/2, ... even if the value are a and b the ratio is what will get used on the formula's...is my understanding correct?
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#59 2014-09-13 08:34:07
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
r = AB / AC, that is what you need to have 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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#60 2014-09-13 08:35:47
- NakulG
- Member
- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
right
But the p1 and P2 and P3 and so on .. itself are not touching each other ... these are only dependent on the ratio, so these should touch, or am i missing something here ...
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#61 2014-09-13 08:38:11
- NakulG
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- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
maybe i should calculate the points of tangency ad see if these lie on the circle circumference
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#62 2014-09-13 08:39:12
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
If you do not start with the right radius how can the circles touch?
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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#63 2014-09-13 08:41:25
- NakulG
- Member
- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
ohhh,
it is 2 am in the morning, i think i will get back to this later in the day tomorrow .., thanks for helping, i will continue to find the solution ... in the meantime if you have any suggestions please let me know ...
Thanks in advance
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#64 2014-09-13 08:43:02
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
Find the 3 circles that form the Arbelos 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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#65 2014-09-15 04:34:25
- NakulG
- Member
- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
Got it, the open office calc program has a challenge in terms of making a bubble chart that is relative rather than absolute area size.
Next is the construction using compass and scale...
Thanks for the help...
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#66 2014-09-15 04:41:59
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
You got the first 3? Then go ahead with the rest and let me know how you do.
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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#67 2014-09-15 05:11:34
- NakulG
- Member
- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
Ok yes, but we don't need the first three as the ab /ac is a ratio, so we can in fact start from any circle number and construct the chain - on a spreadsheet program, but for paper and compass exercise we ended all the circles 1,2 and 3. I will construct using compass and let you know the steps...
Thanks so much.
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#68 2014-09-15 05:29:10
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Pappus nested circles
Alright, try to include a image of your completed work.
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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#69 2017-08-16 20:51:49
- NakulG
- Member
- Registered: 2014-09-02
- Posts: 186
Re: Pappus nested circles
Hi
Can anyone help prove that R in the attached figure is = 1/2 X (ABXBC)
Thanks
Nakul
Last edited by NakulG (2017-08-17 18:42:47)
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