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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
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

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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
Member
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
Member
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

PappusCircle_1000.gif

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
Member
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)

ARBELOS.png

Thanks
Nakul

Last edited by NakulG (2017-08-17 18:42:47)

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