Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#26 2014-09-13 05:26:33

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

If it is fine, can you please give me your email id, i can send the spreadsheet to you, with all calculations and the resulting chart.

Offline

#27 2014-09-13 05:28:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

You are showing me the output, debugging a program is something you have to do because you understand what you did.

I can help with the mathematics of how you entered the first equation into excel. If you did that right then the rest you will have to figure. Did you enter it correctly? Show how you entered it.


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

#28 2014-09-13 05:31:02

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

yes i can do the debugging,i agree. But the circles need to touch / tangential, bu they are not as i construct the chart, maybe  am doing something incorrect ...

Offline

#29 2014-09-13 05:33:09

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

i can go thru formula by formula if that is fine by you...

Offline

#30 2014-09-13 05:36:09

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

That might find the error.


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

#31 2014-09-13 05:39:04

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

in the first formula i entered r as 0.5, and varied n from 1 to 10  for x, then y and then R.
Cell D6 has the ratio r = 0.5, cell C7 = 0, c8=1 and so on and so forth ...

big_smile$6*(1+D$6)/(2*($C7*$C7*(1-D$6)*(1-D$6)+D$6))

Offline

#32 2014-09-13 05:45:34

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

Inline14.gif

$6*(1+D$6)/(2*($C7*$C7*(1-D$6)*(1-D$6)+D$6))

The first one looks okay. The next one...


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

#33 2014-09-13 05:48:45

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

for the next one Y coordinate
C22 = n ( n varies form 0 to 10) , D21 = 0.5 The ratio r

=$C22*D$21*(1-D$21)/($C22*$C22*(1-D$21)*(1-D$21)+D$21)

Offline

#34 2014-09-13 05:54:26

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

=$C22*D$21*(1-D$21)/($C22*$C22*(1-D$21)*(1-D$21)+D$21)

Inline17.gif

Inline20.gif

Inline60.gif

Inline63.gif

Inline66.gif

The second one looks okay.


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

#35 2014-09-13 06:00:41

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

the subsequent ones are as follows 3rd formula
here D36 = ratio = 0.5 and C37 = n (varying from 0 to 10
=(1-D$36)*D$36/(2*($C37*$C37*(1-D$36)*(1-D$36)+D$36))

similarly

4th formula
X for Tn

here d52 = 0.5 the ratio 'r' and C53 = n varying from 0 to 10

big_smile$52*(7+D$52)/(2*(4+4*$C53*($C53-1)*(1-D$52)*(1-D$52)+D$52*(D$52-1)))

y for Tn

here C69 = n varying from 0 to 10 and D68 = 0.5 the ratio
=2*(2*$C69-1)*D$68*(1-D$68)/((4+4*$C69*($C69-1)*(1-D$68)*(1-D$68)+D$68*(D$68-1)))

r for Tn
here D84 = 0.5 the ratio and C85 = n varying from 0 to 10
big_smile$84*(1-D$84)/(2*(4+4*$C85*($C85-1)*(1-D$84)*(1-D$84)+D$84*(D$84-1)))

Offline

#36 2014-09-13 06:02:11

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

now for calculating the area i am calculating the r using the circle formula of x^2 + y^2 = r^2.

Offline

#37 2014-09-13 06:03:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

here D36 = ratio = 0.5 and C37 = n (varying from 0 to 10
=(1-D$36)*D$36/(2*($C37*$C37*(1-D$36)*(1-D$36)+D$36))

Inline20.gif

here d52 = 0.5 the ratio 'r' and C53 = n varying from 0 to 10

$52*(7+D$52)/(2*(4+4*$C53*($C53-1)*(1-D$52)*(1-D$52)+D$52*(D$52-1)))

Inline60.gif

Inline63.gif

Inline66.gif

Third one looks okay.

Fourth one has an error.


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

#38 2014-09-13 06:14:39

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

ohhh. please tell me the error...

Offline

#39 2014-09-13 06:20:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

Right at the beginning of line 4.


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

#40 2014-09-13 06:25:37

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

ok, ... i am still not able to see it...

Offline

#41 2014-09-13 06:30:39

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

How about a D in front of that 52?


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

#42 2014-09-13 06:32:58

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

Ok Thanks

There is a D in front to 52 it gets converted to a smiley when it is represented in this website..


......D$52*(7+D$52)/(2*(4+4*$C53*($C53-1)*(1-D$52)*(1-D$52)+D$52*(D$52-1)))

Offline

#43 2014-09-13 06:35:29

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

The fourth line looks okay then.

here C69 = n varying from 0 to 10 and D68 = 0.5 the ratio

=2*(2*$C69-1)*D$68*(1-D$68)/((4+4*$C69*($C69-1)*(1-D$68)*(1-D$68)+D$68*(D$68-1)))

Inline63.gif

Fifth looks okay.

r for Tn
here D84 = 0.5 the ratio and C85 = n varying from 0 to 10

$D84*(1-D$84)/(2*(4+4*$C85*($C85-1)*(1-D$84)*(1-D$84)+D$84*(D$84-1)))

Inline66.gif

Last looks okay. How did you arrive at r = .5?


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

#44 2014-09-13 08:02:24

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

i have assumed r as 0.5 1 /2 AB = 1, AC=2

Offline

#45 2014-09-13 08:03:56

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

Have you tried other guesses?


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

#46 2014-09-13 08:04:12

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

i think the way the radius / area is calculated needs to be looked into ...

Offline

#47 2014-09-13 08:05:45

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

yes i have tried other guesses , r = 0.5, 0.33, 0.25 .. and so on upto 0.1

will the spreadsheet help in deciphering the error ..? i can send that to you if it is not much of a bother ...

Offline

#48 2014-09-13 08:07:38

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

as i change the r i get some weird patterns ... in the graph

Offline

#49 2014-09-13 08:10:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Pappus nested circles

Are you using the mathworld page or what?


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

#50 2014-09-13 08:11:05

NakulG
Member
Registered: 2014-09-02
Posts: 186

Re: Pappus nested circles

i am using openoffice.org spreadsheet program....

Offline

Board footer

Powered by FluxBB