Pappus nested circles

NakulG · 2014-09-13 05:26:33

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.

bobbym · 2014-09-13 05:28:36

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.

NakulG · 2014-09-13 05:31:02

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 ...

NakulG · 2014-09-13 05:33:09

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

bobbym · 2014-09-13 05:36:09

That might find the error.

NakulG · 2014-09-13 05:39:04

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 ...

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

bobbym · 2014-09-13 05:45:34

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

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

NakulG · 2014-09-13 05:48:45

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)

bobbym · 2014-09-13 05:54:26

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

The second one looks okay.

NakulG · 2014-09-13 06:00:41

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

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

NakulG · 2014-09-13 06:02:11

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

bobbym · 2014-09-13 06:03:19

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))

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)))

Third one looks okay.

Fourth one has an error.

NakulG · 2014-09-13 06:14:39

ohhh. please tell me the error...

bobbym · 2014-09-13 06:20:19

Right at the beginning of line 4.

NakulG · 2014-09-13 06:25:37

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

bobbym · 2014-09-13 06:30:39

How about a D in front of that 52?

NakulG · 2014-09-13 06:32:58

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)))

bobbym · 2014-09-13 06:35:29

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)))

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)))

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

NakulG · 2014-09-13 08:02:24

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

bobbym · 2014-09-13 08:03:56

Have you tried other guesses?

NakulG · 2014-09-13 08:04:12

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

NakulG · 2014-09-13 08:05:45

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 ...

NakulG · 2014-09-13 08:07:38

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

bobbym · 2014-09-13 08:10:06

Are you using the mathworld page or what?

NakulG · 2014-09-13 08:11:05

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

Math Is Fun Forum

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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

Re: Pappus nested circles

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