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#76 Re: Help Me ! » Pappus nested circles » 2014-09-13 08:28:22
AB and AC,
AB=1 and AC=2
for r = 0.5
#77 Re: Help Me ! » Pappus nested circles » 2014-09-13 08:25:09
first 2 are not drawn, the third circle is the p for n=1, that is drawn...
#78 Re: Help Me ! » Pappus nested circles » 2014-09-13 08:20:53
wolfram alpha page ...
http://mathworld.wolfram.com/PappusChain.html
#79 Re: Help Me ! » Pappus nested circles » 2014-09-13 08:11:05
i am using openoffice.org spreadsheet program....
#80 Re: Help Me ! » Pappus nested circles » 2014-09-13 08:07:38
as i change the r i get some weird patterns ... in the graph
#81 Re: Help Me ! » Pappus nested circles » 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 ...
#82 Re: Help Me ! » Pappus nested circles » 2014-09-13 08:04:12
i think the way the radius / area is calculated needs to be looked into ...
#83 Re: Help Me ! » Pappus nested circles » 2014-09-13 08:02:24
i have assumed r as 0.5 1 /2 AB = 1, AC=2
#84 Re: Help Me ! » Pappus nested circles » 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)))
#85 Re: Help Me ! » Pappus nested circles » 2014-09-13 06:25:37
ok, ... i am still not able to see it...
#86 Re: Help Me ! » Pappus nested circles » 2014-09-13 06:14:39
ohhh. please tell me the error...
#87 Re: Help Me ! » Pappus nested circles » 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.
#88 Re: Help Me ! » Pappus nested circles » 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$84-1)))
#89 Re: Help Me ! » Pappus nested circles » 2014-09-13 05:48:45
for the next one Y coordinate
C22 = n ( n varies form 0 to 10) , D21 = 0.5 The ratio r
=$C22*D$21*(1-D$21)/($C22*$C22*(1-D$21)*(1-D$21)+D$21)
#90 Re: Help Me ! » Pappus nested circles » 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))
#91 Re: Help Me ! » Pappus nested circles » 2014-09-13 05:33:09
i can go thru formula by formula if that is fine by you...
#92 Re: Help Me ! » Pappus nested circles » 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 ...
#93 Re: Help Me ! » Pappus nested circles » 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.
#94 Re: Help Me ! » Pappus nested circles » 2014-09-13 05:22:35
Apologies for pushing so much data thru.
No.
for the first equation the values are as follows (r varies from 0.5 to 0.1) and n varies for 0 to 10
Pn Xn Ratio (r)
n 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
0 0.75000 0.66667 0.62500 0.60000 0.58333 0.57143 0.56250 0.55556 0.55000
1 0.50000 0.28571 0.19231 0.14286 0.11290 0.09302 0.07895 0.06849 0.06044
2 0.25000 0.10526 0.06250 0.04348 0.03302 0.02649 0.02206 0.01887 0.01647
3 0.13636 0.05128 0.02941 0.02013 0.01515 0.01208 0.01002 0.00855 0.00744
4 0.08333 0.02985 0.01689 0.01149 0.00862 0.00686 0.00568 0.00484 0.00421
5 0.05556 0.01942 0.01092 0.00741 0.00555 0.00441 0.00365 0.00311 0.00270
6 0.03947 0.01361 0.00762 0.00516 0.00386 0.00307 0.00254 0.00216 0.00188
7 0.02941 0.01005 0.00562 0.00380 0.00284 0.00226 0.00187 0.00159 0.00138
8 0.02273 0.00772 0.00431 0.00292 0.00218 0.00173 0.00143 0.00122 0.00106
9 0.01807 0.00612 0.00341 0.00231 0.00172 0.00137 0.00113 0.00096 0.00084
10 0.01471 0.00496 0.00277 0.00187 0.00140 0.00111 0.00092 0.00078 0.00068
#95 Re: Help Me ! » Pappus nested circles » 2014-09-13 05:17:17
I am taking r 0.5 for creating the chart and for n varying from 1 to 10.
#96 Re: Help Me ! » Pappus nested circles » 2014-09-13 05:14:03
Yn Ratio
n 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
0 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
1 0.33333 0.28571 0.23077 0.19048 0.16129 0.13953 0.12281 0.10959 0.09890
2 0.33333 0.21053 0.15000 0.11594 0.09434 0.07947 0.06863 0.06038 0.05389
3 0.27273 0.15385 0.10588 0.08054 0.06494 0.05438 0.04677 0.04103 0.03654
4 0.22222 0.11940 0.08108 0.06130 0.04926 0.04117 0.03535 0.03098 0.02757
5 0.18519 0.09709 0.06550 0.04938 0.03962 0.03308 0.02839 0.02486 0.02211
6 0.15789 0.08163 0.05488 0.04131 0.03311 0.02763 0.02370 0.02075 0.01846
7 0.13725 0.07035 0.04719 0.03549 0.02843 0.02372 0.02034 0.01781 0.01583
8 0.12121 0.06178 0.04138 0.03110 0.02491 0.02077 0.01781 0.01559 0.01386
9 0.10843 0.05505 0.03683 0.02767 0.02216 0.01847 0.01584 0.01386 0.01233
10 0.09804 0.04963 0.03319 0.02492 0.01995 0.01663 0.01426 0.01248 0.01110
Rn Ratio
n 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
0 0.25000 0.33333 0.37500 0.40000 0.41667 0.42857 0.43750 0.44444 0.45000
1 0.16667 0.14286 0.11538 0.09524 0.08065 0.06977 0.06140 0.05479 0.04945
2 0.08333 0.05263 0.03750 0.02899 0.02358 0.01987 0.01716 0.01509 0.01347
3 0.04545 0.02564 0.01765 0.01342 0.01082 0.00906 0.00780 0.00684 0.00609
4 0.02778 0.01493 0.01014 0.00766 0.00616 0.00515 0.00442 0.00387 0.00345
5 0.01852 0.00971 0.00655 0.00494 0.00396 0.00331 0.00284 0.00249 0.00221
6 0.01316 0.00680 0.00457 0.00344 0.00276 0.00230 0.00198 0.00173 0.00154
7 0.00980 0.00503 0.00337 0.00253 0.00203 0.00169 0.00145 0.00127 0.00113
8 0.00758 0.00386 0.00259 0.00194 0.00156 0.00130 0.00111 0.00097 0.00087
9 0.00602 0.00306 0.00205 0.00154 0.00123 0.00103 0.00088 0.00077 0.00068
10 0.00490 0.00248 0.00166 0.00125 0.00100 0.00083 0.00071 0.00062 0.00055
Tn Xn Ratio
n 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
0 0.50000 0.32353 0.23770 0.18750 0.15468 0.13158 0.11446 0.10127 0.09079
1 0.50000 0.32353 0.23770 0.18750 0.15468 0.13158 0.11446 0.10127 0.09079
2 0.32609 0.16667 0.10902 0.08036 0.06342 0.05230 0.04446 0.03865 0.03417
3 0.19231 0.08462 0.05235 0.03750 0.02909 0.02372 0.02000 0.01728 0.01520
4 0.11905 0.04867 0.02941 0.02083 0.01606 0.01303 0.01096 0.00945 0.00830
5 0.07895 0.03107 0.01857 0.01308 0.01005 0.00814 0.00684 0.00589 0.00517
6 0.05556 0.02140 0.01271 0.00893 0.00685 0.00554 0.00465 0.00400 0.00351
7 0.04098 0.01558 0.00922 0.00647 0.00496 0.00401 0.00336 0.00289 0.00254
8 0.03138 0.01183 0.00698 0.00489 0.00375 0.00303 0.00254 0.00218 0.00192
9 0.02475 0.00927 0.00547 0.00383 0.00293 0.00237 0.00198 0.00171 0.00150
10 0.02000 0.00746 0.00439 0.00307 0.00235 0.00190 0.00159 0.00137 0.00120
Yn Ratio
n 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
0 -0.13333 -0.11765 -0.09836 -0.08333 -0.07194 -0.06316 -0.05622 -0.05063 -0.04604
1 0.13333 0.11765 0.09836 0.08333 0.07194 0.06316 0.05622 0.05063 0.04604
2 0.26087 0.18182 0.13534 0.10714 0.08850 0.07531 0.06552 0.05797 0.05197
3 0.25641 0.15385 0.10830 0.08333 0.06766 0.05693 0.04912 0.04320 0.03854
4 0.22222 0.12389 0.08519 0.06481 0.05228 0.04380 0.03768 0.03306 0.02945
5 0.18947 0.10169 0.06914 0.05233 0.04208 0.03518 0.03022 0.02649 0.02358
6 0.16296 0.08560 0.05784 0.04365 0.03504 0.02927 0.02513 0.02201 0.01958
7 0.14208 0.07365 0.04959 0.03736 0.02996 0.02501 0.02146 0.01879 0.01672
8 0.12552 0.06452 0.04333 0.03261 0.02614 0.02181 0.01871 0.01638 0.01457
9 0.11221 0.05734 0.03845 0.02891 0.02316 0.01932 0.01657 0.01451 0.01290
10 0.10133 0.05156 0.03453 0.02596 0.02079 0.01734 0.01487 0.01302 0.01157
Rn Ratio
n 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
0 0.03333 0.02941 0.02459 0.02083 0.01799 0.01579 0.01406 0.01266 0.01151
1 0.03333 0.02941 0.02459 0.02083 0.01799 0.01579 0.01406 0.01266 0.01151
2 0.02174 0.01515 0.01128 0.00893 0.00737 0.00628 0.00546 0.00483 0.00433
3 0.01282 0.00769 0.00542 0.00417 0.00338 0.00285 0.00246 0.00216 0.00193
4 0.00794 0.00442 0.00304 0.00231 0.00187 0.00156 0.00135 0.00118 0.00105
5 0.00526 0.00282 0.00192 0.00145 0.00117 0.00098 0.00084 0.00074 0.00065
6 0.00370 0.00195 0.00131 0.00099 0.00080 0.00067 0.00057 0.00050 0.00045
7 0.00273 0.00142 0.00095 0.00072 0.00058 0.00048 0.00041 0.00036 0.00032
8 0.00209 0.00108 0.00072 0.00054 0.00044 0.00036 0.00031 0.00027 0.00024
9 0.00165 0.00084 0.00057 0.00043 0.00034 0.00028 0.00024 0.00021 0.00019
10 0.00133 0.00068 0.00045 0.00034 0.00027 0.00023 0.00020 0.00017 0.00015
Ratio 0.5
Pn Xn Yn Area n Rn
n 0 0.75000 0.00000 1.76715 0.25000 0.56250 0.00000 0.56250 0.75000
1 0.50000 0.33333 1.13446 0.16667 0.25000 0.11111 0.36111 0.60093
2 0.25000 0.33333 0.54542 0.08333 0.06250 0.11111 0.17361 0.41667
3 0.13636 0.27273 0.29209 0.04545 0.01860 0.07438 0.09298 0.30492
4 0.08333 0.22222 0.17696 0.02778 0.00694 0.04938 0.05633 0.23733
5 0.05556 0.18519 0.11743 0.01852 0.00309 0.03429 0.03738 0.19334
6 0.03947 0.15789 0.08322 0.01316 0.00156 0.02493 0.02649 0.16275
7 0.02941 0.13725 0.06190 0.00980 0.00087 0.01884 0.01970 0.14037
8 0.02273 0.12121 0.04778 0.00758 0.00052 0.01469 0.01521 0.12332
9 0.01807 0.10843 0.03796 0.00602 0.00033 0.01176 0.01208 0.10993
10 0.01471 0.09804 0.03088 0.00490 0.00022 0.00961 0.00983 0.09914
Tn 0 0.50000 -0.13333 0.84125 0.03333 0.25000 0.01778 0.26778 0.51747
1 0.50000 0.13333 0.84125 0.03333 0.25000 0.01778 0.26778 0.51747
2 0.32609 0.26087 0.54785 0.02174 0.10633 0.06805 0.17439 0.41760
3 0.19231 0.25641 0.32273 0.01282 0.03698 0.06575 0.10273 0.32051
4 0.11905 0.22222 0.19966 0.00794 0.01417 0.04938 0.06356 0.25210
5 0.07895 0.18947 0.13236 0.00526 0.00623 0.03590 0.04213 0.20526
6 0.05556 0.16296 0.09313 0.00370 0.00309 0.02656 0.02964 0.17217
7 0.04098 0.14208 0.06869 0.00273 0.00168 0.02019 0.02187 0.14787
8 0.03138 0.12552 0.05259 0.00209 0.00098 0.01576 0.01674 0.12939
9 0.02475 0.11221 0.04148 0.00165 0.00061 0.01259 0.01320 0.11491
10 0.02000 0.10133 0.03352 0.00133 0.00040 0.01027 0.01067 0.10329
#97 Re: Help Me ! » Pappus nested circles » 2014-09-13 05:12:00
AB r Ratio
AC AB 1 1 1 1 1 1 1 1 1
AC 2 3 4 5 6 7 8 9 10
Pn Xn Ratio
n 0.50 0.33 0.25 0.20 0.17 0.14 0.13 0.11 0.10
0 0.75000 0.66667 0.62500 0.60000 0.58333 0.57143 0.56250 0.55556 0.55000
1 0.50000 0.28571 0.19231 0.14286 0.11290 0.09302 0.07895 0.06849 0.06044
2 0.25000 0.10526 0.06250 0.04348 0.03302 0.02649 0.02206 0.01887 0.01647
3 0.13636 0.05128 0.02941 0.02013 0.01515 0.01208 0.01002 0.00855 0.00744
4 0.08333 0.02985 0.01689 0.01149 0.00862 0.00686 0.00568 0.00484 0.00421
5 0.05556 0.01942 0.01092 0.00741 0.00555 0.00441 0.00365 0.00311 0.00270
6 0.03947 0.01361 0.00762 0.00516 0.00386 0.00307 0.00254 0.00216 0.00188
7 0.02941 0.01005 0.00562 0.00380 0.00284 0.00226 0.00187 0.00159 0.00138
8 0.02273 0.00772 0.00431 0.00292 0.00218 0.00173 0.00143 0.00122 0.00106
9 0.01807 0.00612 0.00341 0.00231 0.00172 0.00137 0.00113 0.00096 0.00084
10 0.01471 0.00496 0.00277 0.00187 0.00140 0.00111 0.00092 0.00078 0.00068
#98 Re: Help Me ! » Pappus nested circles » 2014-09-13 05:03:31
Hope this helps
#99 Re: Help Me ! » Pappus nested circles » 2014-09-13 04:59:14
i cant figure out how to attach the file / upload image ....
#100 Re: Help Me ! » Pappus nested circles » 2014-09-13 04:53:40
same formulas for x, y & r for P and T, that are in wolfram alpha page on pappus chain...
http://mathworld.wolfram.com/PappusChain.html
I can send the whole spreadsheet with the chart etc.