已知等腰三角形的腰长和内切圆半径求第三边长

luyuanhong

[这个贴子最后由luyuanhong在 2011/10/03 07:33pm 第 2 次编辑]

天山草

呵呵，在例 3 中，还有一个解，就是∠ABC 是锐角的情况，此时 AC=1.0541741

昌建

三角形内切圆的半径：r =√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］/2，错误的
三角形的两条边长，10，10，第三边值取一个小数，三角形的内切圆的直径值没有，1，2，3，...正整数....存在
三角形的三条边长，10，10，1.0541741，代入公式r =√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］≠1
三角形的三条边长，10，10，19.899239185，代入公式r =√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］≠1

天山草

[这个贴子最后由天山草在 2011/10/04 08:16am 第 3 次编辑]

下面引用由昌建在 2011/10/03 05:45pm 发表的内容：
三角形内切圆的半径：r =√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］/2，错误的
三角形的两条边长，10，10，第三边值取一个小数，三角形的内切圆的直径值没有，1，2，3，...正整数....存在

昌建同志，您是说第三边取任何一个带小数的数，都不可能使内切圆直径纹丝不差地、没有一丁点儿误差地、绝对地等于 1 吗？
10，10，1.0541741 代入公式直径正好等于 1.0000000……，你要是嫌精度不够，可以再多算几位，比如 1.05417407962258，代入公式直径是 1.000000000000……，还不满意吗？我可以算到 1.000……后面有一千个零。如果你嫌一千个零还不够多，我也能算出一个第三边的表达式，让直径准确地等于 1。
敢问昌建网友，您现在是初中生？还是高中生？还是中年人？还是退休老人？

昌建

三角形内切圆的半径：r =√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］/2，错误的
三角形的两条边长，10，10，第三边值取一个小数，三角形的内切圆的直径值没有，1，2，3，...正整数....存在
三角形的三条边长，10，10，19.899239185.....，代入公式r =√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］≠1
假设第三边数小数点取10位有限小数：代入公式r =√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］≠1
√［(20-19.899239185)×19.899239185×19.899239185÷39.899239185］≠1
因为：(20-19.899239185)×19.899239185×19.899239185÷39.899239185
有30多位有限小数除以10多位有限小数.两个相同数相除等于1，两个不同数相除不等于1
所以：三角形的两条边长，10，10，第三边值取一个小数，三角形的内切圆的直径值没有，1，2，3，...正整数....存在

ysr

为何是1,应该是1/2吧,昌建同志,错误和误差的区别要搞清楚

昌建

三角形内切圆的半径：r =√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］/2=0.5
三角形内切圆的直径：d=√［(a+b-c)(a-b+c)(-a+b+c)/(a+b+c)］=1
ysr ：那里不一样的，有何错误和误差的区别在那？有问题？

ysr

发个数据:
序号   边长  边长  边长  直径的平方  半径
1101019.8992221.0001692590.500042313
2101019.8992231.000159410.500039851
3101019.8992241.0001495610.500037389
4101019.8992251.0001397120.500034927
5101019.8992261.0001298630.500032465
6101019.8992271.0001200140.500030003
7101019.8992281.0001101650.500027541
8101019.8992291.0001003160.500025078
9101019.899231.0000904670.500022616
10101019.8992311.0000806180.500020154
11101019.8992321.0000707690.500017692
12101019.8992331.000060920.50001523
13101019.8992341.0000510710.500012768
14101019.8992351.0000412220.500010305
15101019.8992361.0000313730.500007843
16101019.8992371.0000215240.500005381
17101019.8992381.0000116750.500002919
18101019.8992391.0000018260.500000456
19101019.899240.9999919770.499997994
20101019.8992410.9999821270.499995532
21101019.8992420.9999722780.49999307
22101019.8992430.9999624290.499990607
23101019.8992440.999952580.499988145
24101019.8992450.9999427310.499985683
25101019.8992460.9999328820.49998322
26101019.8992470.9999230330.499980758
27101019.8992480.9999131840.499978296
28101019.8992490.9999033350.499975833
29101019.899250.9998934860.499973371
30101019.8992510.9998836370.499970908
31101019.8992520.9998737880.499968446
32101019.8992530.9998639390.499965984
33101019.8992540.999854090.499963521
34101019.8992550.9998442410.499961059
35101019.8992560.9998343920.499958596
36101019.8992570.9998245420.499956134
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38101019.8992590.9998048440.499951209
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40101019.8992610.9997851460.499946284
41101019.8992620.9997752970.499943821
42101019.8992630.9997654480.499941359
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47101019.8992680.9997162030.499929046
48101019.8992690.9997063530.499926583
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52101019.8992730.9996669570.499916732
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65101019.8992860.9995389190.499884716
66101019.8992870.9995290690.499882254
67101019.8992880.999519220.499879791
68101019.8992890.9995093710.499877328
69101019.899290.9994995220.499874865
70101019.8992910.9994896730.499872402
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72101019.8992930.9994699750.499867476
73101019.8992940.9994601260.499865013
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79101019.89930.9994010310.499850235
80101019.8993010.9993911820.499847772
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84101019.8993050.9993517850.49983792
85101019.8993060.9993419360.499835457
86101019.8993070.9993320870.499832994
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88101019.8993090.9993123880.499828068
89101019.899310.9993025390.499825604
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100101019.8993210.9991941980.499798509
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102101019.8993230.99917450.499793582
103101019.8993240.9991646510.499791119
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127101019.8993480.998928270.499731996
128101019.8993490.9989184210.499729532
129101019.899350.9989085720.499727068
130101019.8993510.9988987230.499724605
131101019.8993520.9988888730.499722141
132101019.8993530.9988790240.499719677
133101019.8993540.9988691750.499717214
134101019.8993550.9988593260.49971475
135101019.8993560.9988494770.499712286
136101019.8993570.9988396270.499709823
137101019.8993580.9988297780.499707359
138101019.8993590.9988199290.499704895
139101019.899360.998810080.499702431
140101019.8993610.998800230.499699968
141101019.8993620.9987903810.499697504
142101019.8993630.9987805320.49969504
143101019.8993640.9987706830.499692576
144101019.8993650.9987608330.499690112
145101019.8993660.9987509840.499687648
146101019.8993670.9987411350.499685185
147101019.8993680.9987312860.499682721
148101019.8993690.9987214370.499680257
149101019.899370.9987115870.499677793
150101019.8993710.9987017380.499675329
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152101019.8993730.998682040.499670401
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154101019.8993750.9986623410.499665473
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157101019.8993780.9986327930.499658081
158101019.8993790.9986229440.499655617
159101019.899380.9986130950.499653153
160101019.8993810.9986032450.499650689
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180101019.8994010.998406260.499601406
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182101019.8994030.9983865610.499596478
183101019.8994040.9983767120.499594013
184101019.8994050.9983668630.499591549
185101019.8994060.9983570130.499589085
186101019.8994070.9983471640.49958662
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188101019.8994090.9983274660.499581691
189101019.899410.9983176160.499579227
190101019.8994110.9983077670.499576763
191101019.8994120.9982979180.499574298
192101019.8994130.9982880680.499571834
193101019.8994140.9982782190.499569369
194101019.8994150.998268370.499566905
195101019.8994160.998258520.49956444
196101019.8994170.9982486710.499561976
197101019.8994180.9982388220.499559511
198101019.8994190.9982289720.499557047
199101019.899420.9982191230.499554582
200101019.8994210.9982092740.499552118
201101019.8994220.9981994240.499549653
202101019.8994230.9981895750.499547189
203101019.8994240.9981797260.499544724
204101019.8994250.9981698760.49954226
205101019.8994260.9981600270.499539795
206101019.8994270.9981501780.49953733
207101019.8994280.9981403290.499534866
208101019.8994290.9981304790.499532401
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210101019.8994310.998110780.499527472
211101019.8994320.9981009310.499525007
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213101019.8994340.9980812320.499520078
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253101019.8994740.9976872580.49942148
254101019.8994750.9976774080.499419015
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256101019.8994770.9976577090.499414084
257101019.8994780.997647860.499411619
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325101019.8995460.9969780970.499243953
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327101019.8995480.9969583980.49923902
328101019.8995490.9969485480.499236554
329101019.899550.9969386990.499234088
330101019.8995510.9969288490.499231622
331101019.8995520.9969190.499229156
332101019.8995530.996909150.49922669
333101019.8995540.9968993010.499224223
334101019.8995550.9968894510.499221757
335101019.8995560.9968796020.499219291
336101019.8995570.9968697520.499216825
337101019.8995580.9968599030.499214358
338101019.8995590.9968500530.499211892
339101019.899560.9968402040.499209426
340101019.8995610.9968303540.49920696
341101019.8995620.9968205050.499204493
342101019.8995630.9968106550.499202027
343101019.8995640.9968008050.499199561
344101019.8995650.9967909560.499197094
345101019.8995660.9967811060.499194628
346101019.8995670.9967712570.499192162
347101019.8995680.9967614070.499189695
348101019.8995690.9967515580.499187229
349101019.899570.9967417080.499184762
350101019.8995710.9967318590.499182296
351101019.8995720.9967220090.49917983
352101019.8995730.996712160.499177363
353101019.8995740.996702310.499174897
354101019.8995750.996692460.49917243
355101019.8995760.9966826110.499169964
356101019.8995770.9966727610.499167497
357101019.8995780.9966629120.499165031
358101019.8995790.9966530620.499162564
359101019.899580.9966432130.499160098
360101019.8995810.9966333630.499157631
361101019.8995820.9966235140.499155165
362101019.8995830.9966136640.499152698
363101019.8995840.9966038140.499150232
364101019.8995850.9965939650.499147765
365101019.8995860.9965841150.499145298
366101019.8995870.9965742660.499142832
367101019.8995880.9965644160.499140365
368101019.8995890.9965545670.499137898
369101019.899590.9965447170.499135432
370101019.8995910.9965348670.499132965
371101019.8995920.9965250180.499130498
372101019.8995930.9965151680.499128032
373101019.8995940.9965053190.499125565
374101019.8995950.9964954690.499123098
375101019.8995960.996485620.499120632
376101019.8995970.996475770.499118165
377101019.8995980.996465920.499115698
378101019.8995990.9964560710.499113231
379101019.89960.9964462210.499110765
380101019.8996010.9964363720.499108298
381101019.8996020.9964265220.499105831
382101019.8996030.9964166720.499103364
383101019.8996040.9964068230.499100897
384101019.8996050.9963969730.49909843
385101019.8996060.9963871240.499095964
386101019.8996070.9963772740.499093497
387101019.8996080.9963674240.49909103
388101019.8996090.9963575750.499088563
389101019.899610.9963477250.499086096
390101019.8996110.9963378760.499083629
391101019.8996120.9963280260.499081162
392101019.8996130.9963181760.499078695
393101019.8996140.9963083270.499076228
394101019.8996150.9962984770.499073761
395101019.8996160.9962886280.499071294
396101019.8996170.9962787780.499068827
397101019.8996180.9962689280.49906636
398101019.8996190.9962590790.499063893
399101019.899620.9962492290.499061426
400101019.8996210.996239380.499058959
401101019.8996220.996229530.499056492
402101019.8996230.996219680.499054025
403101019.8996240.9962098310.499051558
404101019.8996250.9961999810.499049091
405101019.8996260.9961901310.499046624
406101019.8996270.9961802820.499044157
407101019.8996280.9961704320.49904169
408101019.8996290.9961605820.499039223
409101019.899630.9961507330.499036755
410101019.8996310.9961408830.499034288
411101019.8996320.9961310340.499031821
412101019.8996330.9961211840.499029354
413101019.8996340.9961113340.499026887
414101019.8996350.9961014850.499024419
415101019.8996360.9960916350.499021952
416101019.8996370.9960817850.499019485
417101019.8996380.9960719360.499017018
418101019.8996390.9960620860.49901455
419101019.899640.9960522360.499012083
420101019.8996410.9960423870.499009616
421101019.8996420.9960325370.499007149
422101019.8996430.9960226870.499004681
423101019.8996440.9960128380.499002214
424101019.8996450.9960029880.498999747
425101019.8996460.9959931390.498997279
426101019.8996470.9959832890.498994812
427101019.8996480.9959734390.498992344
428101019.8996490.995963590.498989877
429101019.899650.995953740.49898741
430101019.8996510.995943890.498984942
431101019.8996520.9959340410.498982475
432101019.8996530.9959241910.498980007
433101019.8996540.9959143410.49897754
434101019.8996550.9959044920.498975072
435101019.8996560.9958946420.498972605
436101019.8996570.9958847920.498970137
437101019.8996580.9958749430.49896767
438101019.8996590.9958650930.498965202
439101019.899660.9958552430.498962735

ysr

不清楚重发
序号   边长  边长  边长  直径的平方  半径
397101019.899620.9962690.499066
398101019.899620.9962590.499064
399101019.899620.9962490.499061
400101019.899620.9962390.499059
401101019.899620.996230.499056
402101019.899620.996220.499054
403101019.899620.996210.499052
404101019.899630.99620.499049
405101019.899630.996190.499047
406101019.899630.996180.499044
407101019.899630.996170.499042
408101019.899630.9961610.499039
409101019.899630.9961510.499037
410101019.899630.9961410.499034
411101019.899630.9961310.499032
412101019.899630.9961210.499029
413101019.899630.9961110.499027
414101019.899640.9961010.499024
415101019.899640.9960920.499022
416101019.899640.9960820.499019
417101019.899640.9960720.499017
418101019.899640.9960620.499015
419101019.899640.9960520.499012
420101019.899640.9960420.49901
421101019.899640.9960330.499007
422101019.899640.9960230.499005
423101019.899640.9960130.499002
424101019.899650.9960030.499
425101019.899650.9959930.498997
426101019.899650.9959830.498995
427101019.899650.9959730.498992
428101019.899650.9959640.49899
429101019.899650.9959540.498987
430101019.899650.9959440.498985
431101019.899650.9959340.498982
432101019.899650.9959240.49898
433101019.899650.9959140.498978
434101019.899660.9959040.498975
435101019.899660.9958950.498973
436101019.899660.9958850.49897
437101019.899660.9958750.498968
438101019.899660.9958650.498965
439101019.899660.9958550.498963
1101019.899221.0001690.500042
2101019.899221.0001590.50004
3101019.899221.000150.500037
4101019.899231.000140.500035
5101019.899231.000130.500032
6101019.899231.000120.50003
7101019.899231.000110.500028
8101019.899231.00010.500025
9101019.899231.000090.500023
10101019.899231.0000810.50002
11101019.899231.0000710.500018
12101019.899231.0000610.500015
13101019.899231.0000510.500013
14101019.899241.0000410.50001
15101019.899241.0000310.500008
16101019.899241.0000220.500005
17101019.899241.0000120.500003
18101019.899241.0000020.5
19101019.899240.9999920.499998
20101019.899240.9999820.499996
21101019.899240.9999720.499993
22101019.899240.9999620.499991
23101019.899240.9999530.499988
24101019.899250.9999430.499986
25101019.899250.9999330.499983
26101019.899250.9999230.499981
27101019.899250.9999130.499978
28101019.899250.9999030.499976
29101019.899250.9998930.499973
30101019.899250.9998840.499971
31101019.899250.9998740.499968
32101019.899250.9998640.499966
33101019.899250.9998540.499964
34101019.899260.9998440.499961
35101019.899260.9998340.499959
36101019.899260.9998250.499956
37101019.899260.9998150.499954
38101019.899260.9998050.499951
39101019.899260.9997950.499949
40101019.899260.9997850.499946
41101019.899260.9997750.499944
42101019.899260.9997650.499941
43101019.899260.9997560.499939
44101019.899270.9997460.499936
45101019.899270.9997360.499934
46101019.899270.9997260.499932
47101019.899270.9997160.499929
48101019.899270.9997060.499927
49101019.899270.9996970.499924
50101019.899270.9996870.499922
51101019.899270.9996770.499919
52101019.899270.9996670.499917
53101019.899270.9996570.499914
54101019.899280.9996470.499912
55101019.899280.9996370.499909
56101019.899280.9996280.499907
57101019.899280.9996180.499904
58101019.899280.9996080.499902
59101019.899280.9995980.499899
60101019.899280.9995880.499897
61101019.899280.9995780.499895
62101019.899280.9995680.499892
63101019.899280.9995590.49989
64101019.899290.9995490.499887
65101019.899290.9995390.499885
66101019.899290.9995290.499882
67101019.899290.9995190.49988
68101019.899290.9995090.499877
69101019.899290.99950.499875
70101019.899290.999490.499872
71101019.899290.999480.49987
72101019.899290.999470.499867
73101019.899290.999460.499865
74101019.89930.999450.499863
75101019.89930.999440.49986
76101019.89930.9994310.499858
77101019.89930.9994210.499855
78101019.89930.9994110.499853
79101019.89930.9994010.49985
80101019.89930.9993910.499848
81101019.89930.9993810.499845
82101019.89930.9993710.499843
83101019.89930.9993620.49984
84101019.899310.9993520.499838
85101019.899310.9993420.499835
86101019.899310.9993320.499833
87101019.899310.9993220.499831
88101019.899310.9993120.499828
89101019.899310.9993030.499826
90101019.899310.9992930.499823
91101019.899310.9992830.499821
92101019.899310.9992730.499818
93101019.899310.9992630.499816
94101019.899320.9992530.499813
95101019.899320.9992430.499811
96101019.899320.9992340.499808
97101019.899320.9992240.499806
98101019.899320.9992140.499803
99101019.899320.9992040.499801
100101019.899320.9991940.499799
101101019.899320.9991840.499796
102101019.899320.9991750.499794
103101019.899320.9991650.499791
104101019.899330.9991550.499789
105101019.899330.9991450.499786
106101019.899330.9991350.499784
107101019.899330.9991250.499781
108101019.899330.9991150.499779

ysr

1
10
10
19.89922
1.000169
0.500042

2
10
10
19.89922
1.000159
0.50004

3
10
10
19.89922
1.00015
0.500037

4
10
10
19.89923
1.00014
0.500035

5
10
10
19.89923
1.00013
0.500032

6
10
10
19.89923
1.00012
0.50003

7
10
10
19.89923
1.00011
0.500028

8
10
10
19.89923
1.0001
0.500025

9
10
10
19.89923
1.00009
0.500023

10
10
10
19.89923
1.000081
0.50002

11
10
10
19.89923
1.000071
0.500018

12
10
10
19.89923
1.000061
0.500015

13
10
10
19.89923
1.000051
0.500013

14
10
10
19.89924
1.000041
0.50001

15
10
10
19.89924
1.000031
0.500008

16
10
10
19.89924
1.000022
0.500005

17
10
10
19.89924
1.000012
0.500003

18
10
10
19.89924
1.000002
0.5

19
10
10
19.89924
0.999992
0.499998

20
10
10
19.89924
0.999982
0.499996

21
10
10
19.89924
0.999972
0.499993

22
10
10
19.89924
0.999962
0.499991

23
10
10
19.89924
0.999953
0.499988

24
10
10
19.89925
0.999943
0.499986

25
10
10
19.89925
0.999933
0.499983

26
10
10
19.89925
0.999923
0.499981

27
10
10
19.89925
0.999913
0.499978

28
10
10
19.89925
0.999903
0.499976

29
10
10
19.89925
0.999893
0.499973

30
10
10
19.89925
0.999884
0.499971

31
10
10
19.89925
0.999874
0.499968

32
10
10
19.89925
0.999864
0.499966

33
10
10
19.89925
0.999854
0.499964

34
10
10
19.89926
0.999844
0.499961

35
10
10
19.89926
0.999834
0.499959

36
10
10
19.89926
0.999825
0.499956

37
10
10
19.89926
0.999815
0.499954

38
10
10
19.89926
0.999805
0.499951

39
10
10
19.89926
0.999795
0.499949

40
10
10
19.89926
0.999785
0.499946

41
10
10
19.89926
0.999775
0.499944

42
10
10
19.89926
0.999765
0.499941

43
10
10
19.89926
0.999756
0.499939

44
10
10
19.89927
0.999746
0.499936

45
10
10
19.89927
0.999736
0.499934

46
10
10
19.89927
0.999726
0.499932

47
10
10
19.89927
0.999716
0.499929

48
10
10
19.89927
0.999706
0.499927

49
10
10
19.89927
0.999697
0.499924

50
10
10
19.89927
0.999687
0.499922

51
10
10
19.89927
0.999677
0.499919

52
10
10
19.89927
0.999667
0.499917

53
10
10
19.89927
0.999657
0.499914

54
10
10
19.89928
0.999647
0.499912

55
10
10
19.89928
0.999637
0.499909

56
10
10
19.89928
0.999628
0.499907

57
10
10
19.89928
0.999618
0.499904

58
10
10
19.89928
0.999608
0.499902

59
10
10
19.89928
0.999598
0.499899

60
10
10
19.89928
0.999588
0.499897

61
10
10
19.89928
0.999578
0.499895

62
10
10
19.89928
0.999568
0.499892

63
10
10
19.89928
0.999559
0.49989

64
10
10
19.89929
0.999549
0.499887

65
10
10
19.89929
0.999539
0.499885

66
10
10
19.89929
0.999529
0.499882

67
10
10
19.89929
0.999519
0.49988

68
10
10
19.89929
0.999509
0.499877

69
10
10
19.89929
0.9995
0.499875

70
10
10
19.89929
0.99949
0.499872

71
10
10
19.89929
0.99948
0.49987

72
10
10
19.89929
0.99947
0.499867

73
10
10
19.89929
0.99946
0.499865

74
10
10
19.8993
0.99945
0.499863

75
10
10
19.8993
0.99944
0.49986

76
10
10
19.8993
0.999431
0.499858

77
10
10
19.8993
0.999421
0.499855

78
10
10
19.8993
0.999411
0.499853

79
10
10
19.8993
0.999401
0.49985

80
10
10
19.8993
0.999391
0.499848

81
10
10
19.8993
0.999381
0.499845

82
10
10
19.8993
0.999371
0.499843

83
10
10
19.8993
0.999362
0.49984

84
10
10
19.89931
0.999352
0.499838

85
10
10
19.89931
0.999342
0.499835

86
10
10
19.89931
0.999332
0.499833

87
10
10
19.89931
0.999322
0.499831

88
10
10
19.89931
0.999312
0.499828

89
10
10
19.89931
0.999303
0.499826

90
10
10
19.89931
0.999293
0.499823

91
10
10
19.89931
0.999283
0.499821

92
10
10
19.89931
0.999273
0.499818

93
10
10
19.89931
0.999263
0.499816

94
10
10
19.89932
0.999253
0.499813

95
10
10
19.89932
0.999243
0.499811

96
10
10
19.89932
0.999234
0.499808

97
10
10
19.89932
0.999224
0.499806

98
10
10
19.89932
0.999214
0.499803

99
10
10
19.89932
0.999204
0.499801

100
10
10
19.89932
0.999194
0.499799

101
10
10
19.89932
0.999184
0.499796

102
10
10
19.89932
0.999175
0.499794

103
10
10
19.89932
0.999165
0.499791

104
10
10
19.89933
0.999155
0.499789

105
10
10
19.89933
0.999145
0.499786

106
10
10
19.89933
0.999135
0.499784