The new data
of integration and analysis
of the 30 simulations of 3-body periodic free fall simulations.
Alexander Gofen, December 2021
These 30 simulations of 3-body periodic free fall cases with equal masses were initially reported by Xiaoming Li and Shijun Liao in 2018:
http://numericaltank.sjtu.edu.cn/free-fall-3b/free-fall-3b-movies.htm
https://doi.org/10.1016/j.newast.2019.01.003
Below follows the computer data in support of the findings reported here.
#1, HalfPeriod = 1.0870484632;š 254 steps (0 step splits).š Total: 254.š Took 0.046881 sec.
Initial edges
ao1 = 0.572637259800556
ao2 = 0.607722685204271
ao3 = 1
Final edges
a1 = 0.866632205927504
a2 = 0.416307142567752
a3 = 1.19641713142014
The best Proportions
a2/ao1 = 0.726999746249045
a1/ao2 = 1.42603234505917
a3/ao3 = 1.19641713142014
No similarity
Final velocities
4.69201525612887E-009
5.80851143543854E-009
-3.98598884727846E-010
3.49416540245241E-009
-4.29341636906406E-009
-9.30267683904969E-009
========================================
#2, HalfPeriod = 0.8448182464;š 266 steps (0 step splits).š Total: 266.š Took 0.046465 sec.
Initial edges
ao1 = 0.353447287737379
ao2 = 0.73191686113172
ao3 = 1
Final edges
a1 = 0.519096075201661
a2 = 0.483476350302595
a3 = 0.832797261244673
The best Proportions
a2/ao1 = 1.36788813233681
a1/ao2 = 0.70922819621755
a3/ao3 = 0.832797261244673
No similarity
Final velocities
1.84847592293928E-009
2.97061806232781E-009
-1.41089078927717E-009
2.15359327571628E-009
-4.37585143548682E-010
-5.12421135046498E-009
========================================
#3, HalfPeriod = 2.2709562794;š 415 steps (0 step splits).š Total: 415.š Took 0.071382 sec.
Initial edges
ao1 = 0.645756550176801
ao2 = 0.727691128224223
ao3 = 1
Final edges
a1 = 0.519220183357862
a2 = 0.852431244261169
a3 = 1.21403381063613
The best Proportions
a1/ao1 = 0.804049425771532
a2/ao2 = 1.1714190419517
a3/ao3 = 1.21403381063613
No similarity
Final velocities
3.89925732057172E-009
4.31299112774815E-009
9.63303487628783E-009
-1.54022823774323E-009
-1.35322922071391E-008
-2.77276288808724E-009
========================================
#4, HalfPeriod = 2.57931955145;š 584 steps (0 step splits).š Total: 584.š Took 0.097313 sec.
Initial edges
ao1 = 0.656114690088622
ao2 = 0.894333471111357
ao3 = 1
Final edges
a1 = 1.00000000002744
a2 = 0.894333471345107
a3 = 0.656114689950851
The best Proportions
a3/ao1 = 0.99999999979002
a2/ao2 = 1.00000000026137
a1/ao3 = 1.00000000002744
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 93.9289556195626œ 15.2469889476221œ 24.7954758122167œ
a2 133.971420366541œ 55.2894536946006œ 15.2469889347618œ
a3 147.346612970012œ 133.971420358047œ 93.9289555982083œ
Correspondence of edges
ao1 ao2 ao3
ša3ššš a2ššš a1
Permutation
123
321
Final velocities
-4.28584709035567E-010
-2.37367255134091E-010
1.74820772747042E-010
4.17386302024202E-010
2.53763924491474E-010
-1.80019034462126E-010
========================================
#5, HalfPeriod = 2.48238475725;š 610 steps (0 step splits).š Total: 610.š Took 0.102214 sec.
Initial edges
ao1 = 0.686289213357226
ao2 = 0.804409980650713
ao3 = 1
Final edges
a1 = 0.51131491557514
a2 = 1.01096250172966
a3 = 1.32387108532136
The best Proportions
a1/ao1 = 0.745042914304106
a2/ao2 = 1.25677518435544
a3/ao3 = 1.32387108532136
No similarity
Final velocities
-9.75787326797525E-009
-1.10250875528665E-009
-1.08593175709594E-008
1.68599670846931E-008
2.06171908450077E-008
-1.57574583028121E-008
========================================
#6, HalfPeriod = 2.43360014965;š 1348 steps (0 step splits).š Total: 1348.š Took 0.217915 sec.
Initial edges
ao1 = 0.569625019297788
ao2 = 0.97618618747143
ao3 = 1
Final edges
a1 = 1.00000000202946
a2 = 0.976186185441073
a3 = 0.569625019472307
The best Proportions
a3/ao1 = 1.00000000030637
a2/ao2 = 0.999999997920113
a1/ao3 = 1.00000000202946
Angles between edges
ššššššššššššššššš ao1šššššššššššššššššššššššššššššššššš šao2ššššššššššššššššššššššššššššš ao3
a1 33.4281661650412œ 42.1271972154496œ 75.6053289606549œ
a2 66.9062979114059œ 8.64906546908488œ 42.1271972142901œ
a3 142.461661681974œ 66.9062983014829œ 33.4281665562776œ
Correspondence of edges
ao1 ao2 ao3
ša3ššš a2ššš a1
Permutation
123
321
Final velocities
8.85865490185057E-009
7.3268894074105E-009
-3.68612207960915E-009
-1.23664665743978E-008
-5.17253289974493E-009
5.03957702993737E-009
========================================
#7, HalfPeriod = 2.7227795554;š 742 steps (0 step splits).š Total: 742.š Took 0.123361 sec.
Initial edges
ao1 = 0.681773207106269
ao2 = 0.783059117517935
ao3 = 1
Final edges
a1 = 1.25531246764058
a2 = 0.432096830797854
a3 = 1.58003911803375
The best Proportions
a2/ao1 = 0.63378382472942
a1/ao2 = 1.60308773572492
a3/ao3 = 1.58003911803375
No similarity
Final velocities
-3.78487788614719E-009
4.5888135913822E-009
3.34695531565679E-010
1.93745887206284E-009
3.45018233731051E-009
-6.52627241712251E-009
========================================
#8, HalfPeriod = 2.5591645882;š 998 steps (0 step splits).š Total: 998.š Took 0.162514 sec.
Initial edges
ao1 = 0.566715076527791
ao2 = 0.946252265711369
ao3 = 1
Final edges
a1 = 0.566715076561325
a2 = 0.946252265151476
a3 = 1.00000000032959
The best Proportions
a1/ao1 = 1.00000000005917
a2/ao2 = 0.999999999408305
a3/ao3 = 1.00000000032959
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 38.8690207477758œ 117.219875343873œ 150.933490915343œ
a2 117.219875429262œ 164.42926997464œ 130.715654403171œ
a3 150.933491002139œ 130.715654401763œ 97.0020388302941œ
Correspondence of edges
ao1 ao2 ao3
ša1ššš a2ššš a3
Permutation
123
123
Final velocities
-1.51048418247993E-009
6.59224679445941E-010
-1.57756571794423E-009
-2.13133476981224E-009
3.08804982757424E-009
1.47211007873484E-009
========================================
#9, HalfPeriod = 2.59998784075;š 862 steps (0 step splits).š Total: 862.š Took 0.142159 sec.
Initial edges
ao1 = 0.657224861170368
ao2 = 0.746042662279047
ao3 = 1
Final edges
a1 = 0.418696403387921
a2 = 1.20911852734592
a3 = 1.54669230607388
The best Proportions
a1/ao1 = 0.637067201995857
a2/ao2 = 1.62070963026732
a3/ao3 = 1.54669230607388
No similarity
Final velocities
4.86142058771208E-009
-9.47748416712948E-010
8.16237099253696E-009
-1.10729692186229E-008
-1.30237915488106E-008
1.20207176001471E-008
========================================
#10, HalfPeriod = 2.4457471081;š 506 steps (0 step splits).š Total: 506.š Took 0.084257 sec.
Initial edges
ao1 = 0.46474868843111
ao2 = 0.913197648375442
ao3 = 1
Final edges
a1 = 0.464748688619675
a2 = 0.913197647909834
a3 = 0.999999999688458
The best Proportions
a1/ao1 = 1.00000000040573
a2/ao2 = 0.999999999490135
a3/ao3 = 0.999999999688458
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 97.4211319750022œ 10.7928104307885œ 16.849104623815œ
a2 10.7928104276219œ 75.8355111165917œ 103.477426171195œ
a3 16.8491046486026œ 103.477426192816œ 131.11934124742œ
Correspondence of edges
ao1 ao2 ao3
ša1ššš a2ššš a3
Permutation
123
123
Final velocities
-3.28984116141264E-010
1.01889721362755E-009
-2.86138741553596E-009
-1.03587999886984E-009
3.19037155266373E-009
1.6982755490689E-011
========================================
#11, HalfPeriod = 2.1373553632;š 944 steps (0 step splits).š Total: 944.š Took 0.160084 sec.
Initial edges
ao1 = 0.362278706239516
ao2 = 0.965726821308478
ao3 = 1
Final edges
a1 = 0.884397512716539
a2 = 0.751618380818297
a3 = 0.428335304775042
The best Proportions
a3/ao1 = 1.18233640950416
a2/ao2 = 0.778292954315918
a1/ao3 = 0.884397512716539
No similarity
Final velocities
1.60631454143069E-008
-1.93862848632553E-009
-1.15198748849052E-008
-7.36645991180864E-009
-4.54327057494327E-009
9.30508825051327E-009
========================================
#12, HalfPeriod = 2.1381634767;š 930 steps (0 step splits).š Total: 930.š Took 0.155005 sec.
Initial edges
ao1 = 0.36379418308769
ao2 = 0.95474135494826
ao3 = 1
Final edges
a1 = 0.800513479863829
a2 = 0.686199523272231
a3 = 0.478535114791668
The best Proportions
a3/ao1 = 1.31540067719093
a2/ao2 = 0.718728187184704
a1/ao3 = 0.800513479863829
No similarity
Final velocities
-3.8075705336926E-009
6.13012713852922E-009
5.38739695580003E-009
-2.50478458812289E-009
-1.57982639475843E-009
-3.62534258528799E-009
========================================
#13, HalfPeriod = 2.98529966345;š 888 steps (0 step splits).š Total: 888.š Took 0.147908 sec.
Initial edges
ao1 = 0.597785204114922
ao2 = 0.857199210019888
ao3 = 1
Final edges
a1 = 1.2491981993678
a2 = 1.19266118202226
a3 = 0.454451039469221
The best Proportions
a3/ao1 = 0.760224636442916
a2/ao2 = 1.39134657158001
a1/ao3 = 1.2491981993678
No similarity
Final velocities
-2.76692474062367E-009
6.13512844940454E-009
4.23257892766806E-009
-4.71973654168916E-009
-1.46565413611569E-009
-1.41539189214691E-009
========================================
#14, HalfPeriod = 3.8241131109;š 766 steps (0 step splits).š Total: 766.š Took 0.127649 sec.
Initial edges
ao1 = 0.679289996641939
ao2 = 0.921456266427119
ao3 = 1
Final edges
a1 = 0.679289996759996
a2 = 0.999999999906395
a3 = 0.921456266288986
The best Proportions
a1/ao1 = 1.00000000017379
a3/ao2 = 0.999999999850092
a2/ao3 = 0.999999999906395
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 5.33608528907246E-008œ 75.6383359097635œ 116.790552658371œ
a2 63.2094472309557œ 138.847783191836œ 179.999999940341œ
a3 104.361663992048œ 179.999999953788œ 138.847783298464œ
Correspondence of edges
ao1 ao2 ao3
ša1ššš a3ššš a2
Permutation
123
132
ao1||a1
ao2||a3
ao3||a2
Final velocities
-2.81389363172109E-010
-1.89353579775668E-010
3.3674373726193E-010
-4.83937461027224E-011
-5.53543426373704E-011
2.37747320860568E-010
========================================
#15, HalfPeriod = 3.20200098125;š 497 steps (0 step splits).š Total: 497.š Took 0.083289 sec.
Initial edges
ao1 = 0.436752842635604
ao2 = 0.84000976765171
ao3 = 1
Final edges
a1 = 0.436752842610689
a2 = 1.00000000015532
a3 = 0.84000976763397
The best Proportions
a1/ao1 = 0.999999999942955
a3/ao2 = 0.999999999978881
a2/ao3 = 1.00000000015532
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššš ššao3
a1 2.24813269240838E-007œ 98.1192298360194œ 123.737606145236œ
a2 56.2623942798428œ 154.381623892635œ 179.999999798567œ
a3 81.8807705812267œ 179.999999808532œ 154.381623496765œ
Correspondence of edges
ao1 ao2 ao3
ša1ššš a3ššš a2
Permutation
123
132
ao1||a1
ao2||a3
ao3||a2
Final velocities
1.59891943543773E-010
-2.38673290715695E-010
4.38746287022805E-010
3.27045241555564E-010
-5.98638236177325E-010
-8.83719544346765E-011
========================================
#16, HalfPeriod = 3.26937279405;š 617 steps (0 step splits).š Total: 617.š Took 0.103132 sec.
Initial edges
ao1 = 0.47058769165938
ao2 = 0.71827887142899
ao3 = 1
Final edges
a1 = 0.870430892162538
a2 = 0.437574805235382
a3 = 0.923327306307398
The best Proportions
a2/ao1 = 0.929847535307207
a1/ao2 = 1.21182861808374
a3/ao3 = 0.923327306307398
No similarity
Final velocities
8.08351115906515E-009
8.6240913048561E-009
3.7958650394476E-009
-5.11789547910256E-009
-1.18793762235832E-008
-3.50619577981133E-009
========================================
#17, HalfPeriod = 4.05340742565;š 665 steps (0 step splits).š Total: 665.š Took 0.111089 sec.
Initial edges
ao1 = 0.622323187959103
ao2 = 0.817359130903657
ao3 = 1
Final edges
a1 = 0.556501426090904
a2 = 1.02100547619331
a3 = 0.948796074219301
The best Proportions
a1/ao1 = 0.894232188127105
a3/ao2 = 1.1608068452974
a2/ao3 = 1.02100547619331
No similarity
Final velocities
-6.36996776303572E-010
1.5920278224403E-009
-2.16505405843789E-009
-2.84821212665279E-009
2.80205083930189E-009
1.25618430439037E-009
========================================
#18, HalfPeriod = 2.69762248625;š 1251 steps (0 step splits).š Total: 1251.š Took 0.204697 sec.
Initial edges
ao1 = 0.309097112311281
ao2 = 0.718590490501491
ao3 = 1
Final edges
a1 = 0.309097111598536
a2 = 0.718590493477556
a3 = 1.00000000170251
The best Proportions
a1/ao1 = 0.999999997694106
a2/ao2 = 1.00000000414153
a3/ao3 = 1.00000000170251
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 42.475261539959œ 108.406753649891œ 117.057419661337œ
a2 108.406753346697œ 100.711231463453œ 92.0605654520073œ
a3 117.057419406016œ 92.0605654041339œ 83.4098993926884œ
Correspondence of edges
ao1 ao2 ao3
ša1ššš a2ššš a3
Permutation
123
123
Final velocities
-6.09139093441026E-010
4.30494471823168E-009
-8.16387008256009E-009
1.20806355604974E-008
8.77300915445948E-009
-1.63855802926238E-008
========================================
#19, HalfPeriod = 4.050523709;š 943 steps (0 step splits).š Total: 943.š Took 0.155798 sec.
Initial edges
ao1 = 0.496074907565996
ao2 = 0.572812200041699
ao3 = 1
Final edges
a1 = 0.572812199936607
a2 = 0.496074907644495
a3 = 1.00000000000121
The best Proportions
a2/ao1 = 1.00000000015824
a1/ao2 = 0.999999999816534
a3/ao3 = 1.00000000000121
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 137.019924002653œ 1.50331610105463œ 20.6846187271769œ
a2 84.4568358851656œ 137.019924011127œ 117.838621385005œ
a3 62.1613786232646œ 159.315381273028œ 140.134078646906œ
Correspondence of edges
ao1 ao2 ao3
ša2ššš a1ššš a3
Permutation
123
213
Final velocities
1.67308271810341E-010
3.71973915075851E-010
-1.89597233719125E-011
1.66529639877106E-011
-1.48348556891818E-010
-3.88626881069336E-010
========================================
#20, HalfPeriod = 4.41075095455;š 900 steps (0 step splits).š Total: 900.š Took 0.148016 sec.
Initial edges
ao1 = 0.50495622673102
ao2 = 0.603836666752218
ao3 = 1
Final edges
a1 = 0.57054532177866
a2 = 0.521881491284074
a3 = 1.03349165990653
The best Proportions
a2/ao1 = 1.03351828070846
a1/ao2 = 0.944866970148371
a3/ao3 = 1.03349165990653
No similarity
Final velocities
-2.60625331865581E-009
-1.9387764236181E-009
-2.46467814842173E-009
4.91755506656238E-011
5.07093146590779E-009
1.88960087241376E-009
========================================
#21, HalfPeriod = 2.7112520343;š 1494 steps (0 step splits).š Total: 1494.š Took 0.243828 sec.
Initial edges
ao1 = 0.244664806328298
ao2 = 0.782266109233721
ao3 = 1
Final edges
a1 = 0.273707764999851
a2 = 0.648263619592147
a3 = 0.85510438323065
The best Proportions
a1/ao1 = 1.1187050933373
a2/ao2 = 0.828699609941127
a3/ao3 = 0.85510438323065
No similarity
Final velocities
-1.82701920250567E-009
-3.65151745228918E-009
4.45341399524509E-009
-1.07715936163873E-009
-2.62639489930463E-009
4.72867672411193E-009
========================================
#22, HalfPeriod = 2.7236858497;š 1795 steps (0 step splits).š Total: 1795.š Took 0.292785 sec.
Initial edges
ao1 = 0.245966087104846
ao2 = 0.770004101810938
ao3 = 1
Final edges
a1 = 0.245966088142438
a2 = 0.770004096687312
a3 = 0.999999991949072
The best Proportions
a1/ao1 = 1.00000000421843
a2/ao2 = 0.999999993345976
a3/ao3 = 0.999999991949072
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 87.6043906513413œ 68.6019765891483œ 74.2970072774863œ
a2 68.6019736356242œ 135.191659123886œ 129.496628435548œ
a3 74.2970050620852œ 129.496627697425œ 123.801597009087œ
Correspondence of edges
ao1 ao2 ao3
ša1ššš a2ššš a3
Permutation
123
123
Final velocities
-7.5933034627829E-009
-1.39570028743378E-008
-6.80829967783411E-009
-5.91206006827951E-008
1.44016030984568E-008
7.30776034174097E-008
========================================
#23, HalfPeriod = 4.24869750795;š 982 steps (0 step splits).š Total: 982.š Took 0.162128 sec.
Initial edges
ao1 = 0.501239096468276
ao2 = 0.527663184454187
ao3 = 1
Final edges
a1 = 0.579378212139716
a2 = 0.477840861129729
a3 = 0.933298136228007
The best Proportions
a2/ao1 = 0.953319213318733
a1/ao2 = 1.09800764807767
a3/ao3 = 0.933298136228007
No similarity
Final velocities
-1.57756291337748E-009
-5.86367709351802E-011
-2.92085679156739E-010
1.02586635176695E-009
1.8696485894002E-009
-9.67229579252899E-010
========================================
#24, HalfPeriod = 4.7122162672;š 968 steps (0 step splits).š Total: 968.š Took 0.158934 sec.
Initial edges
ao1 = 0.511991659345909
ao2 = 0.620785780313771
ao3 = 1
Final edges
a1 = 0.565374734177531
a2 = 0.537062141254861
a3 = 1.07146897754872
The best Proportions
a2/ao1 = 1.0489665826607
a1/ao2 = 0.910740471361581
a3/ao3 = 1.07146897754872
No similarity
Final velocities
-2.71696106089151E-009
-1.87260278471617E-009
-1.61342787868553E-009
-1.82369241602076E-010
4.33038894554607E-009
2.05497203033318E-009
========================================
#25, HalfPeriod = 2.89052023895;š 2264 steps (0 step splits).š Total: 2264.š Took 0.371775 sec.
Initial edges
ao1 = 0.237958481621947
ao2 = 0.801383085656181
ao3 = 1
Final edges
a1 = 0.237958482449773
a2 = 0.801383079746826
a3 = 0.99999999538486
The best Proportions
a1/ao1 = 1.00000000347887
a2/ao2 = 0.999999992626055
a3/ao3 = 0.99999999538486
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššš ššao3
a1 29.9131648425869œ 112.238395218678œ 120.633895872402œ
a2 112.238395468441œ 105.610044470294œ 97.2145438165699œ
a3 120.63389614317œ 97.2145437955651œ 88.8190431418409œ
Correspondence of edges
ao1 ao2 ao3
ša1ššš a2ššš a3
Permutation
123
123
Final velocities
1.78327288962003E-009
-9.28528738061907E-009
2.92091492197285E-008
-2.99235871624063E-008
-3.09924219573553E-008
3.9208874604066E-008
========================================
#26, HalfPeriod = 5.0108652409;š 1419 steps (0 step splits).š Total: 1419.š Took 0.231581 sec.
Initial edges
ao1 = 0.521409117437041
ao2 = 0.580774996660905
ao3 = 1
Final edges
a1 = 0.889797446725436
a2 = 0.370074068035938
a3 = 1.22894822519622
The best Proportions
a2/ao1 = 0.7097575697468
a1/ao2 = 1.53208635330587
a3/ao3 = 1.22894822519622
No similarity
Final velocities
5.27075403137514E-009
1.33564328087929E-008
3.57313684289627E-009
3.20884800461817E-009
-8.84389087674474E-009
-1.6565280844304E-008
========================================
#27, HalfPeriod = 5.1670439078;š 1030 steps (0 step splits).š Total: 1030.š Took 0.171388 sec.
Initial edges
ao1 = 0.383169707015193
ao2 = 0.671957136857783
ao3 = 1
Final edges
a1 = 0.671957138828835
a2 = 0.383169706144309
a3 = 1.0000000015663
The best Proportions
a2/ao1 = 0.999999997727157
a1/ao2 = 1.0000000029333
a3/ao3 = 1.0000000015663
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 38.7401826467327œ 179.999999867939œ 166.126225147501œ
a2 179.99999997332œ 38.740182748141œ 24.866407766191œ
a3 155.133592232403œ 13.8737750085871œ 2.66804264453623E-008œ
Correspondence of edges
ao1 ao2 ao3
ša2ššš a1ššš a3
Permutation
123
213
ao1||a2
ao2||a1
ao3||a3
Final velocities
4.88310367868002E-009
-2.95439262568413E-009
3.36011390862949E-009
4.61565620908666E-010
-8.24321759329972E-009
2.49282700364383E-009
========================================
#28, HalfPeriod = 5.92137948935;š 1227 steps (0 step splits).š Total: 1227.š Took 0.202606 sec.
Initial edges
ao1 = 0.524365290707931
ao2 = 0.648201419235729
ao3 = 1
Final edges
a1 = 0.928783526346898
a2 = 0.390762512913875
a3 = 1.22846866613691
The best Proportions
a2/ao1 = 0.745210485587856
a1/ao2 = 1.43286253128232
a3/ao3 = 1.22846866613691
No similarity
Final velocities
5.72760607337104E-009
8.79852228680383E-009
3.41334205527838E-009
1.18503715137826E-009
-9.14094811074653E-009
-9.98355945109426E-009
========================================
#29, HalfPeriod = 3.646941059;š 2350 steps (0 step splits).š Total: 2350.š Took 0.383539 sec.
Initial edges
ao1 = 0.24324751934175
ao2 = 0.822299525395652
ao3 = 1
Final edges
a1 = 0.243247518849951
a2 = 0.822299529094189
a3 = 1.00000000257555
The best Proportions
a1/ao1 = 0.999999997978196
a2/ao2 = 1.0000000044978
a3/ao3 = 1.00000000257555
Angles between edges
ššššššššššššššššš ao1ššššššššššššššššššššššššššššššššššš ao2ššššššššššššššššššššššššššššš ao3
a1 49.5539386272383œ 81.8651326332434œ 92.3752474118586œ
a2 81.8651323758748œ 146.715796363643œ 136.205681585028œ
a3 92.3752471477452œ 136.205681591773œ 125.695566813158œ
Correspondence of edges
ao1 ao2 ao3
ša1ššš a2ššš a3
Permutation
123
123
Final velocities
-4.35082468140733E-010
5.47041649075864E-009
-1.51353003260516E-008
1.82362110440909E-008
1.55703827663707E-008
-2.37066275842281E-008
========================================
#30, HalfPeriod = 3.0919988294;š 3326 steps (0 step splits).š Total: 3326.š Took 0.535024 sec.
Initial edges
ao1 = 0.197997380720087
ao2 = 0.84825304182892
ao3 = 1
Final edges
a1 = 0.199777943909853
a2 = 0.82489784491022
a3 = 0.988497373898988
The best Proportions
a1/ao1 = 1.00899286234641
a2/ao2 = 0.972466710088839
a3/ao3 = 0.988497373898988
No similarity
Final velocities
-3.09127018087252E-007
-1.4727981482216E-007
-7.39582387753688E-007
-9.72884906216035E-007
1.0487094060464E-006
1.12016472116146E-006
========================================