Equal circles in regular polygons
Pack n equal circles into the regular m-gon with centre (1,1), circumradius 1, and first vertex (2,1) so as to maximise their common radius.
Formal definition
- ContainerThe editor and certificate normalise the container to the exact regular m-gon with centre (1,1), circumradius 1, and first vertex (2,1), while public scores follow the literature convention. Boundary contact is allowed.
- SubmissionSubmit {radius, placements:[{x,y,turn},…]}, with each value written as a decimal string of at most nine places. Here x, y are centre coordinates; circles require turn = 0 and polygons use turn = tan(θ/2). Coordinates and turn must lie in [−4, 4], with 0 < radius ≤ 4.
- ConstraintsExactly n congruent pieces lie wholly inside the container with pairwise disjoint interiors. Polygons may rotate independently by arbitrary angles.
- PrecisionInput decimals are parsed as exact rationals and regular-polygon vertices are defined algebraically, with zero floating-point tolerance in feasibility checks.
- ObjectiveMaximise the circle radius r (with container circumradius fixed at 1).
Getting a feel for it
Literature targets and coordinate certificates
Literature targets are converted at their published precision, while nine-decimal coordinate certificates are stored and displayed alongside the source values. Pentagon and hexagon rows n = 41–100 and octagon rows n = 41–48 cite Packomania's value and author without importing its coordinates; they start from an ordinary site grid baseline.
SourceONE LEADERBOARD PER n
Current best solutions by n
Smaller instances have dedicated visual pages for inspection and interactive editing, while larger n are consolidated in the index table below for direct comparison and submission.
Discussion (1) ↓Instancem = 5 · n = 1
CURRENT RECORD(1+√5)/4
Proven optimum
Answer sourcePackomania (author unspecified)
Solution methodPublished reference construction
Instancem = 5 · n = 2
CURRENT RECORD(1+√5)√(10+2√5)/(4(1+√5+√(10+2√5)))
Proven optimum
Answer sourcePackomania (author unspecified)
Solution methodPublished reference construction
Instancem = 5 · n = 3
CURRENT RECORD0.389795792best known [0.389795792432, 0.389795792434]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 4
CURRENT RECORD0.354680462best known [0.354680462503, 0.354680462505]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 5
CURRENT RECORD0.340440645best known [0.340440645253, 0.340440645255]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 6
CURRENT RECORD0.309016994best known [0.309016994374, 0.309016994376]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 7
CURRENT RECORD0.277511094best known [0.277511095116, 0.277511095118]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 8
CURRENT RECORD0.257541824best known [0.257541824499, 0.257541824501]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 9
CURRENT RECORD0.243640224best known [0.243640224398, 0.2436402244]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 10
CURRENT RECORD0.230721507best known [0.230721507965, 0.230721507967]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 11
CURRENT RECORD0.224333593best known [0.224333593339, 0.224333593341]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 5 · n = 12
CURRENT RECORD0.21738464best known [0.21738464052, 0.217384640522]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 13
CURRENT RECORD0.207999994best known [0.207999994721, 0.207999994723]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 14
CURRENT RECORD0.202386815best known [0.202386816022, 0.202386816024]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 15
CURRENT RECORD0.197735768best known [0.197735768365, 0.197735768367]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 5 · n = 16
CURRENT RECORD0.191785608best known [0.191785609134, 0.191785609136]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 17
CURRENT RECORD0.183126736best known [0.183126736786, 0.183126736788]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 18
CURRENT RECORD0.178473321best known [0.178473321195, 0.178473321197]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 19
CURRENT RECORD0.173441904best known [0.173441904329, 0.173441904331]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 5 · n = 20
CURRENT RECORD0.169279411best known [0.169279411748, 0.16927941175]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 21
CURRENT RECORD0.165404018best known [0.165404018639, 0.165404018641]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 22
CURRENT RECORD0.161673301best known [0.161673301785, 0.161673301787]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 23
CURRENT RECORD0.158923367best known [0.158923367388, 0.15892336739]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 5 · n = 24
CURRENT RECORD0.156027298best known [0.156027298449, 0.156027298451]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 5 · n = 25
CURRENT RECORD0.15312221best known [0.153122210788, 0.15312221079]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 26
CURRENT RECORD0.150683336best known [0.150683336699, 0.150683336701]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 27
CURRENT RECORD0.148137584best known [0.148137584794, 0.148137584796]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 28
CURRENT RECORD0.145444423best known [0.145444423783, 0.145444423785]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 29
CURRENT RECORD0.143333012best known [0.143333013134, 0.143333013136]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 30
CURRENT RECORD0.141698173best known [0.141698173814, 0.141698173816]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 31
CURRENT RECORD0.138616362best known [0.138616362209, 0.138616362211]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 5 · n = 32
CURRENT RECORD0.13579361best known [0.135793611067, 0.135793611069]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 33
CURRENT RECORD0.134134799best known [0.134134799537, 0.134134799539]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 34
CURRENT RECORD0.131960534best known [0.131960534657, 0.131960534659]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 5 · n = 35
CURRENT RECORD0.130170592best known [0.130170592941, 0.130170592943]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 36
CURRENT RECORD0.128215138best known [0.128215138244, 0.128215138246]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 5 · n = 37
CURRENT RECORD0.126679668best known [0.126679668745, 0.126679668747]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 38
CURRENT RECORD0.125056797best known [0.125056798043, 0.125056798045]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 5 · n = 39
CURRENT RECORD0.124185741best known [0.124185741466, 0.124185741468]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 5 · n = 40
CURRENT RECORD0.122413791best known [0.122413791779, 0.122413791781]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 6 · n = 1
CURRENT RECORD√3/2
Proven optimum
Answer sourcePackomania (author unspecified)
Solution methodPublished reference construction
Instancem = 6 · n = 2
CURRENT RECORD2√3−3
Proven optimum
Answer sourcePackomania (author unspecified)
Solution methodPublished reference construction
Instancem = 6 · n = 3
CURRENT RECORD√3/4
Proven optimum
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 4
CURRENT RECORD0.375015221best known [0.37501522134, 0.375015221342]
Hard
Answer sourceShahriar Manzoor
Solution methodPublished reference construction
Instancem = 6 · n = 5
CURRENT RECORD0.33340497best known [0.333404971007, 0.333404971009]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 6
CURRENT RECORD0.316987297best known [0.316987298107, 0.316987298109]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 7
CURRENT RECORD0.316987297best known [0.316987298107, 0.316987298109]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 8
CURRENT RECORD0.26958537best known [0.269585370785, 0.269585370787]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 9
CURRENT RECORD0.249261972best known [0.249261972965, 0.249261972967]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 10
CURRENT RECORD0.242756322best known [0.24275632254, 0.242756322542]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 11
CURRENT RECORD0.232050807best known [0.232050807568, 0.23205080757]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 12
CURRENT RECORD0.232050807best known [0.232050807568, 0.23205080757]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 13
CURRENT RECORD0.21650635best known [0.216506350945, 0.216506350947]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 6 · n = 14
CURRENT RECORD0.214290684best known [0.214290684432, 0.214290684434]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 15
CURRENT RECORD0.20155921best known [0.201559210542, 0.201559210544]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 6 · n = 16
CURRENT RECORD0.200025787best known [0.200025787345, 0.200025787347]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 6 · n = 17
CURRENT RECORD0.194813312best known [0.194813312768, 0.19481331277]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 6 · n = 18
CURRENT RECORD0.19399769best known [0.193997690564, 0.193997690566]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 19
CURRENT RECORD0.19399769best known [0.193997690564, 0.193997690566]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 20
CURRENT RECORD0.17615287best known [0.176152871146, 0.176152871148]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 21
CURRENT RECORD0.17514975best known [0.175149750124, 0.175149750126]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 6 · n = 22
CURRENT RECORD0.168017815best known [0.168017815755, 0.168017815757]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 23
CURRENT RECORD0.166338331best known [0.166338331557, 0.166338331559]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 24
CURRENT RECORD0.163462238best known [0.163462238507, 0.163462238509]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 25
CURRENT RECORD0.159724476best known [0.15972447701, 0.159724477012]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 26
CURRENT RECORD0.158493648best known [0.158493649053, 0.158493649055]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 27
CURRENT RECORD0.158493648best known [0.158493649053, 0.158493649055]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 28
CURRENT RECORD0.15166001best known [0.151660010857, 0.151660010859]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 29
CURRENT RECORD0.150002435best known [0.150002435354, 0.150002435356]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 6 · n = 30
CURRENT RECORD0.150002435best known [0.150002435354, 0.150002435356]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 6 · n = 31
CURRENT RECORD0.144498618best known [0.144498618554, 0.144498618556]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 6 · n = 32
CURRENT RECORD0.142908786best known [0.142897923361, 0.142897923363]
Numerically ahead (under review)
Record holderJoost de Winter
Solution methodAI · OpenAI: GPT-6.1 Sol
Instancem = 6 · n = 33
CURRENT RECORD0.142870299best known [0.142870299181, 0.142870299183]
Hard
Record holdercondor
Solution methodAI · OpenAI: GPT-6.1 Sol
Instancem = 6 · n = 34
CURRENT RECORD0.140313381best known [0.140313381691, 0.140313381693]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 6 · n = 35
CURRENT RECORD0.139827762best known [0.139827762739, 0.139827762741]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 36
CURRENT RECORD0.139768253best known [0.1397682537, 0.139768253702]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 37
CURRENT RECORD0.139768253best known [0.1397682537, 0.139768253702]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 38
CURRENT RECORD0.131624252best known [0.131624252389, 0.131624252391]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 6 · n = 39
CURRENT RECORD0.129882646best known [0.129882647186, 0.129882647188]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 6 · n = 40
CURRENT RECORD0.129711778best known [0.129711778825, 0.129711778827]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 1
CURRENT RECORD√(2+√2)/2
Proven optimum
Answer sourcePackomania (author unspecified)
Solution methodPublished reference construction
Instancem = 8 · n = 2
CURRENT RECORD√(2+√2)/(2+√(2+√2))
Proven optimum
Answer sourcePackomania (author unspecified)
Solution methodPublished reference construction
Instancem = 8 · n = 3
CURRENT RECORD0.435387434best known [0.435387434218, 0.43538743422]
Hard
Record holdercondor
Solution methodAI · OpenAI: GPT-6.1 Sol
Instancem = 8 · n = 4
CURRENT RECORD0.400543816best known [0.400543816309, 0.400543816311]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 5
CURRENT RECORD0.348203325best known [0.348203325453, 0.348203325455]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 6
CURRENT RECORD0.317727657best known [0.317727658061, 0.317727658063]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 8 · n = 7
CURRENT RECORD0.310945216best known [0.31094521683, 0.310945216832]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 8
CURRENT RECORD0.285852433best known [0.285852433676, 0.285852433678]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 9
CURRENT RECORD0.27059805best known [0.270598050072, 0.270598050074]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 10
CURRENT RECORD0.251932403best known [0.251932403489, 0.251932403491]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 11
CURRENT RECORD0.239556874best known [0.23955687425, 0.239556874252]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 12
CURRENT RECORD0.234100964best known [0.234100964946, 0.234100964948]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 8 · n = 13
CURRENT RECORD0.223537235best known [0.22353723521, 0.223537235212]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 14
CURRENT RECORD0.219348902best known [0.219348902643, 0.219348902645]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 15
CURRENT RECORD0.21023689best known [0.210236890634, 0.210236890636]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 16
CURRENT RECORD0.204286601best known [0.204286601357, 0.204286601359]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 17
CURRENT RECORD0.198194125best known [0.198194125495, 0.198194125497]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 18
CURRENT RECORD0.193696359best known [0.193696359492, 0.193696359494]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 19
CURRENT RECORD0.191508243best known [0.191508243903, 0.191508243905]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 20
CURRENT RECORD0.185530744best known [0.185530744907, 0.185530744909]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 8 · n = 21
CURRENT RECORD0.18067026best known [0.180670260258, 0.18067026026]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 22
CURRENT RECORD0.17550094best known [0.175500940766, 0.175500940768]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 8 · n = 23
CURRENT RECORD0.172561559best known [0.172561559661, 0.172561559663]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 24
CURRENT RECORD0.168652863best known [0.168652864097, 0.168652864099]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 8 · n = 25
CURRENT RECORD0.166450891best known [0.166450891365, 0.166450891367]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 26
CURRENT RECORD0.163606136best known [0.163606136258, 0.16360613626]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 27
CURRENT RECORD0.161395047best known [0.161395047684, 0.161395047686]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 8 · n = 28
CURRENT RECORD0.160404294best known [0.160404294688, 0.16040429469]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 29
CURRENT RECORD0.154929849best known [0.154929849311, 0.154929849313]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 30
CURRENT RECORD0.152319579best known [0.152319579408, 0.15231957941]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 31
CURRENT RECORD0.149878153best known [0.149878153405, 0.149878153407]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 32
CURRENT RECORD0.14729738best known [0.147297380424, 0.147297380426]
Hard
Record holderzzzcy
Solution methodAI · OpenAI: GPT-6 Astra
Instancem = 8 · n = 33
CURRENT RECORD0.145306599best known [0.145306599844, 0.145306599846]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
Instancem = 8 · n = 34
CURRENT RECORD0.143477532best known [0.143477532363, 0.143477532365]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 35
CURRENT RECORD0.142256369best known [0.142256369269, 0.142256369271]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 36
CURRENT RECORD0.139934447best known [0.139934447381, 0.139934447383]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 37
CURRENT RECORD0.138229583best known [0.138229583692, 0.138229583694]
Hard
Answer sourceEckard Specht
Solution methodPublished reference construction
Instancem = 8 · n = 38
CURRENT RECORD0.136097981best known [0.136097981332, 0.136097981334]
Hard
Record holderw33d
Solution methodAI · Anthropic: Claude Fable 5.1
Instancem = 8 · n = 39
CURRENT RECORD0.13496283best known [0.134962830725, 0.134962830727]
Hard
Answer sourceStefan Zorcic
Solution methodPublished reference construction
Instancem = 8 · n = 40
CURRENT RECORD0.132682453best known [0.132682454148, 0.13268245415]
Hard
Answer sourcePaolo Amore
Solution methodPublished reference construction
COMPUTATIONAL FRONTIER
N = 41–48 index
Each row is an independently scored sub-problem. External benchmarks retain their published precision, while arena constructions are verified on the exact nine-decimal grid.
NCURRENT RECORDKNOWN BESTRECORD SOURCESTATUS
620.099195312[0.099194901496, 0.099194901498] ↗Joost de Winter#338Numerically ahead (under review)Submit ↗
Data and citation
All sub-problems in this family — authoritative scores, proof status, coordinates, and sources — are published at the stable URL below under CC BY 4.0. Because scores update as records fall, please cite the file's generatedAt timestamp.
GET https://minmaxarena.com/data/circles-in-regular-polygons.json
Cite the frozen 2026-10 edition: live records change, whereas a frozen edition stays fixed and reproducible.
GET https://minmaxarena.com/data/editions/2026-10/circles-in-regular-polygons.json
BibTeX (click to copy)
@misc{minmaxarena-circles-in-regular-polygons-2026-10,
title = {{Equal circles in regular polygons} (P82)},
author = {{MinMax Arena}},
year = {2026},
note = {Machine-verified records, 2026-10 edition},
url = {https://minmaxarena.com/data/editions/2026-10/circles-in-regular-polygons.json},
license = {CC BY 4.0}
}DISCUSSION
Discussion
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