Solutions for Ancient Greek Geometry (https://sciencevsmagic.net/geo)
Most solutions taken from the about thread. See the comments below for more additions since my last check-in.
- Triangle: 5 moves
- Triangle: In-Origin, 6 moves
- Square: In-Origin, 8 moves; an elegant alternate 8-move solution
- Pentagon: 11 moves by John Chrysostom. Two non-in-origin solutions: by Thomas, alternative. Three more: Alternative, 16 moves based on this construction. Alternative found from the previous by making a pentagram with a point already found by not needing the upper points. Another alternative by using someting related in the in-origin pentagon with the pentagon using this construction.
- Hexagon, In-Origin, 9 moves
- Octagon: 13 moves by underwatercolor
- In-Origin: 14 moves. Alternative by @mrflip; another Alternative by @mrflip
- Decagon, In-Origin, 16 moves
- Dodecagon: 16 moves In-origin: 17 moves
- In-origin pentadecagon: 22 moves by @mrflip
- Hexadecagon: 23 moves by @ILoveMath62 In-Origin: 24 moves
- Heptadecagon, 38 moves by @ILoveMath62 In-origin: 40 moves by @ILoveMath62
- In-origin icosagon: 28 moves by @mrflip
- In-origin icositetragon: 30 moves by @mrflip
- In-origin triacontagon: 37 moves (36 reported possible)
- In-origin triacontakaidigon: 42 moves (40 reported possible)
- Triacontakaitetragon, 55 moves by @ILoveMath62. In-origin: 58 moves (57 reported possible)
- Tetracontagon: 49 moves by @ILoveMath62 In-origin: 51 moves by @mrflip
- In-origin tetracontakaioctagon: 55 moves by @ILoveMath62
- Pentacontakaimonogon, 75 moves reported possible
- Hexacontagon, 69 moves reported possible
- Hexacontakaitetragon, 76 moves reported possible
- Hexacontakaioctagon, 91 moves reported possible
- Circles 2, 5 moves
- Circles 2, In-Origin, 7 moves
- Circle 3, 9 moves
- Circle 3, In-Origin, 10 moves by John Chrysostom
- Circle 4, In-Origin, 12 moves by John Chrysostom
- Circle 5, 15 moves by @ILoveMath62
- Circle 5, In-Origin, 23 moves from @pizzystrizzy
- Circle 7, 13 moves by Jason
- Circle 7, In-Origin, 14 moves by @bikerusl
- Circle 13, 40 moves by @ILoveMath62
- Circle 15, 41 moves by @ILoveMath62
- Circle 19, 36 moves by @ILoveMath62
- Origin circle circumscribed triangle: 6 moves by John Chrysostom
- Origin circle circumscribed square: 10 moves
- Origin circle circumscribed pentagon: 16 moves
- Origin circle circumscribed hexagon: 11 moves
Abuse of floating-point math can make the widget approve non-constructible polygons (polygons with edge count 7, 9, 11, 13, 14, 18, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 33, 35, ..., which cannot be precisely constructed using straightedge and compass):
- pseudo-digon: 11 moves
- pseudo-heptagon: 16 moves by @ILoveMath62
- pseudo-nonagon: 19 moves by @ILoveMath62
- pseudo-hendecagon: 27 moves by @ILoveMath62
- pseudo-nonadecagon: 47 moves by @ILoveMath62
- pseudo-icosipentagon: 44 moves by @ILoveMath62
- These polygons are ones that can't be approximated easily. They can only be made from a neusis construction, angle trisection, or you approximating it yourself. (The 13-gon below used to come from an approximation, which was when it was 49 moves instead of 30. It now is from an approximation that wasn't shared on the web) All these approximations below aren't shared on the web, they're all from tangent approximations. They're all by me.
- Tridecagon: 30 moves
- Icositrigon: 46 moves
- Icosiheptagon: 49 moves
- Icosinonagon: 57 moves
- Triacontakaihenagon: 63 moves
- Triacontakaiheptagon: 65 moves
- Tetracontakaihenagon: 62 moves
- Tetracontakaitrigon: 68 moves
- Tetracontakaipentagon: 67 moves
- Tetracontakaiheptagon: 77 moves
- Tetracontakainonagon: 79 moves
- Pentacontakaitrigon: 79 moves
- Pentacontakainonagon: 87 moves
- These are polygons that can be made from others. (I'll be showing only the non-constructables)
- Tetradecagon: 24 moves from heptagon (23 moves reported possible)
- Octadecagon: 32 moves from this nonagon approximation
- Icosihenagon: 30 moves from heptagon
- Icosidigon: 46 moves from this hendecagon approximation
- Icosihexagon: 43 moves from tridecagon
- Icosioctagon: 36 moves from heptagon
- Triacontakaitrigon, 58 moves reported possible
- Triacontakaipentagon: 52 moves from heptagon. 50 is possible by making it in the origin circle and not making the very small circle, but the error would probably be too large.
- Triacontakaihexagon: 52 moves from octadecagon
- (coming soon)
- Triacontakainonagon: 77 moves from this tridecagon approximation
- Tetracontakaidigon: 50 moves from heptagon. This probably won't load.
- Tetracontakaitetragon, 68 moves reported possible.
- Tetracontakaihexagon: 69 moves from icositrigon
- Pentacontagon: 70 moves from icosipentagon (69 moves reported possible)
- Pentacontakaidigon, 74 moves reported possible.
- Pentacontakaitetragon: 76 moves from icosiheptagon
- (coming soon)
- Pentacontakaihexagon, 70 moves reported possible
- Pentacontakaiheptagon: 88 moves from nonadecagon
- Pentacontakaioctagon, 86 moves reported possible