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
- Hexagon, In-Origin, 9 moves
- Square, In-Origin, 8 moves ; an elegant alternate 8-move solution
- Octagon, 13 moves by underwatercolor
- Octagon, In-Origin, 14 moves; Alternative by @mrflip; another Alternative by @mrflip
- Dodecagon, In-Origin, 17 moves alt
- Pentagon, In-Origin, 11 moves by John Chrysostom. Two non-in-origin solutions: by Thomas, alternative
- Alternative, 16 moves based on this construction
- 10-Gon, In-Origin, 17 moves (16 reported possible)
- In-origin 15-gon: 22 moves by @mrflip
- In-Origin 16-gon: 24 moves by John Chrysostom (23 moves reported possible)
- 17-Gon, 45 moves by @mrflip, improving version from @Eddy119 citing H. W. Richmond — 40 moves reported possible! In-Origin, 49 moves by @Eddy119, tweaked by @mrflip
- In-origin 20-gon: 28 moves by @mrflip
- In-origin 24-gon: 30 moves by @mrflip
- In-origin 30-gon: 37 moves reported possible
- In-origin 32-gon: 40 moves reported possible
- 34-gon, 61 moves by @mrflip: 57 moves reported possible. In-origin 34-gon in 65 by @mrflip
- In-origin 40-gon: 51 moves by @mrflip, 49 moves reported possible
- In-origin 48-gon: 56 moves by @mrflip
- 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, 22 moves by @pizzystrizzy
- Circle 5, In-Origin, 23 moves from @pizzystrizzy
- Circle 7, 13 moves by Jason
- Circle 7, In-Origin, 14 moves by @bikerusl
- Circle 15, 47 moves by @pizzystrizzy
- Circle 19, 37 moves by @ pizzystrizzy
- Origin circle circumscribed triangle: 6 moves by John Chrysostom
- Origin circle circumscribed square: 10 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-2-gon in 11 moves
- pseudo-11-gon in 44 moves by @Eddy119
Well, to construct a 13-gon, you have to trisect a certain angle... check http://web.archive.org/web/20151219180208/http://apollonius.math.nthu.edu.tw/d1/ne01/jyt/linkjstor/regular/7.pdf out for 3θ (3 times the desired angle) or https://commons.wikimedia.org/wiki/File:01-Dreizehneck-N%C3%A4herung.svg for a very good approximation... I tried to do both but I just couldn't...