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
i think all non-constructible polygons should theoretically be floating point since mathematically it's not exact? I'm not sure what numbers the computer calculates and detects, but as in the main post and Wiki, constructible polygons are mathematically defined (by the "the Gauss–Wantzel theorem").
So, from the number list in the main post, I think 30-gon and 32-gon could be exact if Doomslug682 did it right (could also be approximations though, need to check actual construction to verify, at a glance I'm guessing they're exact), the rest has to be approximations
32-gon should be hard to fake, it's just bisecting an octagon repeatedly
Haven't done this in a long time...
P.S. (don't want to email ping) 23 and 25-gon might be impressive because according to past me (I forgot) trisecting angles can be very closely approximated, but 23 and 25 can't be done that way, so Doomslug682 did it some other way, I forgot everything though!
P.P.S. ugh this link is dead for me... http://web.archive.org/web/20151219180208/http://apollonius.math.nthu.edu.tw/d1/ne01/jyt/linkjstor/regular/7.pdfP.P.P.S. it's back, seems like Internet Archive was down momentarily