Ancient Greek Geometry walkthrough / answers / cheats

Ancient Greek Geometry.md

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.

Polygons

• 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

Circle Packs

• 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

Circumscribed Polygons

• Origin circle circumscribed triangle: 6 moves by John Chrysostom
• Origin circle circumscribed square: 10 moves
• Origin circle circumscribed hexagon: 11 moves

Non-Constructible Figures

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

46-gon in 70 moves:
46-gon

Circle Pack 13 (there's also a second one) in 40 moves

Dodecagon in 16 moves.

(in-origin?) Decagon in 16 moves.

Nonagon in 19 moves.

(unincluded) Square Pack 5 in 27 moves

I had to use the old 18-gon to make this. 36-gon in 55 moves

25-gon in 70 moves according to this somewhat simple approximation

18-gon 19-gon 22-gon 27-gon 35-gon 37-gon 39-gon 41-gon 43-gon 45-gon 47-gon 49-gon 53-gon 54-gon 57-gon

Two hexagon alternatives: 1. 9 moves 2. 9 moves

Line segment with length π with an error of only 8.49e-8

Origin circle circumscribed octagon in 15 moves

hi

Hello!

Have you made any polygons yet? If yes, share some.

Finally made the 59-gon after many, many attempts. 87 moves.

@Ian-Zander, the reason why my link for the 50-gon originally led to the 49-gon was pretty much the same reason as when the link that @Doomslug682 posted for the 33-gon led to the 32-gon.

I made this like a year ago and its pretty close to a 9-gon https://sciencevsmagic.net/geo/#1A0.0A1.2A0.5A0.4A1.3A0.1L5.0L4.16A15.16L2.16L21.16L22.16L27.16L15.16L19.20L4.16L25.18A8.9L41.41L42.15L42.6A40.42L66.66L9.73A41.83A73.86L87.73A91.87L85.27A118.122L121.15L122.121L20.121A122

Octagon in 12 moves

oh mb. i thought a nonagon was impossible

I made this like a year ago and its pretty close to a 9-gon https://sciencevsmagic.net/geo/#1A0.0A1.2A0.5A0.4A1.3A0.1L5.0L4.16A15.16L2.16L21.16L22.16L27.16L15.16L19.20L4.16L25.18A8.9L41.41L42.15L42.6A40.42L66.66L9.73A41.83A73.86L87.73A91.87L85.27A118.122L121.15L122.121L20.121A122

Here’s a really good approximation for the nonagon.

Regular polygons whose edge count is a Pierpont prime are constructible with angle trisection, but the current known angle trisector doesn’t do it perfectly. “You had one job angle trisector. One job.” Let’s say that it does perfectly. Could all regular polygons whose edge count are 1 above a multiple of 3 be constructible with angle trisection? Please figure this out. If it’s true, then a regular hendecagon is constructible with angle trisection, because the icosidigon would be, which is great. If it’s false, try doing it yourself. If it still turns out as false, that’s great too, because we want extremely small errors to the polygons we construct. Floating point causes the widget to be tricked into thinking the polygons are regular.