G.167 inscribe a regular hexagon in a circle — Code¶
Inscribe an equilateral and equiangular hexagon in a given circle.
"""Programmatic construction for Book IV, Proposition 15 (IV.15)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0113.g1 (Inscribed regular hexagon) using geometor.model."""
model = Model("IV.15")
# Points (y-inverted for standard mathematical coordinates)
G = model.set_point(86.00, -145.00, ID="G")
A = model.set_point(86.00, -209.00, classes=["given"], ID="A")
B = model.set_point(30.57, -177.00, ID="B")
C = model.set_point(30.57, -113.00, ID="C")
D = model.set_point(86.00, -81.00, ID="D")
E = model.set_point(141.43, -113.00, ID="E")
F = model.set_point(141.43, -177.00, ID="F")
H = model.set_point(86.00, -17.00, ID="H")
# Given circle ABCDEF and auxiliary circle EGCH
model.construct_circle(G, A)
model.construct_circle(D, G)
# Segments
model.set_segment(A, B)
model.set_segment(B, C)
model.set_segment(C, D)
model.set_segment(D, E)
model.set_segment(E, F)
model.set_segment(F, A)
model.set_segment(A, D)
model.set_segment(B, E)
model.set_segment(C, F)
model.set_segment(G, A)
model.set_segment(G, B)
model.set_segment(G, C)
model.set_segment(G, D)
model.set_segment(G, E)
model.set_segment(G, F)
# Collinear sections
model.set_section([A, G, D])
model.set_section([B, G, E])
model.set_section([C, G, F])
# Polygons
model.set_polygon([A, B, C, D, E, F])
model.set_polygon([E, G, D])
model.set_polygon([D, G, C])
# Angles (wedges)
model.set_wedge(E, G, G, D)
model.set_wedge(G, D, D, E)
model.set_wedge(D, E, E, G)
model.set_wedge(D, G, G, C)
model.set_wedge(C, G, G, B)
model.set_wedge(E, G, G, C)
model.set_wedge(B, G, G, A)
model.set_wedge(A, G, G, F)
model.set_wedge(F, G, G, E)
model.set_wedge(F, E, E, D)
model.set_wedge(A, F, F, E)
return model
if __name__ == "__main__":
construct_g1()