G.163 inscribe a regular pentagon in a circle — Code¶
Inscribe an equilateral and equiangular pentagon in a given circle.
"""Programmatic construction for Book IV, Proposition 11 (IV.11)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0106.g1 (Inscribed regular pentagon) using geometor.model."""
model = Model("IV.11")
# Points (y-inverted for standard mathematical coordinates)
O = model.set_point(79.00, -83.00, ID="O")
A = model.set_point(79.00, -28.00, classes=["given"], ID="A")
B = model.set_point(26.69, -66.00, ID="B")
C = model.set_point(46.67, -127.50, ID="C")
D = model.set_point(111.33, -127.50, ID="D")
E = model.set_point(131.31, -66.00, ID="E")
# Auxiliary golden triangle FGH
F = model.set_point(205.00, -36.00, classes=["given"], ID="F")
G = model.set_point(182.75, -104.48, classes=["given"], ID="G")
H = model.set_point(227.25, -104.48, classes=["given"], ID="H")
# Given circle ABCDE
model.construct_circle(O, A)
# 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, A)
model.set_segment(A, C)
model.set_segment(A, D)
model.set_segment(B, D)
model.set_segment(C, E)
model.set_segment(F, G)
model.set_segment(G, H)
model.set_segment(H, F)
# Polygons
model.set_polygon([A, B, C, D, E])
model.set_polygon([A, C, D])
model.set_polygon([F, G, H])
# Angles (wedges)
model.set_wedge(G, F, F, H)
model.set_wedge(H, G, G, F)
model.set_wedge(F, H, H, G)
model.set_wedge(C, A, A, D)
model.set_wedge(D, C, C, A)
model.set_wedge(A, D, D, C)
model.set_wedge(E, C, C, A)
model.set_wedge(D, C, C, E)
model.set_wedge(C, D, D, B)
model.set_wedge(B, D, D, A)
model.set_wedge(B, A, A, E)
model.set_wedge(A, E, E, D)
model.set_wedge(A, B, B, C)
model.set_wedge(B, C, C, D)
model.set_wedge(C, D, D, E)
return model
if __name__ == "__main__":
construct_g1()