G.585 angles equilateral pentagon — Code¶
If three angles of an equilateral pentagon, taken either in order or not in order, be equal, the pentagon is equiangular.
"""Programmatic construction for Book XIII, Proposition 7 (XIII.7).
If three angles of an equilateral pentagon, taken either in order or not in
order, be equal, the pentagon will be equiangular.
"""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for Book XIII, Proposition 7 using geometor.model."""
model = Model("XIII.7")
# Equilateral pentagon ABCDE
A = model.set_point(103.0, -21.0, classes=["given"], ID="A")
B = model.set_point(25.0, -78.0, classes=["given"], ID="B")
C = model.set_point(55.0, -170.0, classes=["given"], ID="C")
D = model.set_point(151.0, -170.0, classes=["given"], ID="D")
E = model.set_point(181.0, -78.0, classes=["given"], ID="E")
# Intersection F of diagonals AC and BE
F = model.set_point(84.6, -78.0, ID="F")
# Pentagon sides
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)
# Diagonals and sub-segments
model.set_segment(A, C)
model.set_segment(A, F)
model.set_segment(F, C)
model.set_segment(B, E)
model.set_segment(B, F)
model.set_segment(F, E)
model.set_segment(F, D)
model.set_segment(B, D)
# Polygons
model.set_polygon([A, B, C, D, E])
model.set_polygon([A, B, C])
model.set_polygon([A, B, E])
model.set_polygon([F, C, D])
model.set_polygon([F, E, D])
model.set_polygon([B, C, D])
model.set_polygon([B, D, E])
model.set_polygon([A, B, F])
# Angles (wedges)
model.set_wedge(B, C, C, A)
model.set_wedge(A, B, B, E)
model.set_wedge(C, B, B, A)
model.set_wedge(E, B, B, A)
model.set_wedge(B, A, A, E)
model.set_wedge(A, C, C, B)
model.set_wedge(C, F, F, D)
model.set_wedge(E, F, F, D)
model.set_wedge(C, B, B, D)
model.set_wedge(E, A, A, D)
model.set_wedge(D, C, C, E)
model.set_wedge(D, C, C, B)
model.set_wedge(D, B, B, E)
return model
if __name__ == "__main__":
construct_g1()