G.166 circumscribe a circle about a regular pentagon — Code¶
Circumscribe a circle about a given equilateral and equiangular pentagon.
"""Programmatic construction for Book IV, Proposition 14 (IV.14)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0112.g1 (Circle circumscribed about regular pentagon) using geometor.model."""
model = Model("IV.14")
# Points (y-inverted for standard mathematical coordinates)
F = model.set_point(93.00, -97.00, ID="F")
A = model.set_point(93.00, -29.00, classes=["given"], ID="A")
B = model.set_point(28.33, -75.99, classes=["given"], ID="B")
C = model.set_point(53.03, -152.01, classes=["given"], ID="C")
D = model.set_point(132.97, -152.01, classes=["given"], ID="D")
E = model.set_point(157.67, -75.99, classes=["given"], ID="E")
# Circumscribed circle ABCDE
model.construct_circle(F, 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(F, A)
model.set_segment(F, B)
model.set_segment(F, C)
model.set_segment(F, D)
model.set_segment(F, E)
# Polygons
model.set_polygon([A, B, C, D, E])
model.set_polygon([F, C, D])
# Angles (wedges)
model.set_wedge(B, C, C, D)
model.set_wedge(C, D, D, E)
model.set_wedge(C, B, B, A)
model.set_wedge(B, A, A, E)
model.set_wedge(A, E, E, D)
model.set_wedge(F, C, C, D)
model.set_wedge(C, D, D, F)
return model
if __name__ == "__main__":
construct_g1()