G.165 inscribe a circle in a regular pentagon — Code¶
Inscribe a circle in a given equilateral and equiangular pentagon.
"""Programmatic construction for Book IV, Proposition 13 (IV.13)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0111.g1 (Circle inscribed in regular pentagon) using geometor.model."""
model = Model("IV.13")
# Points (y-inverted for standard mathematical coordinates)
F = model.set_point(109.00, -114.00, ID="F")
A = model.set_point(109.00, -29.95, classes=["given"], ID="A")
B = model.set_point(29.06, -88.03, classes=["given"], ID="B")
C = model.set_point(59.60, -182.00, classes=["given"], ID="C")
D = model.set_point(158.40, -182.00, classes=["given"], ID="D")
E = model.set_point(188.94, -88.03, classes=["given"], ID="E")
G = model.set_point(69.03, -58.99, ID="G")
H = model.set_point(44.33, -135.01, ID="H")
K = model.set_point(109.00, -182.00, ID="K")
L = model.set_point(173.67, -135.01, ID="L")
M = model.set_point(148.97, -58.99, ID="M")
# Inscribed circle GHKLM
model.construct_circle(F, K)
# 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)
model.set_segment(F, G)
model.set_segment(F, H)
model.set_segment(F, K)
model.set_segment(F, L)
model.set_segment(F, M)
model.set_segment(C, H)
model.set_segment(C, K)
# Collinear sections
model.set_section([A, G, B])
model.set_section([B, H, C])
model.set_section([C, K, D])
model.set_section([D, L, E])
model.set_section([E, M, A])
# Polygons
model.set_polygon([A, B, C, D, E])
model.set_polygon([B, C, F])
model.set_polygon([D, C, F])
model.set_polygon([F, H, C])
model.set_polygon([F, K, C])
# Angles (wedges)
model.set_wedge(B, C, C, D)
model.set_wedge(C, D, D, E)
model.set_wedge(B, C, C, F)
model.set_wedge(D, C, C, F)
model.set_wedge(C, B, B, F)
model.set_wedge(C, D, D, F)
model.set_wedge(A, B, B, C)
model.set_wedge(A, B, B, F)
model.set_wedge(B, A, A, E)
model.set_wedge(A, E, E, D)
model.set_wedge(F, H, H, C)
model.set_wedge(F, K, K, C)
model.set_wedge(F, G, G, B)
model.set_wedge(F, L, L, D)
model.set_wedge(F, M, M, E)
return model
if __name__ == "__main__":
construct_g1()