G.162 construct a golden isosceles triangle — Code¶
Construct an isosceles triangle having each of the angles at the base double the remaining angle.
"""Programmatic construction for Book IV, Proposition 10 (IV.10)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0102.g1 (Golden Triangle) using geometor.model."""
model = Model("IV.10")
# Points (y-inverted for standard mathematical coordinates)
A = model.set_point(114.00, -115.00, classes=["given"], ID="A")
B = model.set_point(174.18, -35.14, classes=["given"], ID="B")
C = model.set_point(151.19, -65.64, ID="C")
D = model.set_point(209.63, -85.76, ID="D")
E = model.set_point(208.59, -144.88, ID="E")
O = model.set_point(166.57, -115.92, ID="O")
# Circles: BDE (centre A, radius AB) and circumscribed circle ACD (centre O, radius OA)
model.construct_circle(A, B)
model.construct_circle(O, A)
# Segments
model.set_segment(A, B)
model.set_segment(A, C)
model.set_segment(C, B)
model.set_segment(A, D)
model.set_segment(B, D)
model.set_segment(C, D)
# Golden section on AB at C
model.set_section([A, C, B], classes=["golden"])
# Polygons
model.set_polygon([A, B, D])
model.set_polygon([A, C, D])
model.set_polygon([B, C, D])
# Angles (wedges)
model.set_wedge(D, B, B, C)
model.set_wedge(C, D, D, A)
model.set_wedge(A, D, D, C)
model.set_wedge(A, D, D, B)
model.set_wedge(D, C, C, B)
model.set_wedge(B, B, C, D)
model.set_wedge(B, A, D, B)
return model
if __name__ == "__main__":
construct_g1()