"""Programmatic construction for Book XI, Proposition 21 (XI.21).
Any solid angle is contained by plane angles less than four right angles.
"""
from __future__ import annotations
import sympy as sp
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure for Book XI, Proposition 21 using geometor.model."""
model = Model("XI.21")
# 1. Let the angle at A be a solid angle contained by the plane angles
# BAC, CAD, DAB.
# 2. Take points B, C, D at random on AB, AC, AD and join BC, CD, DB.
A = model.set_point(0, 0, classes=["given"], ID="A")
C = model.set_point(sp.Rational(-24, 60), sp.Rational(45, 60), classes=["given"], label="C")
B = model.set_point(sp.Rational(-78, 60), sp.Rational(-69, 60), classes=["given"], label="B")
D = model.set_point(sp.Rational(110, 60), sp.Rational(-25, 60), classes=["given"], label="D")
# Segments
model.set_segment(A, B)
model.set_segment(A, C)
model.set_segment(A, D)
model.set_segment(B, C)
model.set_segment(C, D)
model.set_segment(D, B)
# Triangles
model.set_polygon([A, B, C])
model.set_polygon([A, C, D])
model.set_polygon([A, D, B])
model.set_polygon([B, C, D])
return model
if __name__ == "__main__":
construct_g1()
