G.407 find two segments incommensurable in square which make — Code¶
Find two segments incommensurable in square which make the sum of the squares on them rational but the rectangle contained by them medial.
"""Programmatic construction for Book X, Proposition 33 (X.33)."""
from __future__ import annotations
from geometor.model import Model
def construct_g1() -> Model:
"""Construct the figure 0079.g1 using geometor.model."""
model = Model("X.33")
# Diameter AB extended to C, with D bisecting BC, E on AB, and F on semicircle AFB
A = model.set_point(19.0, -102.0, classes=["given"], ID="A")
E = model.set_point(172.0, -102.0, ID="E")
B = model.set_point(187.0, -102.0, classes=["given"], ID="B")
D = model.set_point(232.5, -102.0, ID="D")
C = model.set_point(278.0, -102.0, classes=["given"], ID="C")
O = model.set_point(103.0, -102.0, ID="O")
F = model.set_point(172.0, -54.1, ID="F")
# Base lines and semicircle AFB
model.construct_line(A, C)
model.construct_circle(O, A)
model.construct_line(A, F)
model.construct_line(F, B)
model.construct_line(E, F)
# Segments
model.set_segment(A, B)
model.set_segment(B, C)
model.set_segment(B, D)
model.set_segment(D, C)
model.set_segment(A, E)
model.set_segment(E, B)
model.set_segment(E, F)
model.set_segment(A, F)
model.set_segment(F, B)
model.set_segment(A, C)
model.set_segment(A, D)
model.set_segment(E, C)
model.set_segment(E, D)
# Sections
model.set_section([A, E, B])
model.set_section([B, D, C])
model.set_section([A, B, C])
# Inscribed right triangles AFB, AFE, FEB
model.set_polygon([A, F, B])
model.set_polygon([A, F, E])
model.set_polygon([F, E, B])
# Right angles at F and E
model.set_wedge(F, A, A, B)
model.set_wedge(E, F, A, F)
model.set_wedge(E, F, F, B)
return model
if __name__ == "__main__":
construct_g1()