def createPlacement(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
A1 = scene.free_point(label='A1')
B1 = scene.free_point(label='B1')
C1 = scene.free_point(label='C1')
A1.inside_triangle_constraint(triangle)
B1.inside_triangle_constraint(triangle)
C1.inside_triangle_constraint(triangle)
angleA = A.angle(B, C)
angleA.ratio_constraint(A.angle(B, C1), 3)
angleA.ratio_constraint(A.angle(C1, B1), 3)
angleA.ratio_constraint(A.angle(B1, C), 3)
angleB = B.angle(A, C)
angleB.ratio_constraint(B.angle(C, A1), 3)
angleB.ratio_constraint(B.angle(A1, C1), 3)
angleB.ratio_constraint(B.angle(C1, A), 3)
angleC = C.angle(A, B)
angleC.ratio_constraint(C.angle(A, B1), 3)
angleC.ratio_constraint(C.angle(B1, A1), 3)
angleC.ratio_constraint(C.angle(A1, B), 3)
return iterative_placement(scene)
def createPlacement(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
bisectorA = A.angle(B, C).bisector_line()
bisectorB = B.angle(A, C).bisector_line()
bisectorC = C.angle(A, B).bisector_line()
X_bisector = bisectorA.intersection_point(bisectorB, label='X_bisector')
Y_bisector = bisectorA.intersection_point(bisectorC, label='Y_bisector')
altitudeA = A.line_through(scene.perpendicular_foot_point(A, B.line_through(C)))
altitudeB = B.line_through(scene.perpendicular_foot_point(B, A.line_through(C)))
altitudeC = C.line_through(scene.perpendicular_foot_point(C, A.line_through(B)))
X_altitude = altitudeA.intersection_point(altitudeB, label='X_altitude')
Y_altitude = altitudeA.intersection_point(altitudeC, label='Y_altitude')
perpA = B.segment(C).perpendicular_bisector_line()
perpB = A.segment(C).perpendicular_bisector_line()
perpC = A.segment(B).perpendicular_bisector_line()
X_perp = perpA.intersection_point(perpB, label='X_perp')
Y_perp = perpA.intersection_point(perpC, label='Y_perp')
medianA = A.line_through(B.segment(C).middle_point())
medianB = B.line_through(A.segment(C).middle_point())
medianC = C.line_through(A.segment(B).middle_point())
X_median = medianA.intersection_point(medianB, label='X_median')
Y_median = medianA.intersection_point(medianC, label='Y_median')
return iterative_placement(scene)
def createPlacement(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
O = scene.circumcentre_point(triangle, label='O')
return iterative_placement(scene)
def testTwoObtuseAngles(self):
scene = Scene()
A, B, C = scene.nondegenerate_triangle(labels=('A', 'B', 'C')).points
A.angle(B, C).is_obtuse_constraint()
B.angle(A, C).is_obtuse_constraint()
explainer = Explainer(scene)
self.assertRaises(ContradictionError, explainer.explain)
def createScene(self):
scene = Scene()
A, B, C = scene.nondegenerate_triangle(labels=('A', 'B', 'C')).points
A.segment(C).perpendicular_constraint(B.segment(C),
comment='Given: AC ⟂ BC')
D = A.segment(B).middle_point(label='D')
return scene
def createScene(self):
scene = Scene()
A, B, C = scene.nondegenerate_triangle(labels=('A', 'B', 'C')).points
D = A.segment(B).free_point(label='D')
E = A.segment(C).free_point(label='E')
X = D.line_through(C).intersection_point(E.line_through(B), label='X')
return scene
def createScene(self):
scene = Scene()
A = scene.free_point(label='A')
B = scene.free_point(label='B')
A.segment(B).middle_point(label='C')
A.line_through(B, label='AB')
return scene
def createPlacement(self):
scene = Scene()
A, B, C = scene.nondegenerate_triangle(labels=('A', 'B', 'C')).points
A.segment(B).congruent_constraint(A.segment(C))
altitude = A.perpendicular_line(B.line_through(C), label='AD')
D = altitude.intersection_point(B.line_through(C, label='BC'))
B.segment(C).ratio_constraint(A.segment(D), 2 / sp.sqrt(3))
return iterative_placement(scene)
def createPlacement(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
D = scene.orthocentre_point(triangle)
D.inside_triangle_constraint(triangle)
A.segment(B).congruent_constraint(C.segment(D))
return iterative_placement(scene)
def createScene(self):
scene = Scene()
A, B, C = scene.nondegenerate_triangle(labels=('A', 'B', 'C')).points
F = B.segment(C).middle_point(label='F')
D = scene.perpendicular_foot_point(C, A.line_through(B), label='D')
E = scene.perpendicular_foot_point(B, A.line_through(C), label='E')
G = scene.perpendicular_foot_point(F, D.line_through(E), label='G')
return scene
def createScene(self):
scene = Scene()
A, B, C = scene.nondegenerate_triangle(labels=('A', 'B', 'C')).points
D = scene.free_point(label='D')
E = scene.free_point(label='E')
A.segment(C).congruent_constraint(B.segment(C))
A.segment(D).congruent_constraint(B.segment(D))
A.segment(E).congruent_constraint(B.segment(E))
return scene
def createPlacement(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
A.segment(B).ratio_constraint(B.segment(C), 2)
A.segment(B).perpendicular_constraint(B.segment(C))
F = scene.incentre_point(triangle, label='F')
E = scene.perpendicular_foot_point(B, A.line_through(F), label='E')
return iterative_placement(scene)
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
D = scene.orthocentre_point(triangle, label='D')
D.inside_triangle_constraint(triangle)
H = A.line_through(D).intersection_point(B.line_through(C), label='H')
G = C.line_through(D).intersection_point(A.line_through(B), label='G')
A.segment(B).congruent_constraint(C.segment(D))
return scene
def createPlacement(self):
scene = Scene()
A, B, C = scene.nondegenerate_triangle(labels=('A', 'B', 'C')).points
A.distance_constraint(B, 5)
C.distance_constraint(B, 3)
C.distance_constraint(A, 4)
D = scene.free_point(label='D')
A.vector(D).parallel_constraint(C.vector(B))
B.vector(D).parallel_constraint(C.vector(A))
return iterative_placement(scene)
def createScene(self):
scene = Scene()
A = scene.free_point(label='A')
B = scene.free_point(label='B')
B.not_equal_constraint(A)
C = scene.free_point(label='C')
D = scene.free_point(label='D')
C.collinear_constraint(A, B)
D.collinear_constraint(A, B)
return scene
def createPlacement(self):
scene = Scene()
A = scene.free_point(label='A', x=1, y=1)
B = scene.free_point(label='B', x=5, y=-3)
C = scene.free_point(label='C', x=3, y=10)
D = scene.free_point(label='D', x=4, y=11)
AB = A.line_through(B)
CD = C.line_through(D)
AB.intersection_point(CD, label='E')
return iterative_placement(scene)
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
altitudeA = scene.altitude(triangle, A)
altitudeB = scene.altitude(triangle, B)
A1 = altitudeA.intersection_point(B.line_through(C), label='A1')
B1 = altitudeB.intersection_point(A.line_through(C), label='B1')
C.angle(A, B).is_acute_constraint()
return scene
def createPlacement(self):
scene = Scene()
A = scene.free_point(label='A')
B = scene.free_point(label='B')
C = scene.free_point(label='C')
M = A.segment(B).middle_point(label='M')
l = C.line_through(M)
D = l.free_point(label='D')
para = scene.parallel_line(A.line_through(B), D)
A1 = para.intersection_point(A.line_through(C), label='A1')
B1 = para.intersection_point(B.line_through(C), label='B1')
return iterative_placement(scene)
def createScene(self):
scene = Scene()
A = scene.free_point(label='A')
B = scene.free_point(label='B')
C = scene.free_point(label='C')
D = scene.free_point(label='D')
E = scene.free_point(label='E')
F = scene.free_point(label='F')
A.not_equal_constraint(B)
A.not_equal_constraint(C)
A.collinear_constraint(B, C)
E.opposite_side_constraint(D, A.line_through(B))
F.same_side_constraint(D, A.line_through(B))
return scene
def napoleonic(A: Scene.Point, B: Scene.Point, C: Scene.Point):
c0 = A.circle_through(B)
c1 = B.circle_through(A)
line = A.line_through(B, layer='auxiliary')
V = c0.intersection_point(c1, label=C.label + '1')
equilateral = Scene.Triangle(A, B, V)
V.opposite_side_constraint(C, line)
scene.centroid_point(equilateral, label=C.label + '2')
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=['A', 'B', 'C'])
A, B, C = triangle.points
def napoleonic(A, B, C):
equilateral = scene.equilateral_triangle(A, B, C.label + '1')
_, _, V = equilateral.points
line = A.line_through(B, layer='auxiliary')
comment = Comment('$%{triangle:equilateral}$ is facing away from $%{triangle:triangle}$', {'equilateral': equilateral, 'triangle': triangle})
V.opposite_side_constraint(C, line, comment=comment)
D = scene.incentre_point(equilateral, label=C.label + '2')
napoleonic(A, B, C)
napoleonic(C, A, B)
napoleonic(B, C, A)
return scene
def createPlacement(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
def napoleonic(A: Scene.Point, B: Scene.Point, C: Scene.Point):
c0 = A.circle_through(B)
c1 = B.circle_through(A)
line = A.line_through(B, layer='auxiliary')
V = c0.intersection_point(c1, label=C.label + '1')
equilateral = Scene.Triangle(A, B, V)
V.opposite_side_constraint(C, line)
scene.centroid_point(equilateral, label=C.label + '2')
napoleonic(A, B, C)
napoleonic(C, A, B)
napoleonic(B, C, A)
return iterative_placement(scene)
def createPlacement(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
A.distance_constraint('B', 5)
C.distance_constraint('B', 4)
C.distance_constraint('A', 3)
scene.incircle(triangle, label='incircle')
scene.circumcircle(triangle, label='circumcircle')
return iterative_placement(scene)
def napoleonic(A, B, C):
circleAB = A.circle_through(B, layer='invisible')
circleBA = B.circle_through(A, layer='invisible')
V = circleAB.intersection_point(circleBA, label=C.label + '_1')
equilateral = Scene.Triangle(A, B, V)
A.scene.equilateral_constraint(equilateral,
comment=LazyComment(
'Given: %s is equilateral',
equilateral))
line = A.line_through(B, layer='auxiliary')
V.opposite_side_constraint(C,
line,
comment=LazyComment(
'Given: %s is outward of %s', V, triangle))
D = scene.circumcentre_point(equilateral, label=C.label + '_2')
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
A.segment(B).perpendicular_constraint(A.segment(C))
I = scene.incentre_point(triangle, label='I')
J = scene.orthocentre_point(Scene.Triangle(A, B, I), label='J')
return scene
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
triangle2 = Scene.Triangle(
*[side.middle_point() for side in triangle.sides])
D = scene.circumcentre_point(triangle, label='D')
E = scene.orthocentre_point(triangle2, label='E')
return scene
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
scene.equilateral_constraint(triangle)
D = B.translated_point(A.vector(B), 2, label='D')
F = scene.perpendicular_foot_point(D, B.line_through(C), label='F')
return scene
def createScene(self):
scene = Scene()
triangle = scene.nondegenerate_triangle(labels=('A', 'B', 'C'))
A, B, C = triangle.points
A.segment(B).perpendicular_constraint(A.segment(C))
I = scene.incentre_point(triangle, label='I')
J = scene.orthocentre_point(Scene.Triangle(A, B, I), label='J')
# Additional constructions
D = A.line_through(B).intersection_point(I.line_through(J), label='D')
E = A.line_through(I).intersection_point(B.line_through(J), label='E')
return scene
def setUp(self):
scene = Scene()
A = scene.free_point(label='A')
B = scene.free_point(label='B')
C = scene.free_point(label='C')
D = scene.free_point(label='D')
E = scene.free_point(label='E')
F = scene.free_point(label='F')
G = scene.free_point(label='G')
H = scene.free_point(label='H')
self.AB = A.segment(B)
self.CD = C.segment(D)
self.EF = E.segment(F)
self.GH = G.segment(H)
self.startTime = time.time()
def createPlacement(self):
scene = Scene()
A = scene.free_point(label='A')
B = scene.free_point(label='B')
C = scene.free_point(label='C')
D = scene.free_point(label='D')
E = scene.free_point(label='E')
scene.convex_polygon_constraint(A, B, C, D, E)
A.segment(B).congruent_constraint(B.segment(C))
A.segment(B).congruent_constraint(C.segment(D))
A.segment(B).congruent_constraint(D.segment(E))
A.segment(B).congruent_constraint(E.segment(A))
A.segment(C).congruent_constraint(B.segment(D))
A.segment(C).congruent_constraint(C.segment(E))
A.segment(C).congruent_constraint(D.segment(A))
A.segment(C).congruent_constraint(E.segment(B))
return iterative_placement(scene)
