def test_sss_isosceles():
geometry.reset()
init_canvas = sketch.Canvas()
init_state = State()
A, B, C = map(Point, 'ABC')
ab, bc, ca = map(Line, 'ab bc ca'.split())
AB, CA = map(Segment, 'AB CA'.split())
init_state.add_relations(
segment_def(AB, A, B) +
segment_def(CA, C, A) +
collinear(ab, A, B) +
collinear(ca, C, A) +
have_length('1m', AB, CA)
)
init_state.add_spatial_relations(
init_canvas.add_isosceles_triangle(A, B, C, ab, bc, ca))
state, canvas = init_state.copy(), init_canvas.copy()
# Original thales + noises
steps = ['SSS: B A C C A B']
print('\nRunning SSS isosceles test:')
state, canvas, action_chain = action_chain_lib.execute_steps(steps, state, canvas)
def test_gelernter_equidistance():
geometry.reset()
init_canvas = sketch.Canvas()
init_state = State()
X = Point()
l1, l2 = Line(), Line()
hp11, hp12, hp21, hp22 = map(HalfPlane, 'hp11 hp12 hp21 hp22'.split())
init_state.add_relations(
divides_halfplanes(l1, hp11, hp12) +
divides_halfplanes(l2, hp21, hp22) +
collinear(l1, X) +
collinear(l2, X) +
distinct(l1, l2)
)
info = init_canvas.add_random_angle(X, l1, l2)
init_state.add_spatial_relations(info)
init_canvas.update_hps(init_state.line2hps)
steps = [
'angle_bisect: hp11 hp21', # l3
'free_p_on_l: l3',
'perp: P2 l1',
'perp: P2 l2',
'ASA:'
]
state, canvas, action_chain = action_chain_lib.execute_steps(
steps, init_state, init_canvas)
prev_state = action_chain[-1].state
proof_goals = list(whittling.extract_all_proof_goals(action_chain, state))
# Check if all the goals are here:
name2goals = extract_name2goals(proof_goals, state, prev_state)
all_target_goals = ['4.P1P3 == 4.P1P4', '4.P3P2 == 4.P4P2']
for goal in all_target_goals:
assert goal in name2goals, goal
state_queue, proof_queue = name2goals[goal]
_, _, proof_steps = whittle(
state, state_queue, proof_queue, action_chain,
init_state, init_canvas, canvas, verbose=False)
assert proof_steps == [4], proof_steps
def init_by_isosceles_triangle():
geometry.reset()
canvas = sketch.Canvas()
state = State()
A, B, C = map(Point, 'ABC')
ab, bc, ca = map(Line, 'ab bc ca'.split())
AB, BC, CA = map(Segment, 'AB BC CA'.split())
state.add_relations(
# [A, B, C, ab, bc, ca, AB, BC, CA] +
segment_def(AB, A, B) + segment_def(BC, B, C) + segment_def(CA, C, A) +
collinear(ab, A, B) + collinear(bc, B, C) + collinear(ca, C, A) +
have_length('1m', AB, CA))
state.add_spatial_relations(canvas.add_triangle(A, B, C, ab, bc, ca))
canvas.update_hps(state.line2hps)
return state, canvas, [(theorems.all_theorems['right'], '')]
def test_asa_isosceles():
geometry.reset()
init_canvas = sketch.Canvas()
init_state = State()
A, B, C = map(Point, 'ABC')
ab, bc, ca = map(Line, 'ab bc ca'.split())
ab_hp, bc_hp, ca_hp = map(HalfPlane, 'ab_hp bc_hp ca_hp'.split())
d_ab, d_bc, d_ca = LineDirection('d_ab'), LineDirection('d_bc'), LineDirection('d_ca')
B_xx, B_xo, B_def = fangle_def(d_ab, d_bc)
C_xx, C_xo, C_def = fangle_def(d_ca, d_bc)
init_state.add_relations(
collinear(ab, A, B) +
collinear(bc, B, C) +
collinear(ca, C, A) +
divides_halfplanes(ab, ab_hp, p1=C) +
divides_halfplanes(ca, ca_hp, p1=B) +
divides_halfplanes(bc, bc_hp, p1=A) +
have_direction(d_ab, ab) +
have_direction(d_ca, ca) +
have_direction(d_bc, bc) +
B_def + C_def
)
line2points = init_canvas.add_isosceles_triangle(A, B, C, ab, bc, ca)
init_state.add_spatial_relations(line2points)
init_canvas.update_hps(init_state.line2hps)
B_angle = B_xx if ab_hp.sign == bc_hp.sign else B_xo
C_angle = C_xx if ca_hp.sign == bc_hp.sign else C_xo
init_state.add_relations(
have_measure('m1', B_angle, C_angle))
state, canvas = init_state.copy(), init_canvas.copy()
# Original thales + noises
steps = ['ASA: C B A B C ab ca']
print('\nRunning ASA isosceles test:')
action_chain_lib.execute_steps(steps, state, canvas)
def test_angle_bisect_isosceles():
geometry.reset()
init_canvas = sketch.Canvas()
init_state = State()
A, B, C = map(Point, 'ABC')
ab, bc, ca = map(Line, 'ab bc ca'.split())
AB, CA = map(Segment, 'AB CA'.split())
ab_hp, ca_hp = map(HalfPlane, 'ab_hp ca_hp'.split())
init_state.add_relations(
distinct(A, B, C) +
distinct(ab, ca) +
segment_def(AB, A, B) +
segment_def(CA, C, A) +
divides_halfplanes(ab, ab_hp, p1=C) +
divides_halfplanes(ca, ca_hp, p1=B) +
collinear(ab, A, B) +
collinear(ca, C, A) +
have_length('1m', AB, CA)
)
line2points = init_canvas.add_isosceles_triangle(A, B, C, ab, bc, ca)
init_state.add_spatial_relations(line2points)
init_canvas.update_hps(init_state.line2hps)
state, canvas = init_state.copy(), init_canvas.copy()
# Original thales + noises
steps = [
'angle_bisect: ab_hp ca_hp',
'lineXsegment: l1 B C',
'SAS: A B P1 A C P1'
]
print('\nRunning test_angle_bisect_isosceles:')
state, canvas, action_chain = action_chain_lib.execute_steps(steps, state, canvas)
def test_base_bisect_sss_isosceles():
geometry.reset()
init_canvas = sketch.Canvas()
init_state = State()
A, B, C = map(Point, 'ABC')
ab, bc, ca = map(Line, 'ab bc ca'.split())
AB, CA = map(Segment, 'AB CA'.split())
init_state.add_relations(
# [A, B, C, AB, BC, CA, ab, bc, ca] +
distinct(A, B, C) +
segment_def(AB, A, B) +
segment_def(CA, C, A) +
collinear(ab, A, B) +
collinear(bc, B, C) +
collinear(ca, C, A) +
have_length('1m', AB, CA)
)
line2points = init_canvas.add_isosceles_triangle(A, B, C, ab, bc, ca)
init_state.add_spatial_relations(line2points)
init_canvas.update_hps(init_state.line2hps)
init_canvas.add_free_points(bc, B, C)
state, canvas = init_state.copy(), init_canvas.copy()
steps = [
'midp: B C', # -> P1
'line: A P1',
'SSS: B A P1 C A P1'
]
print('\nRunning test_base_bisect_sss_isosceles:')
action_chain_lib.execute_steps(steps, state, canvas)