0

1

$\dfrac{1}{\sqrt{3}}$

x

y

z

O_1 = (0, 0)
V: O_1 + (0, 1)
U = Rotate(V, -90°, O_1)
Um: O_1 + (1 / sqrt(3), 0)
a = Segment(O_1, U)
b = Segment(O_1, V)
E_0 = (0.5773502691896258, 0.5773502691896258)
f = Segment(E_0, O_1)
W = Midpoint(V, U)
Ea = Rotate(W, 45°, O_1)
g = CircleArc(O_1, W, Ea)
V2 = Midpoint(V, O_1)
h = Segment(V2, U)
W2 = Intersect(f, h)
i = Segment(V2, W2)
U2 = Midpoint(U, O_1)
j = OrthogonalLine(V2, b)
k = CircleArc(U2, W, O_1)
n = CurveCartesian(sqrt((sqrt((20 * (t^(2) * (1 - (2 * t^(2))))) + (1 - (6 * t^(2)))^(2)) + 1 - (6 * t^(2))) / 10), t, t, 0, 0.7071067811865475)
m = CurveCartesian(t, sqrt((1 - ((2 * t) - 1)^(2)) / 2), t, 0, 0.5773502691896258)
l = ImplicitCurve(((x^(2) * (1 - x)^(2)) * (1 - x^(2) - y^(2))) - (((2 * x^(2)) + y^(2) - (2 * x)) * (x^(2) + y^(2) - x)^(2)))
e = CurveCartesian(t, sqrt((1 - t^(2)) / 2), t, 0, 0.5773502691896258)
c = CircleArc(O_1, U, V)
O = (1.534183531252675, 1.3711006840609912)
u = Vector(O_1, Um)
A' = Translate(O, u)
d = Segment(O, A')
X = Point(d)
Ymin = Rotate(X, -90°, O)
p = Segment(O, X)
X'_1 = Rotate(X, 90°, O)
O' = Rotate(O, 90°, X'_1)
q_1 = Segment(X, O')
r_1 = Segment(O', X'_1)
s = Segment(X'_1, O)
poly1, o, A, o', x'_1 = Polygon(O, X, O', X'_1)
Ymax: O - (0, sqrt(0.5 - (0.5 * p^(2))))
t = Segment(Ymin, Ymax)
Y = Point(t)
O'_1 = Rotate(O, 90°, Y)
Y' = Rotate(Y, 90°, O'_1)
a_1 = Segment(O'_1, Y)
q = Segment(Y, O)
c_1 = Segment(O, Y')
d_1 = Segment(Y', O'_1)
e_1 = Segment(X, Y)
f_1 = Line(O, e_1)
B = Intersect(f_1, a_1)
g_1 = Segment(O'_1, B)
M = Point(g_1)
v = Vector(Y, X)
C' = Translate(M, v)
h_1 = Segment(C', M)
i_1 = Segment(Y', Ymin)
D = Intersect(h_1, i_1)
poly2, ymin, y', o_1 = Polygon(Y', O, Ymin)
poly3, y'_1, o'_1, E, ymin_1 = Polygon(Y', O'_1, Y, Ymin)
P: (p, q)
r: sqrt(1 - p^(2) - q^(2))
texte1: "x = " + p + "
y = " + q + "
z = " + r + ""
Y'_1 = Rotate(Y, 90°, X)
X' = Rotate(X, 90°, Y'_1)
b_1 = Segment(X, Y'_1)
j_1 = Segment(Y'_1, X')
k_1 = Segment(Y, X')
l_1 = Ray(X', Y'_1)
p_1 = Circle(X', r)
F = Intersect(p_1, l_1, 1)
w = Vector(D, Y')
X'' = Translate(X', w)
u_1 = Vector(O, X)
X''' = Translate(X'', u_1)
G = Rotate(X''', 90°, X'')
X'''_1 = Rotate(X'', 90°, G)
v_1 = Vector(O'_1, Y')
H = Translate(X''', v_1)
w_1 = Vector(Y', O)
I = Translate(X''', w_1)
X'''_2 = Translate(X'', w_1)
m_1 = Vector(O, Ymin)
J = Translate(X'''_2, m_1)
n_1 = Segment(G, X'''_1)
s_1 = Segment(X'''_1, X''')
t_1 = Segment(X'', X''')
a_2 = Segment(G, X'')
b_2 = Segment(X''', X'''_2)
c_2 = Segment(X'''_2, I)
d_2 = Segment(H, X'''_1)
u_2 = Vector(Y, Ymin)
I' = Translate(I, u_2)
e_2 = Segment(H, I')
f_2 = Segment(I', I)
g_2 = Segment(X'''_2, J)
h_2 = Segment(X'', J)
poly4, K, h_3, x'''_1, g_3, x'', L = Polygon(X, H, X'''_1, G, X'', Y)
poly5, g_4, x'''_2, x''', x''_1 = Polygon(G, X'''_1, X''', X'')
poly6, h_4, i', i_2, x'''_3 = Polygon(H, I', I, X''')
poly7, j_2, x''_2, x'''_4 = Polygon(X'', X'''_2, J)
X''_1 = Rotate(X', 90°, F)
F' = Rotate(F, 90°, X''_1)
v_2 = Vector(Y, X)
F'_1 = Translate(F, v_2)
k_2 = Segment(F'_1, F)
l_2 = Segment(F, Y'_1)
m_2 = Segment(F, X''_1)
n_2 = Segment(X''_1, F')
p_2 = Segment(X', F')
q_2 = Segment(F'_1, X''_1)
M_1 = Translate(X''_1, Vector[(-v_2)])
R = Rotate(X''_1, 90°, F'_1)
S = Rotate(F'_1, 90°, R)
a_3 = Segment(F'_1, R)
b_3 = Segment(R, S)
c_3 = Segment(S, X''_1)
r_2 = Segment(F', M_1)
N = Point(r_2)
w_2 = Vector(X''_1, F'_1)
M' = Translate(N, w_2)
s_2 = Segment(M', N)
t_2 = OrthogonalLine(X''_1, s_2)
N_1 = Intersect(p_2, t_2)
Q = Intersect(t_2, s_2)
d_3 = Segment(N_1, X''_1)
poly8, f_3, x''_3, q_3, m' = Polygon(F, X''_1, Q, M')
poly9, y'_2, m'_1, q_4, n_3, j_3, x'''_5, i_3, i'_1 = Polygon(Y'_1, M', Q, N_1, J, X'''_2, I, I')
poly10, n_4, q_5, m_3, f' = Polygon(N_1, Q, N, F')
poly11, m_4, q_6, x''_4 = Polygon(Q, X''_1, N)
u_3 = Vector(Q, R)
N' = Translate(N_1, u_3)
Q' = Translate(Q, u_3)
M'_1 = Translate(N, u_3)
F'' = Translate(F', u_3)
poly10', n', q', m'_2, f'' = Polygon(N', Q', M'_1, F'')
v_3 = Vector(Q, X''_1)
F'_2 = Translate(F, v_3)
T = Translate(X''_1, v_3)
Q'_1 = Translate(Q, v_3)
M'' = Translate(M', v_3)
poly8', f'_2, t_3, q'_1, m'' = Polygon(F'_2, T, Q'_1, M'')
e_3 = Vector(Q, S)
A_1 = Translate(Y'_1, e_3)
M''_1 = Translate(M', e_3)
Q'_3 = Translate(Q, e_3)
N'_1 = Translate(N_1, e_3)
J' = Translate(J, e_3)
B_1 = Translate(X'''_2, e_3)
I'_1 = Translate(I, e_3)
I'' = Translate(I', e_3)
poly9', a_4, m''_1, q'_3, n'_1, j', b_4, i'_2, i'' = Polygon(A_1, M''_1, Q'_3, N'_1, J', B_1, I'_1, I'')
k_3 = Vector(Y, I'_1)
Y'' = Translate(Y', k_3)
C_1 = Translate(O'_1, k_3)
Y'_2 = Translate(Y, k_3)
Ymin' = Translate(Ymin, k_3)
poly3', y'', c_4, y'_3, ymin' = Polygon(Y'', C_1, Y'_2, Ymin')
l_3 = Vector(X, N')
X'_2 = Translate(X, l_3)
H' = Translate(H, l_3)
D_1 = Translate(X'''_1, l_3)
G' = Translate(G, l_3)
X'''_3 = Translate(X'', l_3)
Y'_3 = Translate(Y, l_3)
poly4', x'_2, h', d_4, g', x'''_6, y'_4 = Polygon(X'_2, H', D_1, G', X'''_3, Y'_3)
p_3 = Vector(O, B_1)
Y''_1 = Translate(Y', p_3)
O'_2 = Translate(O, p_3)
Ymin'_1 = Translate(Ymin, p_3)
poly2', ymin'_1, y''_1, o'_2 = Polygon(Y''_1, O'_2, Ymin'_1)
r_3 = Vector(O, X'''_3)
O'_3 = Translate(O, r_3)
X'_3 = Translate(X, r_3)
O'' = Translate(O', r_3)
E_1 = Translate(X'_1, r_3)
poly1', o'_3, x'_3, o'', e_4 = Polygon(O'_3, X'_3, O'', E_1)
s_3 = Segment(N', M'')
f_4 = Segment(N', I'')
i_4 = Segment(M'_1, F'')
j_4 = Segment(Y'', X'_3)
k_4 = Segment(X'''_3, I'_1)
l_4 = Segment(I'', I'_1)
p_4 = Segment(B_1, J')
r_4 = Segment(F'_2, T)
s_4 = Segment(E_1, D_1)
t_4 = Segment(E_1, X'''_3)
w_3 = Vector(X'''_2, O'_2)
C = Translate(Y'_1, w_3)
X''_2 = Translate(X', w_3)
a_5 = Segment(C, X''_2)
u_4 = Vector(Q, F'_1)
Q'_2 = Translate(Q, u_4)
Z = Translate(X''_1, u_4)
N'_2 = Translate(N, u_4)
poly11', n'_2, q'_2, z = Polygon(Q'_2, Z, N'_2)