essai

Reproduis les 2 figures suivantes à partir des points

A = (20, 7)
Q = (20, -3)
T_1 = (27, 7)
U_1 = (30, -3)
Z_1 = (28, -14)
V_1 = (21, -14)
u = Vector(V_1, Z_1)
B = (20, 8)
f = Segment(A, B)
C = (21, 9)
g = Segment(B, C)
D = (21, 8)
h = Segment(C, D)
E = (22, 8)
i = Segment(D, E)
j = Segment(E, A)
F = (21, 6)
k = Segment(A, F)
G = (24, 6)
l = Segment(F, G)
H = (25, 5)
m = Segment(G, H)
I = (24, 4)
n = Segment(H, I)
J = (21, 4)
p = Segment(I, J)
K = (20, 6)
q = Segment(A, K)
r = Segment(K, J)
L = (22, 6)
M = (22, 7)
s = Segment(L, M)
N = (23, 6)
t = Segment(M, N)
O = Point(p)
P = (21, 3)
a = Segment(O, P)
b = Segment(P, J)
R = (24, 5)
S = (22, -5)
c = Segment(Q, S)
T = (22, -6)
d = Segment(S, T)
U = (21, -7)
e = Segment(T, U)
V = (21, -9)
f_1 = Segment(U, V)
W = (20, -10)
g_1 = Segment(V, W)
Z = (20, -11)
h_1 = Segment(W, Z)
A_1 = (19, -11)
i_1 = Segment(Z, A_1)
B_1 = (17, -13)
j_1 = Segment(A_1, B_1)
C_1 = (17, -11)
D_1 = (18, -12)
k_1 = Segment(C_1, D_1)
E_1 = (18, -11)
F_1 = (17, -10)
l_1 = Segment(E_1, F_1)
G_1 = (17, -9)
m_1 = Segment(F_1, G_1)
H_1 = (18, -8)
n_1 = Segment(G_1, H_1)
I_1 = (17, -8)
p_1 = Segment(H_1, I_1)
q_1 = Segment(I_1, G_1)
J_1 = (17, -6)
K_1 = (19, -4)
r_1 = Segment(J_1, K_1)
L_1 = (20, -4)
s_1 = Segment(K_1, L_1)
M_1 = (21, -5)
t_1 = Segment(L_1, M_1)
N_1 = (21, -6)
a_1 = Segment(M_1, N_1)
O_1 = (20, -7)
b_1 = Segment(N_1, O_1)
P_1 = (21, -8)
c_1 = Segment(O_1, P_1)
Q_1 = (18, -6)
R_1 = (19, -5)
d_1 = Segment(Q_1, R_1)
S_1 = (20, -6)
e_1 = Segment(R_1, S_1)
W_1 = (19, -6)
A_2 = (18, -10)
B_2 = (20, -9)
f_2 = Segment(A_2, B_2)
g_2 = Segment(A_2, W)
h_2 = Segment(A_2, Z)
C_2 = (17, -5)
D_2 = (19, -3)
i_2 = Segment(C_2, D_2)
j_2 = Segment(D_2, Q)
k_2 = Segment(C_2, B_1)
S'_1 = Mirror(S, k_2)
T' = Mirror(T, k_2)
d' = Segment(S'_1, T')
T'_1 = Mirror(T, k_2)
U' = Mirror(U, k_2)
e' = Segment(T'_1, U')
U'_1 = Mirror(U, k_2)
V' = Mirror(V, k_2)
l_2 = Segment(U'_1, V')
V'_1 = Mirror(V, k_2)
W' = Mirror(W, k_2)
m_2 = Segment(V'_1, W')
W'_1 = Mirror(W, k_2)
Z' = Mirror(Z, k_2)
n_2 = Segment(W'_1, Z')
Z'_1 = Mirror(Z, k_2)
F_2 = Mirror(A_1, k_2)
p_2 = Segment(Z'_1, F_2)
G_2 = Mirror(A_1, k_2)
H_2 = Mirror(B_1, k_2)
q_2 = Segment(G_2, H_2)
I_2 = Mirror(C_1, k_2)
J_2 = Mirror(D_1, k_2)
r_2 = Segment(I_2, J_2)
K_2 = Mirror(E_1, k_2)
L_2 = Mirror(F_1, k_2)
s_2 = Segment(K_2, L_2)
M_2 = Mirror(F_1, k_2)
N_2 = Mirror(G_1, k_2)
t_2 = Segment(M_2, N_2)
O_2 = Mirror(G_1, k_2)
P_2 = Mirror(H_1, k_2)
a_2 = Segment(O_2, P_2)
Q_2 = Mirror(H_1, k_2)
R_2 = Mirror(I_1, k_2)
b_2 = Segment(Q_2, R_2)
S_2 = Mirror(I_1, k_2)
T_2 = Mirror(G_1, k_2)
c_2 = Segment(S_2, T_2)
U_2 = Mirror(J_1, k_2)
V_2 = Mirror(K_1, k_2)
d_2 = Segment(U_2, V_2)
W_2 = Mirror(K_1, k_2)
Z_2 = Mirror(L_1, k_2)
e_2 = Segment(W_2, Z_2)
A_3 = Mirror(L_1, k_2)
B_3 = Mirror(M_1, k_2)
f_3 = Segment(A_3, B_3)
C_3 = Mirror(M_1, k_2)
D_3 = Mirror(N_1, k_2)
g_3 = Segment(C_3, D_3)
E_3 = Mirror(N_1, k_2)
F_3 = Mirror(O_1, k_2)
h_3 = Segment(E_3, F_3)
G_3 = Mirror(O_1, k_2)
H_3 = Mirror(P_1, k_2)
i_3 = Segment(G_3, H_3)
I_3 = Mirror(Q_1, k_2)
J_3 = Mirror(R_1, k_2)
j_3 = Segment(I_3, J_3)
K_3 = Mirror(R_1, k_2)
L_3 = Mirror(S_1, k_2)
k_3 = Segment(K_3, L_3)
M_3 = Mirror(A_2, k_2)
N_3 = Mirror(B_2, k_2)
l_3 = Segment(M_3, N_3)
O_3 = Mirror(A_2, k_2)
W'_2 = Mirror(W, k_2)
m_3 = Segment(O_3, W'_2)
P_3 = Mirror(A_2, k_2)
Z'_2 = Mirror(Z, k_2)
n_3 = Segment(P_3, Z'_2)
Q_3 = Mirror(C_2, k_2)
R_3 = Mirror(D_2, k_2)
p_3 = Segment(Q_3, R_3)
S_3 = Mirror(D_2, k_2)
T_3 = Mirror(W_1, k_2)
E_2 = (15, -7)
U_3 = (19, -7)
r_3 = Segment(E_2, T_3)
s_3 = Segment(U_3, W_1)
V_3 = (14, -3)
q_3 = Segment(S'_1, V_3)
t_3 = Segment(V_3, R_3)

Tool: triangle équilatéral (se) (command triangleéquilatéralse)
triangleéquilatéralse[ <Point>, <Point> ]
Input: A, B
Output: C, a, b, c

a = Segment(A, B)
C = Rotate(B, 60°, A)
b = Segment(C, A)
c = Segment(C, B)

Tool: triangle isocèle (se) (command triangleisocèlese)
Input: A, B
Output: C, a, b, c

a = Segment(A, B)
C = Point(Circle[A, a])
b = Segment(A, C)
c = Segment(B, C)

Tool: triangle rectangle (se) (command trianglerectanglese)
Input: A, B
Output: C, a, b, c

a = Segment(A, B)
C = Point(OrthogonalLine[B, Line[A, B]])
b = Segment(B, C)
c = Segment(C, A)

Tool: triangle rectangle isocèle (se) (command trianglerectangleisocèlese)
Input: A, B
Output: C, a, b, c

a = Segment(A, B)
C = Rotate(B, 90°, A)
b = Segment(C, A)
c = Segment(C, B)

Tool: carré (se) (command carrése)
Input: A, B
Output: C, D, a, b, c, d

a = Segment(A, B)
C = Rotate(A, 270°, B)
D = Rotate(B, 90°, A)
b = Segment(B, C)
c = Segment(C, D)
d = Segment(D, A)

Tool: rectangle (se) (command rectanglese)
Input: A, B
Output: C, D, a, b, c, d

a = Segment(A, B)
C = Point(OrthogonalLine[A, Line[A, B]])
b = Segment(C, A)
D = Intersect(OrthogonalLine[C, Line[A, C]], OrthogonalLine[B, Line[A, B]])
c = Segment(C, D)
d = Segment(D, B)

Tool: parallélogramme (se) (command parallélogrammese)
Input: A, B, C
Output: D, a, b, c, d

a = Segment(A, B)
b = Segment(B, C)
D = Point(A, Vector[B, C])
c = Segment(A, D)
d = Segment(D, C)

Tool: losange (se) (command losangese)
Input: A, B
Output: C, D, a, b, c, d

a = Segment(A, B)
C = Point(Circle[B, a])
b = Segment(B, C)
D = Point(A, Vector[B, C])
c = Segment(A, D)
d = Segment(D, C)

Tool: pavage triangle (command pavagetriangle)
Input: A, B
Output: poly1, C, a, b, c

poly1, a, b, c, C = Polygon(A, B, 3)

Tool: pavage carré (command pavagecarré)
Input: D, E
Output: poly2, F, G, d, e, f, g

poly2, d, e, f, g, F, G = Polygon(D, E, 4)

Tool: pavage pentagone (command pavagepentagone)
Input: H, I
Output: poly3, J, K, L, h, i, j, k, l

poly3, h, i, j, k, l, J, K, L = Polygon(H, I, 5)

Tool: pavage héxagone (command pavagehéxagone)
Input: M, N
Output: poly4, O, P, Q, R, m, n, o, p, q, r

poly4, m, n, o, p, q, r, O, P, Q, R = Polygon(M, N, 6)

Tool: pavage héptagone (command pavagehéptagone)
Input: S, T
Output: poly5, U, V, W, Z, A1, s, t, u, v, w, z, a1

poly5, s, t, u, v, w, z, a1, U, V, W, Z, A1 = Polygon(S, T, 7)

Tool: pavage octogone (command pavageoctogone)
Input: B1, C1
Output: poly6, D1, E1, F1, G1, H1, I1, b1, c1, d1, e1, f1, g1, h1, i1

poly6, b1, c1, d1, e1, f1, g1, h1, i1, D1, E1, F1, G1, H1, I1 = Polygon(B1, C1, 8)

Tool: pavage nonagone (command pavagenonagone)
Input: J1, K1
Output: poly7, L1, M1, N1, O1, P1, Q1, R1, j1, k1, l1, m1, n1, o1, p1, q1, r1

poly7, j1, k1, l1, m1, n1, o1, p1, q1, r1, L1, M1, N1, O1, P1, Q1, R1 = Polygon(J1, K1, 9)

Tool: pavage décagone (command pavagedécagone)
Input: S1, T1
Output: poly8, U1, V1, W1, Z1, A2, B2, C2, D2, s1, t1, u1, v1, w1, z1, a2, b2, c2, d2

poly8, s1, t1, u1, v1, w1, z1, a2, b2, c2, d2, U1, V1, W1, Z1, A2, B2, C2, D2 = Polygon(S1, T1, 10)

Tool: pavage endécagone (command pavageendécagone)
Input: E2, F2
Output: poly9, G2, H2, I2, J2, K2, L2, M2, N2, O2, e2, f2, g2, h2, i2, j2, k2, l2, m2, n2, o2

poly9, e2, f2, g2, h2, i2, j2, k2, l2, m2, n2, o2, G2, H2, I2, J2, K2, L2, M2, N2, O2 = Polygon(E2, F2, 11)

Tool: pavage héxagone (command pavagehéxagon)
Input: M, N
Output: poly4, O, P, Q, R, m, n, o, p, q, r

poly4, m, n, o, p, q, r, O, P, Q, R = Polygon(M, N, 6)

Tool: Guide âne (command Guideâne)
Input: A, B, C
Output: a, D, E, F, G, H, I, J, K, L, M, N, b, c, d, e, f, g, h, i, j, k, l, m

a = Line(A, B)
b = Line(C, a)
D = Translate(C, Vector[B, C])
c = Line(D, b)
E = Translate(D, Vector[B, C])
d = Line(E, c)
F = Translate(E, Vector[B, C])
G = Translate(F, Vector[B, C])
H = Translate(G, Vector[B, C])
e = Line(F, d)
f = Line(G, e)
g = Line(H, f)
I = Translate(H, Vector[B, C])
J = Translate(I, Vector[B, C])
K = Translate(J, Vector[B, C])
h = Line(I, g)
i = Line(J, h)
j = Line(K, i)
L = Translate(K, Vector[B, C])
M = Translate(L, Vector[B, C])
N = Translate(M, Vector[B, C])
k = Line(L, j)
l = Line(M, j)
m = Line(N, l)

Tool: pavage dodécagone (command pavagedodécagone)
Input: P2, Q2
Output: poly10, R2, S2, T2, U2, V2, W2, Z2, A3, B3, C3, p2, q2, r2, s2, t2, u2, v2, w2, z2, a3, b3, c3

poly10, p2, q2, r2, s2, t2, u2, v2, w2, z2, a3, b3, c3, R2, S2, T2, U2, V2, W2, Z2, A3, B3, C3 = Polygon(P2, Q2, 12)