symétries glissées

demi-tours

symétries axiales

Retourner

OK

Translation

Vecteur

NB. D'ESSAIS

MOYENNE

SCORES

Symétrie axiale

Symetrie glissée (symétrie axiale suivie d'une translation)

Symétrie centrale

type

?

symetriesglissees = true
norme: (2 * Random[1, 4])
rotations = false
demitours = false
symetriesaxiales = false
translations = false
preListeCasesCochees: {If[translations, 0, -1], If[symetriesaxiales, 2, -1], If[demitours, 4, -1], If[rotations, 1, -1], If[symetriesglissees, 3, -1]}
ListeCasesCochees: preListeCasesCochees \ {-1}
nbCasesCochees = Sum({translations, symetriesaxiales, demitours, rotations, symetriesglissees})
A': (12, 0)
preanglerotation = If(RandomUniform[0, 1]  <  0.2, 180, 90)
A = (0, 0)
B = (0, 10)
v = Vector(A, B)
L' = Translate(A', v)
positions = Sequence(Rotate[L', ((2 * k) * π / 32), A'], k, 0, 31)
E_1 = (-1, -1)
F_1 = (-3, -2)
G_1 = (-5, 0)
H_1 = (-3, 2)
I_1 = (0, 1)
J_1 = (1, 3)
K_1 = (1, 4)
L_1 = (-1, 6)
M_1 = (-2, 8)
N_1 = (-2, 9)
T = (-1, 10)
N = (1, 9)
R_1 = (-1, 9)
S_1 = (-1, 8)
T_1 = (0, 6)
U_1 = (2, 4)
V_1 = (2, 3)
W_1 = (1, 1)
A_2 = (-3, 1)
B_2 = (-4, 0)
C_2 = (-3, -1)
poly2, e_1, f_2, g_2, h_2, i_1, j_1, k_1, l_1, m_1, n_1, o_1, p_1, q_1, r_1, s_1, t_1, u_1, v_1, w_1, z_2, a_2, b_2, c_2 = Polygon(E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, T, B, N, R_1, S_1, T_1, U_1, V_1, W_1, A, A_2, B_2, C_2)
D_2 = (-3, 8)
E_2 = (-2, 6)
F_2 = Point(k_1)
poly3, n_2, d_2, e_2, f_3, l_2, m_2 = Polygon(N_1, D_2, E_2, F_2, L_1, M_1)
G_2 = Point(t_1)
H_2 = (0, 8)
poly4, g_3, h_3, r_2, s_2, t_2 = Polygon(G_2, H_2, R_1, S_1, T_1)
Oeil: (2 / 3 * T) + (1 / 3 * N)
A_1 = Point(d_2)
B_1 = Point(l_1)
C = Point(l_1)
D = Point(d_2)
poly1, a, b, c, d_1 = Polygon(A_1, B_1, C, D)
E = Point(s_1)
F = Point(g_3)
G = Point(g_3)
H = Point(s_1)
poly5, e, f, g, h = Polygon(E, F, G, H)
I = (1.391497738380071, 8.690449635175716)
i = Segment(N, I)
J = (1.710228286778361, 8.583379032036033)
j = Segment(I, J)
K = (1.5828701026000305, 8.456020847857703)
k = Segment(I, K)
u = Vector(A, A')
B' = Point(positions)
α = Angle(L', A', B')
retourner: false
d = Line(A', L')
objet: {poly1, poly2, poly3, poly4, poly5, Oeil, i, j, k}
Translation: 0
Rotation: 1
Symetrie: 2
Pointaxe: (Random[-8, 8], Random[-8, 8])
directionaxe = Random(0, 7)
Symetrieglissee: 3
preaxe: y = y(Pointaxe)
Centre: (2 * (Random[-4, 4], Random[-4, 4]))
axe = Rotate(preaxe, (directionaxe * π / 4), Pointaxe)
Originevecteur: Centre
prevecteur: (((Random[0, 1] - 0.5) * 2) * If[Random[0, 1] ≟ 0, (norme, (2 * Random[((-norme)) / 2, norme / 2])), ((2 * Random[((-norme)) / 2, norme / 2]), norme)])
Extremitevecteur = Translate(Originevecteur, prevecteur)
type = Element(ListeCasesCochees, Random[1, nbCasesCochees])
Vecteur = Vector(Centre, Extremitevecteur)
sensrotation: (Random[0, 1] * 2) - 1
prevecteurglissement = UnitVector(axe)
normeglissement = If(Mod[directionaxe, 2] ≟ 0, 1, sqrt(2))
extremiteglissement = Translate(Centre, Vector[((prevecteurglissement * normeglissement) * Random[2, 6])])
vecteurglissement = Vector(Centre, extremiteglissement)
Demitour: 4
anglerotation: preanglerotation°
A'' = If(type ≟ Translation, Translate[A, Vecteur], If[type ≟ Rotation, Rotate[A, (anglerotation * sensrotation), Centre], If[type ≟ Symetrie, Mirror[A, axe], If[type ≟ Symetrieglissee, Mirror[Translate[A, vecteurglissement], axe], If[type ≟ Demitour, Rotate[A, π, Centre]]]]])
B'' = If(type ≟ Translation, Translate[B, Vecteur], If[type ≟ Rotation, Rotate[B, (anglerotation * sensrotation), Centre], If[type ≟ Symetrie, Mirror[B, axe], If[type ≟ Symetrieglissee, Mirror[Translate[B, vecteurglissement], axe], If[type ≟ Demitour, Rotate[B, π, Centre]]]]])
temps: 0
n: 0
deplacement = If(type ≟ Symetrie ∨ type ≟ Symetrieglissee, false, true)
reference: 10
difficulte: 1
textesensrotation = If(sensrotation ≟ -1, "sens des aiguilles d'une montre", "sens contraire des aiguilles d'une montre")
texterotation: "Rotation de " + anglerotation + " dans le " + textesensrotation + ""
pointtexte = (-19, -16)
B2 = Mean(A5:A100)
A2: n
abreviation = If(type ≟ 0, "transl.", If[type ≟ 1, "rot.", If[type ≟ 2, "sym.", If[type ≟ 3, "sym.gl.", If[type ≟ 4, "demi t.", "?"]]]])
tt: retourner ∧ deplacement ∨ (¬retourner) ∧ (¬deplacement)
ecart = If(retourner ≟ deplacement, 50, sqrt((x(A') - x(A''))^(2) + (x(B') - x(B''))^(2) + (y(A') - y(A''))^(2) + (y(B') - y(B''))^(2)))
texte1 = Text("Cochez au moins une case!")
test = Element(ListeCasesCochees, Random[0, nbCasesCochees - 1])
test2 = Element(ListeCasesCochees, 1)
autorisation: 1
rayon: 3
L = Point(objet)
p = Circle(L, B)
M = Point(p)
O = (2, 6)
l = Segment(M, O)
P = (2, 10)
m = Segment(O, P)
Q = (4, 10)
q = Segment(P, Q)
R = (4, 4)
r = Segment(Q, R)
S = (2, 4)
s = Segment(R, S)
U = (2, 0)
t = Segment(S, U)
f_1 = Segment(U, A)
V = (0, 2)
g_1 = Segment(V, A)
W = (-2, 0)
h_1 = Segment(A, W)
Z = (-2, 4)
a_1 = Segment(W, Z)
C_1 = (-6, 4)
b_1 = Segment(Z, C_1)
D_1 = (-6, 6)
c_1 = Segment(C_1, D_1)
i_2 = Segment(D_1, M)
O_1 = Point(i_2)
P_1 = (-4, 4)
Q_1 = Point(a_1)
Z_1 = Point(t)
I_2 = (4, 8)
J_2 = Intersect(p, m, 1)
poly6, o_2, p_2, z_1, q_2, z_3, s_3, r_3, i_3, j_2, o = Polygon(O_1, P_1, Z, Q_1, Z_1, S, R, I_2, J_2, O)
poly7, q_3, z_4, u_2, w = Polygon(Q_1, Z_1, U, W)
poly8, d_3, o_3, p_3, c_3 = Polygon(D_1, O_1, P_1, C_1)
poly9, j_3, i_4, q_4, p_4 = Polygon(J_2, I_2, Q, P)
K_2 = Mirror(J_2, L)
k_2 = CircleSector(L, J_2, K_2)
L_2 = (-4, 8)
k_3 = Segment(K_2, L_2)
e_3 = CircleSector(L, K_2, J_2)
l_3 = Segment(O_1, P_1)
M_2 = Point(r)
N_2 = Point(r)
O_2 = Point(m)
m_3 = Segment(N_2, O_2)
P_2 = (6, 10)
n_3 = Segment(Q, P_2)
Q_2 = (-1.0923492022627699, 7.648432434884716)
R_2 = (5.98268046982035, 9.07352965958163)
S_2 = (6.002504475173572, 11.1946982323764)
T_2 = (6.961267478284174, 11.188460648901524)
U_2 = (6.961267478284174, 9.701685376497062)
V_2 = (6.5296230443602985, 9.078198971940353)
poly10, r_4, s_4, t_3, u_3, v_2 = Polygon(R_2, S_2, T_2, U_2, V_2)
W_2 = Point(p)
Z_2 = (-0.16193856197363243, 6.685696011445337)
c_4 = CircleArc(Q_2, W_2, Z_2)
A_3 = Point(p)
B_3 = Point(p)
d_4 = CircleArc(A_3, B_3, Z_2)
C_3 = Point(c_4)
D_3 = Point(p)
a_3 = Segment(C_3, D_3)
E_3 = Point(c_4)
F_3 = Point(p)
b_3 = Segment(E_3, F_3)
G_3 = Point(c_4)
H_3 = Point(d_4)
f_4 = Segment(G_3, H_3)
I_3 = Point(c_4)
J_3 = Point(d_4)
g_4 = Segment(I_3, J_3)
K_3 = Point(c_4)
L_3 = Point(d_4)
h_4 = Segment(K_3, L_3)
M_3 = Point(c_4)
N_3 = Point(p)
j_4 = Segment(M_3, N_3)
O_3 = Point(c_4)
P_3 = Point(d_4)
k_4 = Segment(O_3, P_3)
objet1: {c_4, d_4, e_3, k_2, p, poly10, Q_2, poly6, poly7, poly8, poly9, a_1, a_3, b_1, b_3, c_1, c_3, d_3, f_1, f_4, g_1, g_4, h_1, h_4, i_2, i_3, i_4, j_2, j_3, j_4, k_3, k_4, l, l_3, m, m_3, n_3, o, o_2, o_3, p_2, p_3, p_4, q, q_2, q_3, q_4, r, r_3, r_4, s, s_3, s_4, t, t_3, u_2, u_3, v_2, w, z_1, z_3, z_4}
image = If(retourner, Rotate[Mirror[Translate[objet1, u], d], α, A'], Rotate[Translate[objet1, u], α, A'])
reponse = If(type ≟ Translation, Translate[objet1, Vecteur], If[type ≟ Rotation, Rotate[objet1, (anglerotation * sensrotation), Centre], If[type ≟ Symetrie, Mirror[objet1, axe], If[type ≟ Symetrieglissee, Mirror[Translate[objet1, vecteurglissement], axe], If[type ≟ Demitour, Rotate[objet1, π, Centre]]]]])