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 = false
rotations = false
demitours = false
symetriesaxiales = false
translations = true
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': (20, 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)
p = Circle(A', 10)
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)
axe = Rotate(preaxe, (directionaxe * π / 4), Pointaxe)
Centre: (Random[-8, 8], Random[-8, 8])
Originevecteur: Centre
perturbationy = RandomUniform(0.2, 0.8)
perturbationx = RandomUniform(0.2, 0.8)
prevecteur: (perturbationx + ((Random[2, 8] * 2) * (Random[0, 1] - 0.5)), perturbationy + ((Random[2, 8] * 2) * (Random[0, 1] - 0.5)))
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
coinG = Translate(A, (-1.5, -1.5))
coinD = Translate(coinG, (16, 0))
reponse = If(type ≟ Translation, Translate[dragon, Vecteur], If[type ≟ Rotation, Rotate[dragon, (anglerotation * sensrotation), Centre], If[type ≟ Symetrie, Mirror[dragon, axe], If[type ≟ Symetrieglissee, Mirror[Translate[dragon, vecteurglissement], axe], If[type ≟ Demitour, Rotate[dragon, π, Centre]]]]])
image = If(retourner, Rotate[Mirror[Translate[dragon, u], d], α, A'], Rotate[Translate[dragon, u], α, A'])