A + (r cos(0π / 6), r sin(0π / 6)) + ((3 (0.5) π r / 3, r) - (r cos(0π / 6), r sin(0π / 6))) t

A + (r cos(π / 6), r sin(π / 6)) + ((2 (0.5) π r / 3, r) - (r cos(π / 6), r sin(π / 6))) t

A + (r cos(2π / 6), r sin(2π / 6)) + ((0.5π r / 3, r) - (r cos(2π / 6), r sin(2π / 6))) t

A + (r cos(3π / 6), r sin(3π / 6)) + ((0 (0.5) π r / 3, r) - (r cos(3π / 6), r sin(3π / 6))) t

si[t<=1,A + (r cos(4π / 6), r sin(4π / 6)) + ((-1 (0.5) π r / 3, r) - (r cos(4π / 6), r sin(4π / 6))) t,A +  (-1 (0.5) π r / 3, r)]

A + (r cos(5π / 6), r sin(5π / 6)) + ((-2 (0.5) π r / 3, r) - (r cos(5π / 6), r sin(5π / 6))) t

A + (r cos(6π / 6), r sin(6π / 6)) + ((-3 (0.5) π r / 3, r) - (r cos(6π / 6), r sin(6π / 6))) t

A + (0.5 (0.5) π r / 3, 0) t

A + (1.5 (0.5) π r / 3, 0) t

si[t<=1,A + (2.5 (0.5) π r / 3, 0) t,A + (2.5 (0.5) π r / 3, 0) ]

Si[t ≤ 1, A + (-0.5 (0.5) π r / 3, 0) t, A + (-0.5 (0.5) π r / 3, 0)]

A + (-3.5 (0.5) π r / 3, -r)

Si[t ≤ 1, A + (r cos(7π / 6), r sin(7π / 6)) + ((-2 (0.5) π r / 3, -r) - (r cos(7π / 6), r sin(7π / 6))) t, A + (-2 (0.5) π r / 3, -r) + (t - 1) (0.5π r / 3, 0)]

Si[t ≤ 1, A + (r cos(8π / 6), r sin(8π / 6)) + ((-1 (0.5) π r / 3, -r) - (r cos(8π / 6), r sin(8π / 6))) t, A + (-0 (0.5) π r / 3, -r) + (t - 1) (0.5π r / 3, 0)]

Si[t ≤ 1, A + (r cos(9π / 6), r sin(9π / 6)) + ((-1 (0.5) π r / 3, -r) - (r cos(9π / 6), r sin(9π / 6))) t, A + (-0 (0.5) π r / 3, -r) + (t - 1) (0.5π r / 3, 0)]

Si[t ≤ 1, A + (r cos(9π / 6), r sin(9π / 6)) + ((-0 (0.5) π r / 3, -r) - (r cos(9π / 6), r sin(9π / 6))) t, A + (-0 (0.5) π r / 3, -r) + (t - 1) (0.5π r / 6, 0)]

Si[t ≤ 1, A + (r cos(11π / 6), r sin(11π / 6)) + ((1 (0.5) π r / 3, -r) - (r cos(11π / 6), r sin(11π / 6))) t, A + (1 (0.5) π r / 3, -r) + (t - 1) (0.5π r / 6, 0)]

Si[t ≤ 1, A + (-0.5 (0.5) π r / 3, 0) t, Si[(t ≤ 2) ∧ (t > 1), A + (-1 (0.5) π r / 3, 0) + t (0.5 (0.5) π r / 3, 0), Si[(t ≥ 2) ∧ (t < 3), A + (-0 (0.5) π r / 3, (t - 2) r), A + (-0 (0.5) π r / 3, r)]]]

A + (2.5 (0.5) π r / 3, 0) t

Si[t ≤ 1, A + (-1.5 (0.5) π r / 3, 0) t, Si[(t ≤ 2) ∧ (t > 1), A + (-2 (0.5) π r / 3, 0) + t (0.5 (0.5) π r / 3, 0), Si[(t ≥ 2) ∧ (t < 3), A + (-1 (0.5) π r / 3, (t - 2) r), A + (-1 (0.5) π r / 3, r)]]]

Si[t ≤ 1, A + (-2.5 (0.5) π r / 3, 0) t, Si[(t ≤ 2) ∧ (t > 1), A + (-3 (0.5) π r / 3, 0) + t (0.5 (0.5) π r / 3, 0), Si[(t ≥ 2) ∧ (t < 3), A + (-2 (0.5) π r / 3, (t - 2) r), A + (-2 (0.5) π r / 3, r)]]]

Si[t ≤ 1, A + (-1.5 (0.5) π r / 3, 0) t, Si[(t ≤ 2) ∧ (t > 1), A + (-2 (0.5) π r / 3, 0) + t (0.5 (0.5) π r / 3, 0), Si[(t ≥ 2) ∧ (t < 3), A + (-1 (0.5) π r / 3, (t - 2) r), A + (-1 (0.5) π r / 3, r)]]]

R

π R

Aire du disque

 : A=π R²

start

stop

reset

laurent.costa@ac-lyon.fr

auto

B = (4.1362903225806456, -11.266935483870991)
r = 6.2 (slider from 1 to 10, step 0.1)
t = 0 (slider from 0 to 5, step 1.0E-4)
A: (x(B), y(B) + r + 2)
B0 = If(t ≤ 1, A + (r, 0) + ((3 * 0.5 * π * r / 3, r) - (r * cos(0 * π / 6), r * sin(0 * π / 6))) * t, A + (3 * 0.5 * π * r / 3, r))
B1 = If(t ≤ 1, A + (r * cos(π / 6), r * sin(π / 6)) + ((2 * 0.5 * π * r / 3, r) - (r * cos(π / 6), r * sin(π / 6))) * t, A + (2 * 0.5 * π * r / 3, r))
B2 = If(t ≤ 1, A + (r * cos(2 * π / 6), r * sin(2 * π / 6)) + ((0.5 * π * r / 3, r) - (r * cos(2 * π / 6), r * sin(2 * π / 6))) * t, A + (0.5 * π * r / 3, r))
B3 = If(t ≤ 1, A + (r * cos(3 * π / 6), r * sin(3 * π / 6)) + ((-0 * 0.5 * π * r / 3, r) - (r * cos(3 * π / 6), r * sin(3 * π / 6))) * t, A + (-0 * 0.5 * π * r / 3, r))
B4 = If(t ≤ 1, A + (r * cos(4 * π / 6), r * sin(4 * π / 6)) + ((-1 * 0.5 * π * r / 3, r) - (r * cos(4 * π / 6), r * sin(4 * π / 6))) * t, A + (-1 * 0.5 * π * r / 3, r))
B5 = If(t ≤ 1, A + (r * cos(5 * π / 6), r * sin(5 * π / 6)) + ((-2 * 0.5 * π * r / 3, r) - (r * cos(5 * π / 6), r * sin(5 * π / 6))) * t, A + (-2 * 0.5 * π * r / 3, r))
B6 = If(t ≤ 1, A + (r * cos(6 * π / 6), r * sin(6 * π / 6)) + ((-3 * 0.5 * π * r / 3, r) - (r * cos(6 * π / 6), r * sin(6 * π / 6))) * t, A + (r * cos(6 * π / 6), r * sin(6 * π / 6)) + (-3 * 0.5 * π * r / 3, r) - (r * cos(6 * π / 6), r * sin(6 * π / 6)))
A1 = If(t ≤ 1, A + (0.5 * 0.5 * π * r / 3, 0) * t, A + (0.5 * 0.5 * π * r / 3, 0))
A2 = If(t ≤ 1, A + (1.5 * 0.5 * π * r / 3, 0) * t, A + (1.5 * 0.5 * π * r / 3, 0))
A3 = If(t ≤ 1, A + (2.5 * 0.5 * π * r / 3, 0) * t, A + (2.5 * 0.5 * π * r / 3, 0))
A_1 = If(t ≤ 1, A + (-0.5 * 0.5 * π * r / 3, 0) * t, A + (-0.5 * 0.5 * π * r / 3, 0))
A_2 = If(t ≤ 1, A + (-1.5 * 0.5 * π * r / 3, 0) * t, A + (-1.5 * 0.5 * π * r / 3, 0))
A_3 = If(t ≤ 1, A + (-2.5 * 0.5 * π * r / 3, 0) * t, A + (-2.5 * 0.5 * π * r / 3, 0))
c1 = CircleSector(A_3, B5, B6)
c2 = CircleSector(A_2, B4, B5)
c3 = CircleSector(A_1, B3, B4)
c4 = CircleSector(A1, B2, B3)
c5 = CircleSector(A2, B1, B2)
c6 = CircleSector(A3, B0, B1)
temps: {314, 18, 55, 14, 4, 4, 2012, "Avril", "Mercredi", 4}
B_6 = If(t ≤ 1, A + (r * cos(6 * π / 6), r * sin(6 * π / 6)) + ((-3 * 0.5 * π * r / 3, -r) - (r * cos(6 * π / 6), r * sin(6 * π / 6))) * t, If[(t > 1) ∧ (t ≤ 2), A + (-3 * 0.5 * π * r / 3, -r) + (t - 1) * (0.5 * π * r / 6, 0), If[(t > 2) ∧ (t ≤ 3), A + (-2.5 * 0.5 * π * r / 3, -r) + (t - 2) * (0, r), A + (-2.5 * 0.5 * π * r / 3, 0)]])
B_5 = If(t ≤ 1, A + (r * cos(7 * π / 6), r * sin(7 * π / 6)) + ((-2 * 0.5 * π * r / 3, -r) - (r * cos(7 * π / 6), r * sin(7 * π / 6))) * t, If[(t > 1) ∧ (t ≤ 2), A + (-2 * 0.5 * π * r / 3, -r) + (t - 1) * (0.5 * π * r / 6, 0), If[(t > 2) ∧ (t ≤ 3), A + (-1.5 * 0.5 * π * r / 3, -r) + (t - 2) * (0, r), A + (-1.5 * 0.5 * π * r / 3, 0)]])
B_4 = If(t ≤ 1, A + (r * cos(8 * π / 6), r * sin(8 * π / 6)) + ((-1 * 0.5 * π * r / 3, -r) - (r * cos(8 * π / 6), r * sin(8 * π / 6))) * t, If[(t > 1) ∧ (t ≤ 2), A + (-1 * 0.5 * π * r / 3, -r) + (t - 1) * (0.5 * π * r / 6, 0), If[(t > 2) ∧ (t ≤ 3), A + (-0.5 * 0.5 * π * r / 3, -r) + (t - 2) * (0, r), A + (-0.5 * 0.5 * π * r / 3, 0)]])
B_3 = If(t ≤ 1, A + (r * cos(9 * π / 6), r * sin(9 * π / 6)) + ((-0 * 0.5 * π * r / 3, -r) - (r * cos(9 * π / 6), r * sin(9 * π / 6))) * t, If[(t > 1) ∧ (t ≤ 2), A + (-0 * 0.5 * π * r / 3, -r) + (t - 1) * (0.5 * π * r / 6, 0), If[(t > 2) ∧ (t ≤ 3), A + (0.5 * 0.5 * π * r / 3, -r) + (t - 2) * (0, r), A + (0.5 * 0.5 * π * r / 3, 0)]])
B_2 = If(t ≤ 1, A + (r * cos(10 * π / 6), r * sin(10 * π / 6)) + ((0.5 * π * r / 3, -r) - (r * cos(10 * π / 6), r * sin(10 * π / 6))) * t, If[(t > 1) ∧ (t ≤ 2), A + (0.5 * π * r / 3, -r) + (t - 1) * (0.5 * π * r / 6, 0), If[(t > 2) ∧ (t ≤ 3), A + (1.5 * 0.5 * π * r / 3, -r) + (t - 2) * (0, r), A + (1.5 * 0.5 * π * r / 3, 0)]])
B_1 = If(t ≤ 1, A + (r * cos(11 * π / 6), r * sin(11 * π / 6)) + ((2 * 0.5 * π * r / 3, -r) - (r * cos(11 * π / 6), r * sin(11 * π / 6))) * t, If[(t > 1) ∧ (t ≤ 2), A + (2 * 0.5 * π * r / 3, -r) + (t - 1) * (0.5 * π * r / 6, 0), If[(t > 2) ∧ (t ≤ 3), A + (2.5 * 0.5 * π * r / 3, -r) + (t - 2) * (0, r), A + (2.5 * 0.5 * π * r / 3, 0)]])
B_0 = If(t ≤ 1, A + (r * cos(12 * π / 6), r * sin(12 * π / 6)) + ((3 * 0.5 * π * r / 3, -r) - (r * cos(12 * π / 6), r * sin(12 * π / 6))) * t, If[(t > 1) ∧ (t ≤ 2), A + (3 * 0.5 * π * r / 3, -r) + (t - 1) * (0.5 * π * r / 6, 0), If[(t > 2) ∧ (t ≤ 3), A + (3.5 * 0.5 * π * r / 3, -r) + (t - 2) * (0, r), A + (3.5 * 0.5 * π * r / 3, 0)]])
D1 = If(t ≤ 1, A + (0.5 * 0.5 * π * r / 3, 0) * t, If[(t ≤ 2) ∧ (t > 1), A + (-0 * 0.5 * π * r / 3, 0) + t * (0.5 * 0.5 * π * r / 3, 0), If[(t ≥ 2) ∧ (t < 3), A + (0.5 * π * r / 3, (t - 2) * r), A + (0.5 * π * r / 3, r)]])
D2 = If(t ≤ 1, A + (1.5 * 0.5 * π * r / 3, 0) * t, If[(t ≤ 2) ∧ (t > 1), A + (0.5 * π * r / 3, 0) + t * (0.5 * 0.5 * π * r / 3, 0), If[(t ≥ 2) ∧ (t < 3), A + (2 * 0.5 * π * r / 3, (t - 2) * r), A + (2 * 0.5 * π * r / 3, r)]])
D3 = If(t ≤ 1, A + (2.5 * 0.5 * π * r / 3, 0) * t, If[(t ≤ 2) ∧ (t > 1), A + 2 * (0.5 * π * r / 3, 0) + t * (0.5 * 0.5 * π * r / 3, 0), If[(t ≥ 2) ∧ (t < 3), A + (3 * 0.5 * π * r / 3, (t - 2) * r), A + (3 * 0.5 * π * r / 3, r)]])
D_1 = If(t ≤ 1, A + (-0.5 * 0.5 * π * r / 3, 0) * t, If[(t ≤ 2) ∧ (t > 1), A + (-1 * 0.5 * π * r / 3, 0) + t * (0.5 * 0.5 * π * r / 3, 0), If[(t ≥ 2) ∧ (t < 3), A + (-0 * 0.5 * π * r / 3, (t - 2) * r), A + (-0 * 0.5 * π * r / 3, r)]])
D_2 = If(t ≤ 1, A + (-1.5 * 0.5 * π * r / 3, 0) * t, If[(t ≤ 2) ∧ (t > 1), A + (-2 * 0.5 * π * r / 3, 0) + t * (0.5 * 0.5 * π * r / 3, 0), If[(t ≥ 2) ∧ (t < 3), A + (-1 * 0.5 * π * r / 3, (t - 2) * r), A + (-1 * 0.5 * π * r / 3, r)]])
D_3 = If(t ≤ 1, A + (-2.5 * 0.5 * π * r / 3, 0) * t, If[(t ≤ 2) ∧ (t > 1), A + (-3 * 0.5 * π * r / 3, 0) + t * (0.5 * 0.5 * π * r / 3, 0), If[(t ≥ 2) ∧ (t < 3), A + (-2 * 0.5 * π * r / 3, (t - 2) * r), A + (-2 * 0.5 * π * r / 3, r)]])
c_3 = CircleSector(D_1, B_4, B_3)
c_4 = CircleSector(D1, B_3, B_2)
C2 = 0
c_5 = CircleSector(D2, B_2, B_1)
c_6 = CircleSector(D3, B_1, B_0)
c = CircleSector(D_3, B_6, B_5)
d = CircleSector(D_2, B_5, B_4)
C: B6 + (0, 0.5)
D: B0 + (0, 0.5)
u = Vector(C, D)
v_1 = Vector(D, C)
a = Line(C, D)
b = OrthogonalLine(A_3, a)
E = Intersect(c1, b)
e = OrthogonalLine(A_3, b)
f = Segment(E, A_3)
g = OrthogonalLine(E, b)
h = Circle(E, r / 2)
F = Intersect(h, g, 2)
i = OrthogonalLine(F, g)
G = Intersect(e, i)
w = Vector(G, F)
z = Vector(F, G)
H = Midpoint(G, F)
I = Midpoint(C, D)
texte3: "" + (Element[temps, 9]) + " " + (Element[temps, 10]) + " " + (Element[temps, 8]) + " " + (Element[temps, 7]) + ""
v = 1 (slider from 0.1 to 3, step 0.1)
texte6 = RotateText("vitesse animation", 1.5707963267948966)