Volume total =

+ 3 

+ 3

+

Faites varier le pourcentage d'augmentation des arêtes de 0% à 100%

%

%

Augm. arêtes

1000

100%

Cliquer ici pour mieux voir que
cette fonction est cubique.

Pourcentage\, de\, l'augmentation\,du\,volume\,=\,\frac{Volume\, ajouté}{Volume\, initial}\,=\,\frac{(Volume\, total\,-\,Volume\,initial)}{Volume\, initial}

r = 0.67 (slider from 0.4 to 0.7, step 0.01)
E = Point(yAxis)
f = Line(E, xAxis)
D: (y(E), 0.0)
h = Line(D, yAxis)
H = Intersect(f, h)
A = Intersect(xAxis, yAxis)
Q = Point(yAxis)
b_5 = Line(Q, xAxis)
k_3 = Segment(A, E)
T: Q + Vector[A, D]
U: Q + Vector[A, E]
Z: Q + Vector[A, H]
T_1 = Midpoint(Z, T)
E_2 = Midpoint(T, T_1)
I = Point(b_5)
c = Circle(A, r)
C_1 = Point(c)
a = Line(C_1, A)
u = Vector(A, C_1)
B: A + y(E) * u
b = Line(E, a)
d = Line(D, a)
e = Line(B, xAxis)
g = Line(B, yAxis)
F = Intersect(b, g)
C = Intersect(d, e)
i = Line(F, f)
j = Line(C, g)
G = Intersect(i, j)
k = Line(G, b)
aug = 0 (slider from 0 to 100, step 1)
B': B + aug / 100.0 * Vector[A, B]
l = Line(B', e)
m = Line(B', yAxis)
D': D + aug / 100.0 * Vector[A, D]
E': E + aug / 100.0 * Vector[A, E]
n = Line(E', xAxis)
p = Line(E', a)
q = Line(D', a)
s = Line(D', m)
F' = Intersect(m, p)
H' = Intersect(n, s)
t = Line(F', n)
C' = Intersect(l, q)
a_1 = Line(C', s)
G' = Intersect(t, a_1)
F_m = Intersect(b, m)
C_m = Intersect(d, l)
i_1 = Line(C_m, m)
G_m = Intersect(k, i_1)
F_s = Intersect(g, p)
j_1 = Line(F_s, n)
G_s = Intersect(j, j_1)
H_s = Intersect(h, n)
H_p = Intersect(f, s)
k_1 = Line(H_p, a)
G_p = Intersect(i, k_1)
C_p = Intersect(e, q)
G_{mp} = Intersect(a_1, k_1)
G_{sm} = Intersect(t, i_1)
l_1 = Line(H', k)
G_{sp} = Intersect(j_1, l_1)
poly1, b_1, c_1, d_1, h_1, e_1, f_1 = Polygon(B, C, D, H, E, F)
g_1 = Segment(F, G)
m_1 = Segment(G, H)
n_1 = Segment(G, C)
poly2, f_m, b', c_m, c_2, g_2, f_2 = Polygon(F_m, B', C_m, C, G, F)
p_1 = Segment(F_m, G_m)
q_1 = Segment(G_m, G)
r_1 = Segment(G_m, C_m)
poly3, g_3, h_2, h_p, d', c_p, c_3 = Polygon(G, H, H_p, D', C_p, C)
s_1 = Segment(G, G_p)
t_1 = Segment(G_p, H_p)
a_2 = Segment(G_p, C_p)
poly4, c_4, c', c_5, c_6 = Polygon(C_m, C', C_p, C)
b_2 = Segment(G_m, G_{mp})
d_2 = Segment(G_{mp}, G_p)
e_2 = Segment(G_{mp}, C')
poly5, f_3, f_s, e', h_s, h_3, g_4 = Polygon(F, F_s, E', H_s, H, G)
i_2 = Segment(F_s, G_s)
j_2 = Segment(G_s, G)
k_2 = Segment(G_s, H_s)
poly6, h_4, h', h_5, h_6 = Polygon(H_s, H', H_p, H)
l_2 = Segment(G_s, G_{sp})
m_2 = Segment(G_{sp}, G_p)
n_2 = Segment(G_{sp}, H')
poly7, f', f_4, f_5, f_6 = Polygon(F', F_s, F, F_m)
p_2 = Segment(F', G_{sm})
q_2 = Segment(G_{sm}, G_s)
r_2 = Segment(G_{sm}, G_m)
s_2 = Segment(G_{sm}, G')
t_2 = Segment(G', G_{sp})
a_3 = Segment(G', G_{mp})
b_3 = Segment(E, E')
d_3 = Segment(B, B')
e_3 = Segment(D, D')
i_3 = Segment(B, A)
j_3 = Segment(A, D)
J: I + Vector[B, B']
K: I + Vector[B, C]
L: I + Vector[B, F]
M: I + Vector[B, G]
N: I + Vector[B, F_m]
O: I + Vector[B, G_m]
P: I + Vector[B, C_m]
poly8, l_4, n_4, j_4, p_4, k_4, m_4 = Polygon(L, N, J, P, K, M)
e_4 = Segment(N, O)
i_4 = Segment(O, M)
q_4 = Segment(O, P)
r_4 = Segment(J, I)
s_4 = Segment(I, L)
t_4 = Segment(I, K)
R: Q + Vector[A, B]
V: Q + Vector[A, F]
W: Q + Vector[A, G]
S: Q + Vector[A, C]
poly9, u_1, v, r_5, s_5, t_5, z = Polygon(U, V, R, S, T, Z)
poly10, u_2, v_1, r_6, s_6, t_6, z_1 = Polygon(U, V, R, S, T, Z)
l_5 = Segment(V, W)
m_5 = Segment(W, Z)
n_5 = Segment(W, S)
p_5 = Segment(U, Q)
q_5 = Segment(Q, T)
a_6 = Segment(Q, R)
A_1: K + I - T
B_1: A_1 + Vector[C, C_p]
D_1: A_1 + Vector[C, C_m]
E_1: A_1 + Vector[C, C']
F_1: A_1 + Vector[C, G]
G_1: A_1 + Vector[C, G_p]
H_1: A_1 + Vector[C, G_m]
I_1: A_1 + Vector[C, G_{mp}]
poly11, h_7, d_7, e_7, b_7, g_7, f_7 = Polygon(H_1, D_1, E_1, B_1, G_1, F_1)
q_6 = Segment(H_1, I_1)
a_7 = Segment(I_1, G_1)
c_7 = Segment(I_1, E_1)
i_7 = Segment(A_1, F_1)
j_7 = Segment(A_1, D_1)
k_7 = Segment(A_1, B_1)
J_1: B_1 + I - T
K_1: J_1 + Vector[G, G_p]
L_1: J_1 + Vector[G, G_s]
M_1: J_1 + Vector[G, G_m]
N_1: J_1 + Vector[G, G_{mp}]
O_1: J_1 + Vector[G, G_{sp}]
P_1: J_1 + Vector[G, G_{sm}]
Q_1: J_1 + Vector[G, G']
poly12, p_8, m_8, n_8, k_8, o_1, l_8 = Polygon(P_1, M_1, N_1, K_1, O_1, L_1)
c_8 = Segment(P_1, Q_1)
d_8 = Segment(Q_1, O_1)
e_8 = Segment(Q_1, N_1)
f_8 = Segment(J_1, M_1)
g_8 = Segment(J_1, K_1)
h_8 = Segment(L_1, J_1)
i_8 = OrthogonalLine(E_2, h)
S_1 = Intersect(g, i_8)
R_1 = Point(i_8)
F_2 = (11.987492199488841, 12.249176158159296)
j_8 = Line(F_2, xAxis)
G_2 = Intersect(j_8, Line[(14.0, 0.0), (14.0, 1.0)])
q_8 = Circle(G_2, aug / 10.0)
H_2 = Intersect(q_8, j_8, 2.0)
distanceBD = Distance(B, D)
I_2 = Point(xAxis)
r_8 = OrthogonalLine(I_2, xAxis)
volume = Function(1.25 + 3.75 * (x - x(I_2)) / 10.0 + 3.75 * (x - x(I_2))^(2.0) / 100.0 + 1.25 * (x - x(I_2))^(3.0) / 1000.0, 0.0, 100.0)
L_2 = Intersect(volume, r_8, 1.0)
distanceL2I2 = Distance(L_2, I_2)
M_2: I_2 + 8.0 * Vector[I_2, L_2]
a_9 = OrthogonalLine(M_2, r_8)
N_2 = Intersect(volume, a_9, 1.0)
b_9 = OrthogonalLine(N_2, a_9)
O_2 = Intersect(b_9, xAxis)
distanceI2O2 = Distance(I_2, O_2)
P_2: I_2 + aug / 100.0 * Vector[I_2, O_2]
c_9 = OrthogonalLine(P_2, xAxis)
Q_2 = Intersect(volume, c_9, 1.0)
d_9 = OrthogonalLine(Q_2, r_8)
R_2 = Intersect(d_9, r_8)
distanceR2I2 = Distance(R_2, I_2)
volume2 = Function(volume(x), x(I_2), x(O_2))
J_2 = Point(r_8)
K_2 = Point(xAxis)
Volume = Vector(I_2, J_2)
Augmentation = Vector(I_2, K_2)
s_8 = Segment(M_2, N_2)
t_8 = Segment(N_2, O_2)
TexteR2I2: "Volume \, = \, " + (distanceR2I2 * 100.0)
e_9 = Segment(P_2, Q_2)
f_9 = Segment(Q_2, R_2)
distanceI2P2 = Distance(I_2, P_2)
TexteI2P2: " Augmentation\, = \, " + (distanceI2P2 * 10.0) + "%"
o = false
texte8: "Volume\,total\, =\," + (y(E)) + "³\,+\,3\,·\," + aug + "%\,·\," + (y(E)) + "³\,+\,3\,·\,(" + aug + "%)²\,·\," + (y(E)) + "³\,+\,(" + aug + "%)³\,·\," + (y(E)) + "³"
texte9: "Volume\,total\, =\," + (y(E)^(3.0)) + " \,+\," + (3.0 * aug / 100.0 * y(E)^(3.0)) + " \,+\," + (3.0 * (aug / 100.0)^(2.0) * y(E)^(3.0)) + " \,+\," + ((aug / 100.0)^(3.0) * y(E)^(3.0)) + " \,=\," + (y(E)^(3.0) + 3.0 * aug / 100.0 * y(E)^(3.0) + 3.0 * (aug / 100.0)^(2.0) * y(E)^(3.0) + (aug / 100.0)^(3.0) * y(E)^(3.0))
Vtotal: y(E)^(3.0) + 3.0 * aug / 100.0 * y(E)^(3.0) + 3.0 * (aug / 100.0)^(2.0) * y(E)^(3.0) + (aug / 100.0)^(3.0) * y(E)^(3.0)
Augmfinal: (3.0 * aug / 100.0 * y(E)^(3.0) + 3.0 * (aug / 100.0)^(2.0) * y(E)^(3.0) + (aug / 100.0)^(3.0) * y(E)^(3.0)) / y(E)^(3.0) * 100.0
Vinitial: y(E)^(3.0)
Vajoute: 3.0 * aug / 100.0 * y(E)^(3.0) + 3.0 * (aug / 100.0)^(2.0) * y(E)^(3.0) + (aug / 100.0)^(3.0) * y(E)^(3.0)
texte10: "=\,\frac{" + Vtotal + "\,-\," + Vinitial + "}{" + Vinitial + "}\,=\,\frac{" + Vajoute + "}{" + Vinitial + "}\,=\," + Augmfinal + "\,%"
U_1 = Intersect(n_4, i_8)
V_1 = Intersect(i_8, k_4)
W_1 = Intersect(i_8, h_7)
Z_1 = Intersect(i_8, b_7)
A_2 = Midpoint(E_2, U_1)
B_2 = Midpoint(V_1, W_1)
C_2: Z_1 + Vector[V_1, B_2]