Área de un cono
Author: Edward M. Knote
Date: 6 Junio 2013

h

r

Deslice

r

r

Generatriz (l)

r

h

Generatriz (l)

Fórmula

A = Point(xAxis)
r = 2.1 (slider from 1 to 5, step 0.1)
c = Circle(A, r)
B, C = Intersect(c, xAxis)
d: r / 11
D: (x(B) + d, y(B))
E: (x(C) - d, y(C))
e = Ellipse(E, D, C)
h = 5.2 (slider from 3 to 7, step 0.1)
F = Intersect(xAxis, yAxis)
G: (x(F), y(F) + 1)
u = Vector(F, G)
B'_1 = Translate(B, Vector[u * h])
C'_1 = Translate(C, Vector[u * h])
A'_1 = Translate(A, Vector[u * h])
e'_1 = Translate(e, Vector[u * h])
p_5 = Arc(e'_1, C'_1, B'_1)
q = Arc(e'_1, B'_1, C'_1)
h_6 = Segment(A'_1, A)
p = Segment(A'_1, C'_1)
α = Angle(A, A'_1, C'_1)
j = Line(A, A'_1)
H, I = Intersect(e'_1, j)
t = Circle(I, r)
K = Intersect(t, j, 2)
d_1 = Circle(K, I)
N = Intersect(d_1, j, 2)
v = Vector(H, N)
n = 3 (slider from 0 to 3, step 0.01)
H'_1 = Translate(H, Vector[v * n])
D' = Translate(D, Vector[u * h])
E' = Translate(E, Vector[u * h])
l = Line(B, B'_1)
m = Line(C, C'_1)
P = Intersect(d_1, l, 1)
Q = Intersect(d_1, m, 1)
z = Vector(B'_1, P)
u_1 = Vector(C'_1, Q)
B'' = Translate(B'_1, Vector[z * n])
C'' = Translate(C'_1, Vector[u_1 * n])
R = Midpoint(B'_1, A'_1)
S = Midpoint(B, A)
a_1 = Line(R, S)
T = Intersect(q, a_1)
U = Intersect(d_1, a_1, 1)
v_1 = Vector(T, U)
T' = Translate(T, Vector[v_1 * n])
B_1 = If(n < 1, B'', P)
D_1 = If(n < 1, T', U)
E_1 = If(n < 1, H'_1, N)
F_1 = If(n < 1, C'', Q)
g_1 = Conic(B_1, D_1, E_1, F_1, I)
h_1 = Conic(I, B_1, D_1, E_1, F_1)
l_1 = OrthogonalLine(I, j)
w_2: r * 3.141592653589793
b_2 = OrthogonalLine(H, j)
H_2 = Intersect(m, l_1)
I_2 = Midpoint(H_2, C'_1)
i_2 = OrthogonalLine(C'_1, m)
m_4 = Segment(K, F_1)
e' = Translate(e, Vector[u * h])
a, b = Tangent(A, e'_1)
J, G_2 = Intersect(e', b)
L, R_2 = Intersect(e', a)
f = Segment(A, J)
g = Segment(A, L)
k = Circle(I, sqrt(h^(2) + r^(2)))
M = Intersect(k, j, 1)
s = Circle(M, sqrt(h^(2) + r^(2)))
i = Segment(M, I)
β: 360° * r / i
γ: β / 2
I'_1 = Rotate(I, γ, M)
I'_2 = Rotate(I, -γ, M)
b_1 = OrthogonalLine(I'_2, i_2)
O = Intersect(b_2, b_1)
V = Midpoint(H, O)
c_1 = Circle(V, O)
w = Vector(O, I'_2)
W = Center(g_1)
e_1 = Segment(W, F_1)
w_1 = Vector(H, A)
H' = Translate(H, Vector[w_1 * (n - 1)])
Z = If(n < 1, H, If[n < 2, H', A])
f_1 = Segment(H, Z)
δ: γ / 2
I' = Rotate(I, -δ, M)
z_1 = Vector(L, I')
k_1 = Translate(c_1, Vector[w * (n - 2)])
A_1 = Center(k_1)
C_1, Q_1 = Intersect(k_1, j)
G_1 = Rotate(C_1, 180° * (n - 2), A_1)
H_1 = If(n < 2, H, If[n ≤ 3, G_1, I'_2])
I_1 = Mirror(H_1, j)
L' = Translate(L, Vector[z_1 * (n - 2)])
J_1 = If(n < 2, L, If[n ≤ 3, L', I'])
K_1 = Mirror(J_1, j)
p_1 = Conic(I_1, H_1, J_1, I, K_1)
i_1 = Vector(A, M)
A' = Translate(A, Vector[i_1 * (n - 2)])
L_1 = If(n < 2, A, If[n ≤ 3, A', M])
j_1, m_1 = Tangent(L_1, p_1)
M_1 = Intersect(p_1, m_1, 1)
N_1 = Intersect(p_1, j_1, 1)
poly1, n_1, l_2, m_2 = Polygon(L_1, M_1, N_1)
q_1 = Arc(p_1, N_1, M_1)
r_1 = Line(L_1, b_2)
O_1 = Intersect(p_1, r_1, 1)
P_1 = Intersect(p_1, r_1, 2)
s_1 = Arc(p_1, P_1, O_1)
poly2, i_3, l_3, o_1 = Polygon(L_1, O_1, I_1)
poly3, p_2, l_4, h_2 = Polygon(L_1, H_1, P_1)
t_1 = Arc(p_1, O_1, I_1)
c_2 = Arc(p_1, H_1, P_1)
a_2 = Segment(L_1, I_1)
d_2 = Segment(L_1, H_1)
e_2 = Arc(p_1, H_1, I_1)
poly4, h_3, i_4, l_5 = Polygon(I_1, L_1, H_1)
f_2 = CircleSector(M, I'_2, I'_1)
g_2 = CircleSector(M, I'_2, I'_1)
k_2 = Arc(p_1, H_1, I_1)
j_2 = Segment(M_1, L_1)
n_2 = Segment(N_1, L_1)
poly5, h_4, i_5, l_6 = Polygon(I_1, L_1, H_1)
q_2 = Arc(p_1, H_1, I_1)
poly6, l_7, j_3, a_3 = Polygon(J, A, L)
R_1 = Point(xAxis)
r_2 = OrthogonalLine(R_1, xAxis)
S_1 = Intersect(i_2, r_2)
s_2 = Circle(R_1, r)
T_1, U_1 = Intersect(s_2, xAxis)
V_1: (x(T_1) + d, y(T_1))
W_1: (x(U_1) - d, y(U_1))
t_2 = OrthogonalLine(T_1, i_2)
b_3 = OrthogonalLine(V_1, i_2)
c_3 = OrthogonalLine(W_1, i_2)
Z_1 = Intersect(i_2, t_2)
A_2 = Intersect(i_2, b_3)
B_2 = Intersect(i_2, c_3)
d_3 = Ellipse(A_2, B_2, Z_1)
e_3, f_3 = Tangent(R_1, d_3)
C_2 = Intersect(d_3, f_3, 1)
D_2 = Intersect(d_3, e_3, 1)
poly7, r_3, c_4, d_4 = Polygon(C_2, D_2, R_1)
g_3 = Ellipse(A_2, B_2, Z_1)
k_3 = OrthogonalLine(U_1, xAxis)
E_2, J_2 = Intersect(g_3, k_3)
m_3 = Segment(S_1, E_2)
n_3 = Segment(S_1, R_1)
F_2 = Intersect(d_3, m_3, 1)
K_2 = Midpoint(g)
L_2 = Midpoint(f_1)
M_2 = Point(j)
N_2 = Midpoint(I_1, A')
O_2 = Midpoint(A', H_1)
u_2 = Vector(M_2, N_2)
v_2 = Vector(M_2, O_2)
p_3 = Line(M_2, r_1)
P_2 = Point(p_3)
z_2 = Vector(P_2, K_2)
u_3 = Vector(P_2, L_2)
o = false
Q_2 = Center(g_3)
ε = Angle(F_2, Q_2, R_1)
q_3 = Segment(I_1, H_1)
S_2 = Intersect(k_2, q_3, 2)