Les pyramides
Author: Daniel Mentrard

http://dmentrard.free.fr/GEOGEBRA/index.htm

Número de lados de la base

O = (1.1206141222422852, -0.16436500532544787)
Arista = 1.3000000000000003 (slider from 0.1 to 5, step 0.1)
Zoom = 1 (slider from 0.5 to 5, step 0.1)
Vista = (-0.8129751596391253, 0.30038494076474276)
ya: y(Vista)
sintheta: sin(ya)
xa: x(Vista)
sinphi: sin(xa)
cosphi: cos(xa)
xy: -(Zoom) * cosphi * sintheta
B_1 = (-1.0125985624092453, -0.20682364237566353)
Y: (x(B_1) + Zoom * cosphi, y(B_1) + Zoom * sinphi * sintheta)
v = Vector(B_1, Y)
B = Translate(O, Vector[Arista * v])
D = Mirror(B, O)
h = Segment(D, O)
X: (x(B_1) + Zoom * sinphi, y(B_1) + xy)
u = Vector(B_1, X)
G = Translate(B, Vector[Arista * u])
H = Mirror(G, O)
L = Midpoint(D, H)
U = Midpoint(H, L)
W = Midpoint(U, L)
b1 = Segment(W, O)
A = Translate(O, Vector[Arista * u])
E = Mirror(A, O)
l = Segment(E, B)
M_1 = Midpoint(l)
N = Midpoint(M_1, E)
P = Midpoint(N, M_1)
m = Line(O, P)
I = Translate(E, Vector[Arista * v])
E2 = Midpoint(E, I)
F2 = Midpoint(E2, E)
G2 = Midpoint(F2, E2)
l2 = Segment(G2, O)
E1 = Midpoint(I, B)
F1 = Midpoint(I, E1)
H1 = Midpoint(E1, F1)
a1 = Segment(O, H1)
J = Mirror(I, O)
poly1, h_1, i_1, g_1, j_1 = Polygon(H, I, G, J)
Q = Intersect(m, h_1)
R = Midpoint(P, Q)
S_1 = Midpoint(Q, R)
T = Midpoint(S_1, R)
p = Conic(B, T, E, D, A)
H2 = Intersect(p, l2)
I1 = Intersect(p, a1)
k2 = Line(I1, O)
C2, D2 = Intersect(p, k2)
B1 = Intersect(p, b1)
j2 = Line(B1, O)
A2, B2 = Intersect(p, j2)
i = Segment(E, O)
I2 = Mirror(H2, i)
J2 = Mirror(I2, h)
d = Segment(O, A)
J2' = Mirror(J2, d)
costheta: cos(ya)
Altura = 2.8000000000000007 (slider from -5 to 5, step 0.1)
Z: (x(B_1) + 0.0, y(B_1) + Zoom * costheta)
w = Vector(B_1, Z)
a = OrthogonalLine(Vista, yAxis)
b = OrthogonalLine(Vista, xAxis)
c: cos(ya)
S = Translate(O, Vector[Altura * w])
e = Segment(O, B)
f = Segment(O, S)
n_1 = Line(D, f)
r = Line(B, f)
s = Line(E, f)
n = 5 (slider from 3 to 8, step 1)
q = Segment(H, G)
t = Segment(I, J)
F, K = Intersect(p, t)
V = Midpoint(L, D)
A1 = Midpoint(L, V)
C1 = Midpoint(H, U)
D1 = Midpoint(V, D)
G1 = Midpoint(E1, B)
f1 = Segment(B1, A)
g1 = Segment(A, I1)
h1 = Segment(I1, B1)
i1 = Segment(D, A)
j1 = Segment(A, B)
k1 = Segment(D, E)
l1 = Segment(E, B)
J1 = Intersect(p, h, 1.0)
K1 = Intersect(g_1, t)
L1 = Midpoint(D, J)
M1 = Midpoint(D, L1)
N1 = Midpoint(D, M1)
O1 = Midpoint(M1, L1)
P1 = Midpoint(O1, L1)
Q1 = Midpoint(O1, P1)
r1 = Segment(Q1, O)
R1 = Intersect(p, r1)
S1 = Midpoint(H, E)
T1, U1 = Intersect(p, q)
s1 = Segment(R1, A)
V1 = Midpoint(H, S1)
t1 = Segment(V1, O)
W1 = Intersect(p, t1)
a2 = Segment(R1, W1)
b2 = Segment(W1, K)
Z1 = Midpoint(B, G)
c2 = Segment(K, Z1)
d2 = Segment(Z1, A)
poly2, r1_1, a_1, z1, k_1, w1 = Polygon(R1, A, Z1, K, W1)
poly3, d_1, a_2, b_1, e_1 = Polygon(D, A, B, E)
poly5, m2, n2, p2, q2, r2, s2, t2, a3, b3, c3 = Polygon(B, I1, H2, I2, B1, D, D2, J2, J2', B2)
poly4, i1_1, b1_1, a_3 = Polygon(B1, A, I1)
B' = Mirror(B, d)
I1' = Mirror(I1, d)
H2' = Mirror(H2, d)
I2' = Mirror(I2, d)
B1' = Mirror(B1, d)
D' = Mirror(D, d)
D2' = Mirror(D2, d)
B2' = Mirror(B2, d)
poly6, a_4, b2_1, i1_2, e_2, b1_2, d2_1 = Polygon(A, B2, I1, E, B1, D2)
M2 = Intersect(j2, i_1)
N2 = Midpoint(M2, G)
j3 = Segment(O, N2)
L2 = Intersect(p, j3)
O2 = Midpoint(G1, B)
P2 = Midpoint(E1, G1)
Q2 = Midpoint(P2, G1)
R2 = Midpoint(Q2, G1)
l3 = Segment(R2, O)
S2 = Intersect(p, l3)
T2 = Midpoint(I, E2)
U2 = Midpoint(T2, E2)
V2 = Midpoint(G2, E2)
S2' = Mirror(S2, l3)
n3 = Segment(V2, O)
W2 = Intersect(p, n3)
p3 = Segment(S2, W2)
A' = Mirror(A, d)
W2' = Mirror(W2, n3)
Z2 = Midpoint(S1, V1)
A3 = Midpoint(S1, Z2)
r3 = Segment(A3, O)
B3 = Intersect(p, r3)
s3 = Segment(W2, B3)
t3 = Segment(O, V)
D3 = Intersect(p, t3)
a4 = Segment(B3, D3)
k3 = Segment(A, B2)
m3 = Segment(B2, S2)
A'_1 = Mirror(A, d)
B2'_1 = Mirror(B2, d)
b4 = Segment(A, D2)
c4 = Segment(D2, D3)
poly7, a_5, f_1, d_2, u1, e_3, k_2, b_2, t1_1 = Polygon(A, F, D, U1, E, K, B, T1)
poly8, b3_1, w2, s2_1, b2_2, a_6, d2_2, d3_1 = Polygon(B3, W2, S2, B2, A, D2, D3)
z = Vector(O, S)
B1'_1 = Translate(B1, z)
A'_2 = Translate(A, z)
I1'_1 = Translate(I1, z)
poly4', i1'_1, b1'_1, a'_2 = Polygon(B1'_1, A'_2, I1'_1)
poly9, b1'_2, b1_3, i1_3, i1'_2 = Polygon(B1'_1, B1, I1, I1'_1)
poly10, a_7, a'_1, b1'_3, b1_4 = Polygon(A, A'_2, B1'_1, B1)
poly11, a'_3, i1'_3, i1_4, a_8 = Polygon(A'_2, I1'_1, I1, A)
D'_1 = Translate(D, z)
A'_3 = Translate(A, z)
B'_1 = Translate(B, z)
E' = Translate(E, z)
poly3', d'_1, a'_4, b'_1, e' = Polygon(D'_1, A'_3, B'_1, E')
g = Segment(A'_2, A)
j = Segment(D'_1, D)
k = Segment(E', E)
c1 = Segment(B'_1, B)
R1' = Translate(R1, z)
A'_4 = Translate(A, z)
Z1' = Translate(Z1, z)
K' = Translate(K, z)
W1' = Translate(W1, z)
poly2', r1', a'_5, z1', k', w1' = Polygon(R1', A'_4, Z1', K', W1')
d1 = Segment(R1', R1)
e1 = Segment(A'_4, A)
m1 = Segment(W1', W1)
n1 = Segment(Z1', Z1)
p1 = Segment(K', K)
A'_5 = Translate(A, z)
B2'_2 = Translate(B2, z)
I1'_2 = Translate(I1, z)
E'_1 = Translate(E, z)
B1'_2 = Translate(B1, z)
D2'_1 = Translate(D2, z)
poly6', a'_6, b2'_2, i1'_4, e'_1, b1'_4, d2'_1 = Polygon(A'_5, B2'_2, I1'_2, E'_1, B1'_2, D2'_1)
q1 = Segment(D2'_1, D2)
e2 = Segment(B2'_2, B2)
f2 = Segment(I1'_2, I1)
g2 = Segment(E'_1, E)
h2 = Segment(B1'_2, B1)
B3' = Translate(B3, z)
W2'_1 = Translate(W2, z)
S2'_1 = Translate(S2, z)
B2'_3 = Translate(B2, z)
A'_6 = Translate(A, z)
D2'_2 = Translate(D2, z)
D3' = Translate(D3, z)
poly8', b3', w2'_1, s2'_1, b2'_3, a'_7, d2'_2, d3' = Polygon(B3', W2'_1, S2'_1, B2'_3, A'_6, D2'_2, D3')
i2 = Segment(D2'_2, D2)
d3 = Segment(D3', D3)
e3 = Segment(B3', B3)
f3 = Segment(B2'_3, B2)
g3 = Segment(S2'_1, S2)
h3 = Segment(W2'_1, W2)
A'_7 = Translate(A, z)
F' = Translate(F, z)
D'_2 = Translate(D, z)
U1' = Translate(U1, z)
E'_2 = Translate(E, z)
K'_1 = Translate(K, z)
B'_2 = Translate(B, z)
T1' = Translate(T1, z)
poly7', a'_8, f', d'_2, u1', e'_2, k'_1, b'_2, t1' = Polygon(A'_7, F', D'_2, U1', E'_2, K'_1, B'_2, T1')
i3 = Segment(F', F)
q3 = Segment(T1', T1)
d4 = Segment(B'_2, B)
e4 = Segment(K'_1, K)
f4 = Segment(E, E'_2)
g4 = Segment(U1', U1)
h4 = Segment(D'_2, D)
C = Point(poly7)