$\text{Grand axe}$

$\Psi$

Montrer/Cacher faisceaux

Oeil

Autre Faisceau

A_1 = (-0.25055229377132127, 0.09489567425244591)
A_2 = (-0.25996447466871964, 0.25036658747033846)
A_3 = (0.2, 0.2)
E = (-0.05862804942699439, -0.06429786181272552)
A_4 = (-0.0757837859079833, 0.3116130919203267)
c = Conic(A_1, A_2, A_3, A_4, E)
F, G, H, I = Vertex(c)
J, K = Focus(c)
O = Center(c)
h_0 = Hyperbola(G, F, Distance[O, K])
h_{3D} = Rotate(h_0, 1.5708, Line[F, G])
L = Point(h_{3D})
p_0 = Plane(F, G, L)
f = AngularBisector(G, L, F)
a = Segment(L, G)
M = Point(a)
p_1 = OrthogonalPlane(M, f)
j = IntersectPath(p_0, p_1)
N = Intersect(j, Line[F, G])
p = OrthogonalPlane(F, Line[H, I])
e = Eccentricity(c)
α = Angle(Vector[(1, 0)], Vector[F, G])
φ: Angle[G, L, F] / 2
b = Segment(L, F)
g = ConeInfinite(L, f, φ)
d = OrthogonalLine(M, f, space)
P = Intersect(f, d)
h = Circle(P, M, f)
i, i_2, i_3 = Cone(h, (-Distance[L, P]))
k = Line((0, 0, 0), f)
θ = Angle(M, N, O)
e': sin(θ) / cos(φ)
l = Segment(M, N)
m = Line(F, G)
β = Angle(f, Line[L, M])
texte1: "\text{Excentricité de la conique: en 2D e \approx " + (LaTeX[e]) + " et, par ailleurs, via la 3D, e=\frac{sin(\psi)}{cos(\theta)} \approx " + (LaTeX[e']) + ""
S = Point(c)
T = (0.786021555835075, 0.33711230770156686)
S_1 = (0.27592425876747106, -0.770341387250449)
n = Line(T, S_1)
d_1 = Line(S, A_1)
d_2 = Line(S, A_2)
d_3 = Line(S, A_3)
d_4 = Line(S, A_4)
A'_1 = Intersect(n, d_1)
A'_2 = Intersect(n, d_2)
A'_3 = Intersect(n, d_3)
A'_4 = Intersect(d_4, n)
brprt_0 = CrossRatio(A'_1, A'_2, A'_3, A'_4)
d'_1 = IntersectPath(p_1, Plane[L, d_1])
d'_2 = IntersectPath(p_1, Plane[L, d_2])
d'_3 = IntersectPath(p_1, Plane[L, d_3])
d'_4 = IntersectPath(p_1, Plane[L, d_4])
q = IntersectPath(p_1, xOyPlane)
A''_1 = Intersect(q, d'_1)
A''_2 = Intersect(q, d'_2)
A''_3 = Intersect(q, d'_3)
A''_4 = Intersect(q, d'_4)
brprt_1 = CrossRatio((x(A''_1), y(A''_1)), (x(A''_2), y(A''_2)), (x(A''_3), y(A''_3)), (x(A''_4), y(A''_4)))
v0 = true
r, s = Axes(h_{3D})
L' = Mirror(L, s)
texte2: "\text{Birapport: b=\frac{\frac{\overline{A'_1A'_3}}{\overline{A'_1A'_4}}}{\frac{\overline{A'_2A'_3}}{\overline{A'_2A'_4}}}=\frac{\frac{\overline{A''_1A''_3}}{\overline{A''_1A''_4}}}{\frac{\overline{A''_2A''_3}}{\overline{A''_2A''_4}}}\approx" + (LaTeX[brprt_0]) + ""
s' = Point(h)
S' = Intersect(Line[L, s'], c)
v1 = true
a_1 = Intersect(d'_1, Line[L, A_1])
a_2 = Intersect(d'_2, Line[L, A_2])
a_4 = Intersect(d'_4, Line[L, A_4])
a_3 = Intersect(d'_3, Line[L, A_3])
e_1 = Line(s', a_1)
e_2 = Line(s', a_2)
e_3 = Line(s', a_3)
e_4 = Line(s', a_4)
e'_4 = Line(S', A_4)
e'_3 = Line(S', A_3)
e'_2 = Line(S', A_2)
e'_1 = Line(S', A_1)