rapport d'homothétie

sphères de l'hexlet

paramètre t

hexlet inversé

Hexlet régulier

hexlet régulier

α = 1.6929693744344996 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
R = 4.2 (slider from 0 to 10, step 0.1)
B: (R, 0)
d = 1.6 (slider from 0 to R, step 0.1)
T: (d, 0)
O = Intersect(xAxis, yAxis)
B' = Rotate(B, α, T)
a = Line(T, B')
N = Midpoint(B, T)
e = Ellipse(O, T, N)
C_2, C_1 = Intersect(e, a)
S_0 = Sphere(O, B)
t = 4.3 rad (slider from 0 to 6.283185307179586, step (0.05 * rad))
S_1 = Sphere(C_1, T)
S_2 = Sphere(C_2, T)
A2: t
A3: A2 + π / 3
A4: A3 + π / 3
A5: A4 + π / 3
A6: A5 + π / 3
A7: A6 + π / 3
B2: (3 * (R^(2) - d^(2)) / ((3 * R^(2)) + d^(2) - ((((4 * d) * R) * sin(α)) * cos(A2))))
B3: (3 * (R^(2) - d^(2)) / ((3 * R^(2)) + d^(2) - ((((4 * d) * R) * sin(α)) * cos(A3))))
B4: (3 * (R^(2) - d^(2)) / ((3 * R^(2)) + d^(2) - ((((4 * d) * R) * sin(α)) * cos(A4))))
B5: (3 * (R^(2) - d^(2)) / ((3 * R^(2)) + d^(2) - ((((4 * d) * R) * sin(α)) * cos(A5))))
B6: (3 * (R^(2) - d^(2)) / ((3 * R^(2)) + d^(2) - ((((4 * d) * R) * sin(α)) * cos(A6))))
B7: (3 * (R^(2) - d^(2)) / ((3 * R^(2)) + d^(2) - ((((4 * d) * R) * sin(α)) * cos(A7))))
c = Circle(zAxis, B)
f = Ray(O, T)
b = OrthogonalPlane(T, f)
A, C = Intersect(b, c)
g = Segment(O, A)
h = Segment(T, A)
i = Tangent(A, c)
P = Intersect(i, f)
j = Segment(A, P)
β = Angle(O, T, A)
γ = Angle(O, A, P)
k = Segment(C_1, C_2)
D2: ((((2 * R / 3) * sin(α)) * cos(A2)), (((2 * R / 3) * cos(α)) * cos(A2)), ((2 * R / 3) * sin(A2)))
D9: ((R / 2 * cos(α)), (((-R)) / 2 * sin(α)), 0)
D10: (-D9)
D3: ((((2 * R / 3) * sin(α)) * cos(A3)), (((2 * R / 3) * cos(α)) * cos(A3)), ((2 * R / 3) * sin(A3)))
D4: ((((2 * R / 3) * sin(α)) * cos(A4)), (((2 * R / 3) * cos(α)) * cos(A4)), ((2 * R / 3) * sin(A4)))
D5: ((((2 * R / 3) * sin(α)) * cos(A5)), (((2 * R / 3) * cos(α)) * cos(A5)), ((2 * R / 3) * sin(A5)))
D6: ((((2 * R / 3) * sin(α)) * cos(A6)), (((2 * R / 3) * cos(α)) * cos(A6)), ((2 * R / 3) * sin(A6)))
D7: ((((2 * R / 3) * sin(α)) * cos(A7)), (((2 * R / 3) * cos(α)) * cos(A7)), ((2 * R / 3) * sin(A7)))
E2 = Sphere(D2, R / 3)
E3 = Sphere(D3, R / 3)
E4 = Sphere(D4, R / 3)
E5 = Sphere(D5, R / 3)
E6 = Sphere(D6, R / 3)
E7 = Sphere(D7, R / 3)
C2 = Dilate(E2, B2, P)
C3 = Dilate(E3, B3, P)
C4 = Dilate(E4, B4, P)
C5 = Dilate(E5, B5, P)
C6 = Dilate(E6, B6, P)
C7 = Dilate(E7, B7, P)
m = false
E9 = Sphere(D9, R / 2)
E10 = Sphere(D10, R / 2)
l = true

Tool: inversion-sphere (command inversion)
centre ouis point de la sphère ; pole ey point invariant de l'inversion
Input: A, C, D, E
Output: b'

b = Sphere(A, C)
c = Segment(D, E)
f = Segment(D, A)
g = Segment(A, C)
b' = Dilate(b, c^(2) / (f^(2) - g^(2)), D)