四面體中的四個內切球
Author: 藍邦偉  老師

$A$

$B$

$C$

$D$

Sphere

g = 5.633 (slider from 0 to 10, step 0.1)
A_1 = (0.5773502691896257, -1, 1)
A_2 = (0.5773502691896257, 1, 1)
A_3 = (-1.1547005383792515, 0, 1)
A_4 = (0, 0, 2.6329931618554516)
a = Sphere(A_1, 1)
b = Sphere(A_2, 1)
c = Sphere(A_3, 1)
d = Sphere(A_4, 1)
e, face1, face2, face4, face3, edge1, edge4, edge2, edge3, edge5, edge6 = Pyramid(A_1, A_2, A_3, A_4)
B_4: (0, 0, g)
f = Segment((0, 0), B_4)
i = Segment((0, 0), B_4)
k = Line(B_4, edge5)
l = Line(B_4, edge3)
m = Line(B_4, edge6)
B_1 = Intersect(k, xOyPlane)
B_2 = Intersect(l, xOyPlane)
B_3 = Intersect(m, xOyPlane)
h, face5, face6, face7, face9, face10, edge8, edge11, edge12, edge9, edge7, edge11, edge10, edge12 = Pyramid(B_4, B_2, B_1, B_3, B_1)
j, face11, face12, face13, edge13, edge8, edge7 = Pyramid(face6, B_4)
n, face14, face15, face16, edge14, edge9, edge12 = Pyramid(face10, B_3)
o, face17, face18, face19, edge15, edge11, edge8 = Pyramid(face12, B_2)
p, face20, face21, face22, edge18, edge16, edge17 = Pyramid(face10, B_2)
q, face23, face24, face25, edge21, edge19, edge20 = Pyramid(face10, B_2)
r, face26, face27, face28, edge12, edge7, edge22 = Pyramid(face10, B_1)
s, face29, face30, face31, edge25, edge23, edge24 = Pyramid(face10, B_2)
A = Midpoint(B_1, B_3)
t = Segment(B_4, A)
a_1 = OrthogonalLine(A_4, t, space)
B = Intersect(a_1, edge9)
C = Intersect(a_1, t)
b_1 = Segment(C, A_4)
c_1 = Segment(B_4, (0, 0, 0))
d_1 = Segment(A, (0, 0, 0))
u = true