Ponto A

Ponto B

|x_A-x_B|

|y_A-y_B|

|z_A-z_B|

Teorema de Pitágoras (auxiliar)

Teorema de Pitágoras

 \overline{ AB }^2 =\left(\sqrt{(x_A-x_B)^2+(y_A-y_B)^2}\right)^2+(|z_A-z_B|)^2

Final

z

y

x

(x_A,y_A,z_A)

(x_B,y_B,z_B)

(x_A,y_A,z_B)

(x_B,y_A,z_B)

Paralelepípedo

 \overline{ CB } =\sqrt{(x_A-x_B)^2+(y_A-y_B)^2}

 \overline{CB } ^2=(x_A-x_B)^2+(y_A-y_B)^2

 \overline{ AB }^2 =(x_A-x_B)^2+(y_A-y_B)^2+(z_A-z_B)^2

 \overline{ AB } =\sqrt {(x_A-x_B)^2+(y_A-y_B)^2+(z_A-z_B)^2}

O = (1.0799999999999992, 0.7800000000000002)
a = Line(O, yAxis)
b = Line(O, xAxis)
A_1 = Point(b)
B_1 = Rotate(A_1, 45°, O)
α = Angle(A_1, O, B_1)
c = Line(O, B_1)
x_A = Point(c)
d = Line(x_A, b)
y_A = Point(b)
e = Line(y_A, c)
E = Intersect(d, e)
f = Line(E, a)
z_A = Point(a)
u = Vector(O, z_A)
A = Translate(E, u)
g = Segment(x_A, E)
h = Segment(E, y_A)
i = Segment(E, A)
y_B = Point(b)
x_B = Point(c)
z_B = Point(a)
j = Line(x_B, b)
k = Line(y_B, c)
G = Intersect(j, k)
l = Line(G, a)
v = Vector(O, z_B)
B = Translate(G, v)
m = Segment(x_B, G)
n = Segment(G, y_B)
p = Segment(G, B)
o = true
q = false
r = Segment(A, B)
w = Vector(z_A, z_B)
C = Translate(A, w)
s = Segment(C, B)
t = Segment(C, A)
z = Vector(x_A, x_B)
D = Translate(C, z)
a1 = Segment(C, D)
b1 = Segment(D, B)
F = Midpoint(a1)
H = Midpoint(b1)
I = Midpoint(t)
J = Midpoint(s)
c1 = false
d1 = false
K = Midpoint(r)
e1 = false
L = Point(a)
u1 = Vector(O, L)
M = Point(a)
f1 = Segment(O, M)
N = Point(b)
g1 = Segment(O, N)
P = Point(b)
v1 = Vector(O, P)
Q = Point(c)
w1 = Vector(O, Q)
R = Point(c)
h1 = Segment(O, R)
i1 = Line(C, b1)
j1 = Line(B, a1)
S = Intersect(i1, j1)
k1 = Segment(C, S)
l1 = Segment(S, B)
m1 = Line(A, b1)
T = Translate(A, z)
n1 = Segment(A, T)
p1 = Segment(T, D)
q1 = Line(T, m1)
r1 = Line(B, p1)
U = Intersect(q1, r1)
s1 = Segment(T, U)
t1 = Segment(U, B)
a2 = Line(U, l1)
V = Intersect(m1, a2)
b2 = Segment(U, V)
c2 = Segment(A, V)
o1 = false
d2 = Segment(V, S)
e2 = Segment(C, B)