وہ نظم جس کا ہر شعر مفہوم کے لحاظ سے اپنی جگہ مکمل ہو
Answers
Answer:
Explanation:
coordinate
z
.
Place the center of a unit sphere at (0,0,1)
(
0
,
0
,
1
)
, so that it touches the origin of the
x
-
y
-plane.
Connect every point in the plane with (0,0,2)
(
0
,
0
,
2
)
, which is the topmost point of the sphere, using lines, and identify the point where a line intersects with the plane with the point where the same line intersects with the sphere. This mapping :ℝ2→{⃗∈ℝ3:|⃗−(0,0,1)|=1}∖{(0,0,2)}
p
:
R
2
→
{
r
→
∈
R
3
:
|
r
→
−
(
0
,
0
,
1
)
|
=
1
}
∖
{
(
0
,
0
,
2
)
}
is continuous and bijective and known as the stereographic projection.
Add the point (0,0,2)
(
0
,
0
,
2
)
to the codomain and the point ∞
∞
to the domain of the mapping and define (∞)=(0,0,2)
p
(
∞
)
=
(
0
,
0
,
2
)
. This definition makes sense, because for every sequence ()
(
a
n
)
n
in ℝ2
R
2
with →∞
a
n
→
∞
as →∞
n
→
∞
, it obviously holds ()→(0,0,2)
p
(
a
n
)
→
(
0
,
0
,
2
)
.