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f
(0) =
A
+
B
=
2
c
f
→
(23.10f)
f
(
V
)=
2
ABV
+
B
2
sinV
+(
A
+
B
)
2
(23.10g)
g
(0) = 0 =
c
g
→
(23.10h)
B
2
A
+
B
sin
V
AB
A
+
B
V
+
g
(
V
)=
(23.10i)
Box 23.5 (Equidistant mapping of the torus
M
2
:=
T
2
A,B
onto the central plane parallel to
T
π/
2
M
2
and onto the circular cylinder
C
A
+
B
).
f
(
V
)=
B
Λ
1
(
V
)=1
∀
V
↔
(23.11a)
g
(
V
)=
B
Λ
2
(
V
)=1
∀
V
↔
(23.11b)
f
(
V
)=
BV
+
c
f
(23.11c)
g
(
V
)=
BV
+
c
g
(23.11d)
f
(0) =
A
+
B
=
c
f
→
(23.11e)
f
(
V
)=
A
+
B
+
BV
(23.11f)
g
(0) = 0 =
c
g
→
(23.11g)
g
(
V
)=
BV
(23.11h)
Fig. 23.3.
Conformal mapping of
T
2
A,B
onto a central plane
P
0
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