Geography Reference
In-Depth Information
2
:=
2
onto the circular cylinder
2
1
Box 23.18 (Conformal mapping of the paraboloid
M
P
C
0
).
and the circular cone
C
f
=
√
1+4
V
2
V
Λ
1
(
V
)=
Λ
2
(
V
)
∀
V
↔
(23.70)
g
=
n
√
1+4
V
2
g
Λ
1
(
V
)=
Λ
2
(
V
)
∀
V
↔
(23.71)
V
ln
1+
√
1+4
V
2
+
c
f
f
(
V
)=
√
1+4
V
2
+ln
V
−
(23.72)
ln
g
=
n
√
1+4
V
2
+ln
V −
ln
1+
√
1+4
V
2
+ln
c
g
(23.73)
g
(
V
)=
c
g
exp
√
1+4
V
2
n
V
n
1+
√
1+4
V
2
n
(23.74)
ln
1+
√
5
+
c
f
→
f
(1) = 1 =
√
5
Λ
1
(1) =
Λ
2
(1) = 1
→
−
(23.75)
√
5+ln
1+
√
5
c
f
=1
−
(23.76)
√
5+
ln
1+
√
5
+
√
1+4
V
2
+
ln
V
1+
√
1+4
V
2
f
(
V
)=1
−
(23.77)
g(1) = 1 = c
g
(
exp
√
5
1+
√
5
)
n
Λ
1
(1) =
Λ
2
(1) = 1
→
→
(23.78)
c
g
=(
1+
√
5
exp
√
5
)
n
(23.79)
g
(
V
)=(
1+
√
5
1+
√
1+4
V
2
exp
√
1+4
V
2
)
n
V
exp
√
5
(23.80)
Box 23.19 (Equiareal mapping of the paraboloid
M
2
:=
P
2
onto the circular cylinder
C
1
and
the circular cone
C
0
).
Λ
1
Λ
2
(
V
)=1
∀V ↔ f
=
V
√
1+4
V
2
(23.81)
gg
=
n
−
1
V
√
1+4
V
2
Λ
1
Λ
2
(
V
)=1
∀
V
↔
(23.82)
√
1+4
V
2
+
c
f
f
(
V
)=
1+4
V
2
12
(23.83)
2
g
2
=
(1 + 4
V
2
)
3
/
2
1
+
c
g
(23.84)
12
n
(1 + 4
V
2
)
3
/
2
6
n
g
(
V
)=
+2
c
g
(23.85)
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