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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