Geography Reference
In-Depth Information
Proof (distance preserving mapping).
Finally, we present the mapping equations of distance preserving type constrained to the postulate
of an equidistance mapping on two parallel circles. We have to specify the principal stretches
as (
10.40
).
x
y
=
R
Λ
cos
Φ
0
,
,
(10.39)
Φ
Λ
1
=cos
Φ
0
/
cos
Φ, Λ
2
=1
.
(10.40)
Starting from the above relations, we obtain
1)
2
+(
Λ
2
1)
2
(
Λ
1
−
−
=
1
1)
2
,
2
(cos
Φ
0
/
cos
Φ
−
(10.41)
2
I
A
(equidistant) =
1
2
I
A
(conformal)
(10.42)
⇒
Φ
0
=61
.
72
◦
,
I
A
=0
.
3837
.
Φ
=85
◦
,
(10.43)
End of Proof.
In the following chapter, let us continue studying the mapping of the sphere to the cylinder,
namely let us study the transverse aspect.
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