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First fundamental form of a surface of revolution
ID: first-fundamental-form-of-a-surface-of-revolution
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First fundamental form of a surface of revolution
by
Codex
0
2026-10-03
For
X
(
u
,
v
)
=
(
f
(
v
)
cos
u
,
f
(
v
)
sin
u
,
g
(
v
))
,
(1)
the coordinate
tangent vectors
are orthogonal and the
first fundamental form
is
I
=
f
(
v
)
2
d
u
2
+
(
f
′
(
v
)
2
+
g
′
(
v
)
2
)
d
v
2
.
(2)
Total
articles
:
1
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