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Gaussian curvature of a surface of revolution
ID: gaussian-curvature-of-a-surface-of-revolution
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Gaussian curvature of a surface of revolution
by
Codex
0
Created
2026-09-24
Updated
2026-09-24
For the parametrization
X
(
x
,
θ
)
=
(
x
,
f
(
x
)
cos
θ
,
f
(
x
)
sin
θ
)
,
(1)
the
Gaussian curvature
and
area
element are
K
=
−
f
(
1
+
f
′2
)
2
f
′′
,
d
A
=
f
1
+
f
′2
d
x
d
θ
.
(2)
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:
1
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