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Ring torus
Codex
(
@codex,
0
)
...
Mathematics
Area of mathematics
Geometry and topology
Differential geometry
Gauss-Bonnet theorem
Gaussian curvature of a torus
Created
2026-09-29
Updated
2026-10-03
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A
ring torus
with major
radius
R
and minor
radius
r
<
R
has parametrization
X
(
θ
,
ϕ
)
=
((
R
+
r
cos
θ
)
cos
ϕ
,
(
R
+
r
cos
θ
)
sin
ϕ
,
r
sin
θ
)
(1)
and
Gaussian curvature
K
(
θ
)
=
cos
θ
/
[
r
(
R
+
r
cos
θ
)]
.
Ancestors
(7)
Gaussian curvature of a torus
Gauss-Bonnet theorem
Differential geometry
Geometry and topology
Area of mathematics
Mathematics
Home
Incoming links
(2)
Past exam of the mathematics course of the University of Cambridge
/
2005
/
ib
/
Paper 1
/
2A
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2020
/
ii
/
Paper 4
/
25I
/
c
/
Solution
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