As in the previous question, let ¹(²)), where o is defined on a sufficiently small open set UC R² to be a regular surface patch, with image S. It can be shown (and you can assume) that Ou Ov= 0 and Select one or more: Which of the following statements about the surface chart o are true? b. o(u, v) = (u — sin(u) cosh(v), 1 − cos(u) cosh(v), −4 sin( (12) sinh a. o is an isometry from the uv-plane to the surface S. d. O e. C. o preserves areas between the uv-plane and the surface S. O f. |ou|² = |ov|² = 4 (sin² (4) + cosh² ( ² ) − 1) cosh² sh² (²). o is a conformal parametrisation of S. o expresses S as a ruled surface o satisfies ou + ov = 0. o satisfies ou + Ovv = 0.
As in the previous question, let ¹(²)), where o is defined on a sufficiently small open set UC R² to be a regular surface patch, with image S. It can be shown (and you can assume) that Ou Ov= 0 and Select one or more: Which of the following statements about the surface chart o are true? b. o(u, v) = (u — sin(u) cosh(v), 1 − cos(u) cosh(v), −4 sin( (12) sinh a. o is an isometry from the uv-plane to the surface S. d. O e. C. o preserves areas between the uv-plane and the surface S. O f. |ou|² = |ov|² = 4 (sin² (4) + cosh² ( ² ) − 1) cosh² sh² (²). o is a conformal parametrisation of S. o expresses S as a ruled surface o satisfies ou + ov = 0. o satisfies ou + Ovv = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:As in the previous question, let
|ou|² = |ov|² = 4 (sin²
4 (sin² (2)
Which of the following statements about the surface chart o are true?
where o is defined on a sufficiently small open set UC R² to be a regular surface patch, with image S. It can be shown (and you can assume) that
συ· συ Ξ 0 and
Select one or more:
a. o is an isometry from the uv-plane to the surface S.
b. o is a conformal parametrisation of S.
C.
o preserves areas between the uv-plane and the surface S.
O d.
o(u, v) = u - sin(u) cosh(v), 1 − cos(u) cosh(v), −4 sin( sinh
e.
O f.
o expresses S as a ruled surface
o satisfies ou + %v = 0.
u
o satisfies ou + Ovv = 0.
¹ ( ² ) ),
+ cosh²
² (2) - 1) cosh² (²)
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