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Differential Geometry | Topology
Q. Show that the circular cylinder S={(x,y,z)∈R^3 |x^2+y^2=1} can be covered by a single surface patch and so a surface.
Differential Geometry | Topology
Q. The hyperboloid of one sheet is S={(x,y,z)∈R^3 |x^2+y^2-z^2=1} show that for every θ,the straight line (x-z)cosθ=(1-y)sinθ,
(x+z)sinθ=(1+y)cosθ
Is contained in S and that every point of hyperboloid lies on one of these deduce that S can be covered by a single surface patch, and hence is a surface.
(x+z)sinθ=(1+y)cosθ
Is contained in S and that every point of hyperboloid lies on one of these deduce that S can be covered by a single surface patch, and hence is a surface.
Differential Geometry | Topology
Q. Show that the circular cylinder S={(x,y,z)∈R^3 |x^2+y^2=1} can be covered by a single surface patch and so a surface.
Differential Geometry | Topology
Hello, I need help with one of my assignment questions. How do you calculate the diameter of a pipe needed to water a track with only knowing the flow rate of 0.7 l/sec
Differential Geometry | Topology
Q.Find equation of the osculating plane and osculating circle of the curve at the given point.
γ(t)=(2 sin3t, t, 2 cos3t), (0, π, -2)
γ(t)=(2 sin3t, t, 2 cos3t), (0, π, -2)
Differential Geometry | Topology
Q. Compute the torsion of the following curves
(i) γ(t)=4/5cos t, 1-sint,(-3)/5cos t
(ii) γ(t)=(t, cosht)
(iii) γ(t)=4/5 (〖cos〗^3t,〖sin〗^3t)
Read answer
(i) γ(t)=4/5cos t, 1-sint,(-3)/5cos t
(ii) γ(t)=(t, cosht)
(iii) γ(t)=4/5 (〖cos〗^3t,〖sin〗^3t)
Read answer
Differential Geometry | Topology
Q.Torsion is defined only when K(S)≠0 (why?)
Differential Geometry | Topology
Q.Torsion is defined only when K(S)≠0 (why?)
Differential Geometry | Topology
Q. Show that if curvature K(t) of a regular curve γ(t) is >0 every where, then k(t) is a smooth function of t. Give an example to show that this may not be the case without the assumption that k>0.
Differential Geometry | Topology
Q. Compute the curvature of the following curves
(i) γ(t)=4/5cos t, 1-sint,(-3)/5cos t
(ii) γ(t)=(t, cosht)
(iii) γ(t)=4/5 (〖cos〗^3t,〖sin〗^3t)
For the astroid in (iii), show that the curvature tends to ∞ as we approach one of the points (±1,0), (0,±1)
(i) γ(t)=4/5cos t, 1-sint,(-3)/5cos t
(ii) γ(t)=(t, cosht)
(iii) γ(t)=4/5 (〖cos〗^3t,〖sin〗^3t)
For the astroid in (iii), show that the curvature tends to ∞ as we approach one of the points (±1,0), (0,±1)
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#340153 on Dec 2023
#340153 on Dec 2023