Do Carmo: Differential Geometry of Curves and surfaces , 1.5, exercise 3 [on hold]

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So I am self-studying Do Carmos book and working through the exercises. I have gotten stuck on this problem because I do not know how to start it, and what the problem asking. So any hints, and clarification would be greatly, appreciated.



  1. Assume that α ( I ) ⊂ R 2 (i.e., α is a plane curve) and give k a sign as in the text. Transport the vectors t ( s ) parallel to themselves in such a way that the origins of t ( s ) agree with the origin of R 2 ; the end points of t ( s ) then describe a parametrized curve s → t ( s ) called the indicatrix of tangents of α . Let θ ( s ) be the angle from e 1 to t ( s ) in the orientation of R 2 . Prove (a) and (b) (notice that we are assuming that k ≠ 0).

a. The indicatrix of tangents is a regular parametrized curve.
b. dt / ds = ( dθ / ds ) n , that is, k = dθ / ds




differential-geometry




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put on hold as off-topic by John Ma, Taroccoesbrocco, Tyrone, José Carlos Santos, Mohammad Riazi-Kermani Aug 4 at 12:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Taroccoesbrocco, Tyrone, José Carlos Santos, Mohammad Riazi-Kermani
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up vote
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down vote

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So I am self-studying Do Carmos book and working through the exercises. I have gotten stuck on this problem because I do not know how to start it, and what the problem asking. So any hints, and clarification would be greatly, appreciated.



  1. Assume that α ( I ) ⊂ R 2 (i.e., α is a plane curve) and give k a sign as in the text. Transport the vectors t ( s ) parallel to themselves in such a way that the origins of t ( s ) agree with the origin of R 2 ; the end points of t ( s ) then describe a parametrized curve s → t ( s ) called the indicatrix of tangents of α . Let θ ( s ) be the angle from e 1 to t ( s ) in the orientation of R 2 . Prove (a) and (b) (notice that we are assuming that k ≠ 0).

a. The indicatrix of tangents is a regular parametrized curve.
b. dt / ds = ( dθ / ds ) n , that is, k = dθ / ds




differential-geometry




share|cite|improve this question











put on hold as off-topic by John Ma, Taroccoesbrocco, Tyrone, José Carlos Santos, Mohammad Riazi-Kermani Aug 4 at 12:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Taroccoesbrocco, Tyrone, José Carlos Santos, Mohammad Riazi-Kermani
If this question can be reworded to fit the rules in the help center, please edit the question.












  • Please edit your question using Latex.
    – mathcounterexamples.net
    Aug 3 at 6:48












up vote
0
down vote

favorite









up vote
0
down vote

favorite











So I am self-studying Do Carmos book and working through the exercises. I have gotten stuck on this problem because I do not know how to start it, and what the problem asking. So any hints, and clarification would be greatly, appreciated.



  1. Assume that α ( I ) ⊂ R 2 (i.e., α is a plane curve) and give k a sign as in the text. Transport the vectors t ( s ) parallel to themselves in such a way that the origins of t ( s ) agree with the origin of R 2 ; the end points of t ( s ) then describe a parametrized curve s → t ( s ) called the indicatrix of tangents of α . Let θ ( s ) be the angle from e 1 to t ( s ) in the orientation of R 2 . Prove (a) and (b) (notice that we are assuming that k ≠ 0).

a. The indicatrix of tangents is a regular parametrized curve.
b. dt / ds = ( dθ / ds ) n , that is, k = dθ / ds




differential-geometry




share|cite|improve this question











So I am self-studying Do Carmos book and working through the exercises. I have gotten stuck on this problem because I do not know how to start it, and what the problem asking. So any hints, and clarification would be greatly, appreciated.



  1. Assume that α ( I ) ⊂ R 2 (i.e., α is a plane curve) and give k a sign as in the text. Transport the vectors t ( s ) parallel to themselves in such a way that the origins of t ( s ) agree with the origin of R 2 ; the end points of t ( s ) then describe a parametrized curve s → t ( s ) called the indicatrix of tangents of α . Let θ ( s ) be the angle from e 1 to t ( s ) in the orientation of R 2 . Prove (a) and (b) (notice that we are assuming that k ≠ 0).

a. The indicatrix of tangents is a regular parametrized curve.
b. dt / ds = ( dθ / ds ) n , that is, k = dθ / ds





differential-geometry





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Aug 3 at 6:09









Dorky96

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put on hold as off-topic by John Ma, Taroccoesbrocco, Tyrone, José Carlos Santos, Mohammad Riazi-Kermani Aug 4 at 12:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Taroccoesbrocco, Tyrone, José Carlos Santos, Mohammad Riazi-Kermani
If this question can be reworded to fit the rules in the help center, please edit the question.




put on hold as off-topic by John Ma, Taroccoesbrocco, Tyrone, José Carlos Santos, Mohammad Riazi-Kermani Aug 4 at 12:04


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Taroccoesbrocco, Tyrone, José Carlos Santos, Mohammad Riazi-Kermani
If this question can be reworded to fit the rules in the help center, please edit the question.











  • Please edit your question using Latex.
    – mathcounterexamples.net
    Aug 3 at 6:48
















  • Please edit your question using Latex.
    – mathcounterexamples.net
    Aug 3 at 6:48















Please edit your question using Latex.
– mathcounterexamples.net
Aug 3 at 6:48




Please edit your question using Latex.
– mathcounterexamples.net
Aug 3 at 6:48















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