How to prove Any curve in space can be written as for a parameter

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Discussion Overview

The discussion revolves around the question of whether any curve in space can be expressed in terms of a parameter, specifically in the context of parametric equations. Participants explore the implications of this statement and its mathematical validity, touching on concepts related to curves in three dimensions and the gradient's relationship to these curves.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants seek clarification on the original question, particularly regarding the phrase "as for a parameter" and the specific mathematical context.
  • One participant suggests that any curve in three dimensions can be represented as a system of parametric equations, x(t), y(t), z(t), but expresses doubt about the universality of this claim.
  • Another participant emphasizes the need for examples and asks for clarification on what type of curve is being discussed, such as equipotential lines.
  • There is a mention of the gradient being normal to the curve, indicating a potential application of the parametric representation.
  • Participants express frustration over the lack of direct answers to the main question and highlight the importance of showing effort in academic inquiries.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the validity of the claim that any curve in space can be expressed parametrically. There are competing views regarding the completeness of this assertion and the need for further clarification and examples.

Contextual Notes

Some participants note the importance of context in understanding the question, including the branch of mathematics involved and the methods of proof that are familiar to the questioner. There are references to forum guidelines regarding assistance with homework questions.

persyan
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how to prove Any curve in space can be written as for a parameter
 
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persyan said:
how to prove Any curve in space can be written as for a parameter

Can you provide more details about your question? What part of mathematics are you studying where this question comes up? And "as for a parameter" is not translating very well. Can you give examples of what you are asking about?
 
berkeman said:
Can you provide more details about your question? What part of mathematics are you studying where this question comes up? And "as for a parameter" is not translating very well. Can you give examples of what you are asking about?
Any curve in space can be written as for a parameter p(t)
prove it
 
Again, the translation is not working so well. What branch of mathematics are you studying? Can you provide a link to similar questions and proofs? What methods of proof are you familiar with?
 
I think he might be saying, any curve in 3 dimensions can be represented as a system of parametric equations, x(t), y(t), z(t). Which is a non-trivial result - in fact, I don't think that's even true.
 
ellipsis said:
I think he might be saying, any curve in 3 dimensions can be represented as a system of parametric equations, x(t), y(t), z(t). Which is a non-trivial result - .
you are right
you are better than mentor
 
persyan said:
you are right
you are better than mentor

At math he definitely is! :D
 
berkeman said:
Again, the translation is not working so well. What branch of mathematics are you studying? Can you provide a link to similar questions and proofs? What methods of proof are you familiar with?
Any curve in space can be written as p(t)
for a parameter t
its used to prove the gradient is normal to the curve
 
persyan said:
Any curve in space can be written as p(t)
for a parameter t
its used to prove the gradient is normal to the curve

Can you show an example of finding the gradient for a curve? What kind of curve? Like equipotential lines?
 
  • #10
berkeman said:
Can you show an example of finding the gradient for a curve? What kind of curve? Like equipotential lines?
why don't you answer main question
prove
Any curve in space can be written
parameteric
 
  • #11
persyan said:
why don't you answer main question
prove
Any curve in space can be written
parameteric

Because the PF rules require that you show effort. Especially if this is a schoolwork question, which many of the Mentors believe it is. You need to show some effort, and tell us what this question is for, or this thread will be locked.
 
  • #12
persyan said:
why don't you answer main question
prove
Any curve in space can be written
parameteric
This is why -- (see Homework Guidelines at https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/)
Giving Full Answers:
On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.

Thread closed.
 

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