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persyan
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how to prove Any curve in space can be written as for a parameter
persyan said:how to prove Any curve in space can be written as for a parameter
Any curve in space can be written as for a parameter p(t)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?
you are rightellipsis 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 - .
persyan said:you are right
you are better than mentor
Any curve in space can be written as p(t)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?
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
why don't you answer main questionberkeman said:Can you show an example of finding the gradient for a curve? What kind of curve? Like equipotential lines?
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/)persyan said:why don't you answer main question
prove
Any curve in space can be written
parameteric
Giving Full Answers:
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A curve in space is a continuous path that can be described as a set of points in three-dimensional space.
A parameter is a variable that represents a specific point along the curve and can be used to define its shape and direction.
Yes, any curve in space can be written as a parameter using a mathematical equation that relates the parameter to the coordinates of points along the curve.
This can be proved mathematically by showing that the equation for the curve can be parametrized, meaning that it can be expressed in terms of a single parameter.
While this proof applies to a wide range of curves in space, there may be some complex curves that cannot be easily parametrized. Additionally, the proof assumes that the curve is continuous and has a well-defined shape, which may not always be the case in real-world scenarios.