Given a general graph on a plane, deform the plane in 3 space

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Discussion Overview

The discussion revolves around the mathematical approach needed to describe a general graph on a plane when deforming the plane in three-dimensional space. Participants explore potential fields of mathematics relevant to this problem, including differential geometry and topology, while also expressing uncertainty about the specifics of the problem and the desired outcome.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • Some participants suggest that differential geometry is a suitable field for addressing the problem of deforming a plane in 3D space.
  • Others propose that differential topology might also be relevant, particularly in relation to intersection theory and deformations.
  • One participant expresses concern that the problem may not require an entire field of study if it is specific enough to have a straightforward solution.
  • Another participant questions the necessity of differential geometry, suggesting that basic manipulation of formulas might suffice to address the problem.
  • There is uncertainty regarding the exact nature of the deformation and what the friend is specifically trying to achieve.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the appropriate mathematical framework for the problem, with differing opinions on the relevance of differential geometry and topology. The discussion remains unresolved regarding the specifics of the problem and the best approach to take.

Contextual Notes

There is a lack of clarity about the exact nature of the deformation and what is meant by "deforming the plane," which may affect the applicability of the suggested mathematical fields. The discussion also highlights the potential for varying interpretations of the problem based on its specificity.

Integral
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I just got a call from a good friend who is in the final terms of his ME degree. He needed some leads on the field of math that was needed to determine a solution to this problem.

Given a general graph on a plane, deform the plane in 3 space, now what is the equation which describes the graph.

I told him differential geometry.

Did I do right?

(I told him he should come in here and post his question, this is just in case he doesn't!
 
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Originally posted by Integral

I told him differential geometry.

Did I do right?


yeah, i would say. or perhaps differential topology.

i have never seen this particular problem, but my differential topology class dealt with intersection theory, which uses deformations one of its tools.
 
Ok, thanks.
I did mention topology to him also.

He was a bit disapointed, he was hopeing for a quick foumula, not an introduction to an intire field!
 
Originally posted by Integral
Ok, thanks.
I did mention topology to him also.

He was a bit disapointed, he was hopeing for a quick foumula, not an introduction to an intire field!

well, i don t know exactly what he wants to do, but if the problem is very specific, it may have a very specific solution, in which case, you won t need to learn a whole field.

perhaps i am not understanding the problem correctly, but to me, what you are asking sounds trivial.

if i have a graph of v=f(u) in the plane, and i want to embed this plane in R3 with embedding (x(u,v),y(u,v),z(u,v)) then the resulting curve will have a graph given by (x(u,v(u)),y(u,v(u)),z(u,v(u)). this holds no matter what the shape of the embedding is, so if you know what you want for your deformation, then you are in business.

this seems trivial to me, so i assume i am misunderstanding the problem. but the point is, it may well be that he doesn t need to learn the whole body of differential geometry/differential topology. we can t say until we know what the question is.

is he going to post it here?
 
Originally posted by Integral
I just got a call from a good friend who is in the final terms of his ME degree. He needed some leads on the field of math that was needed to determine a solution to this problem.

Given a general graph on a plane, deform the plane in 3 space, now what is the equation which describes the graph.

I told him differential geometry.

Did I do right?

(I told him he should come in here and post his question, this is just in case he doesn't!


Why on Earth would you need any differential geometry for this problem?

Perhaps you should try and get him to explain what he means by deforming the plane. Basic manipulation of formulae should give you the answer
 
I was hoping that he would come in here and post more information.

Guess not.

Thanks for the input I will pass it along next time I see him.
 

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