Finding Slopes of Warped Plane: A,B,C,D,X

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Discussion Overview

The discussion revolves around the concept of finding slopes on a warped 3-dimensional plane defined by points A, B, C, D, with a midpoint X. Participants explore the implications of the plane being warped and how that affects the equations and calculations related to its slopes.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions the definition of "warped," suggesting that if the plane is not flat, it cannot be treated as a mathematical plane, and thus standard plane formulas may only yield approximations.
  • Another participant provides the general equation for planes and suggests expressing z as a function of x and y, indicating that the warped nature of the plane complicates the calculations.
  • A clarification is made regarding the nature of the object in question, specifying it as a 3D rectangular shape that is slightly bent, which raises further questions about how to quantify the warping.
  • One participant emphasizes that without specific information on how the plane is warped, it is impossible to perform any calculations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definition of a warped plane and its implications for calculations. Multiple competing views remain regarding how to approach the problem.

Contextual Notes

The discussion lacks specific details about the nature of the warping, which affects the ability to derive equations or slopes. There are also unresolved questions about whether the plane is infinite or a bounded quadrilateral.

laminatedevildoll
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Suppose that there's a flat 3-d plane with points A,B,C,D. The midpoint is X. How do I find the equations for each of the points if the plane is slightly warped (meaning, that its sort slightly of bent). If I were to find the slopes on each side of the plane, would it matter that it's slightly warped?

Thnx
 
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What do you mean by 'warped'? If it's not flat then it's not a mathematical plane, and using plane formulas will give you at best approximations.

The general equation for planes is ax + by + cz = d; if it's not a purely vertical plane then you can express z as a function of x and y, z(x , y) = ux + vy + w, with u = - a/c, v = - b/c, w = d/c.

edit: A question, are you talking about an infinite (unbounded) plane, or a quadrilateral with corners A,B,C,D?
 
Last edited by a moderator:
rachmaninoff said:
What do you mean by 'warped'? If it's not flat then it's not a mathematical plane, and using plane formulas will give you at best approximations.

The general equation for planes is ax + by + cz = d; if it's not a purely vertical plane then you can express z as a function of x and y, z(x , y) = ux + vy + w, with u = - a/c, v = - b/c, w = d/c.

edit: A question, are you talking about an infinite (unbounded) plane, or a quadrilateral with corners A,B,C,D?

Just a 3d rectangular shaped object with sides A,B,C,D. Warped meaning that when you take a rectangular piece of paper and if you slightly bent the sides at the long ends of the paper, one corner will be higher than its opposite side, up and down.
 
Then it is not a "flat plane"! Without being given more information about exactly how it is warped, there is no way to calculate anything.
 

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