Surfaces of constant gradient-magnitude

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SUMMARY

The discussion focuses on the mathematical exploration of surfaces of constant gradient-magnitude, specifically using the potential function defined as U = √((∂F/∂x)² + (∂F/∂y)²). This formulation is particularly relevant in two-dimensional cases. Participants encourage further investigation into the implications of this definition, emphasizing the need to clarify what constitutes "interesting" outcomes from this approach.

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JanEnClaesen
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In other words, when we take for potential function instead of F the square root of (6F/6x)²+(6F/6y)² (in the particular case of two-dimensions). Does this lead to anything interesting?
 
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Define "interesting".
Why don't you follow it and see?

Note: I think you mean $$U=\sqrt{\frac{\partial F}{\partial x^2}+\frac{\partial F}{\partial y^2}}$$ ... the Σ button on the toolbar has symbols includeing ∂
 

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