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]]>For nodal lines, I meant for the eigenfunctions. They show where is average-valued. For the isosceles case, we already know where they lie, by the of Laugesen and Siudeja. ]]>

As for your steepest descent comment:

do you mean we should plot the nodal line in the same fixed triangle as time increases (in the heat equation), and then look at the direction of steepest descent? This is relatively easy to do.

or do you mean we should plot the nodal line for triangles with angles which are close, and somehow study the nodal lines in there? This I don’t readily see how to do, since the domain (and hence the location of the nodal lines) will change from triangle to triangle.

Let me know if this is still of interest, and I can throw up some graphics.

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