i know the concept of harmonic functions or the conformal mapping and also i know some characteristics of the conformal mapping( i think ). i have already faced a theorem: "the conformal mapping keeps the harmonic ratio of every four points as a constant value." now, i ask you if you know the proof of it. the mathematical form: ((z1-z2)/(z1-z4)) / ((z3-z2)/(z3-z4)) = ((w1-w2)/(w1-w4)) / ((w3-w2)/(w3-w4)) i admit that almost i have no idea for the proof. i thank you very much, if you help me.
2026-03-30 00:24:35.1774830275
harmonic ratio of every four points in conformal mapping
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thank you every one. I have found my answer, lol! it was not hard but i got afraid at first. remember mobius mapping. we have from it: wi - wj = ((ad-bc)(zi-zj))/((czi+d)(czj+d)) . now if you write this for all the terms in the left side, you will earn the right side. thanks