# Frenet–Serret formulas, what are the possible applications?

by andonrangelov
Tags: applications, formulas, frenet–serret
 P: 24 Unfortunately, because I'm not familiar with the strange quantum mechanics, I did not understand too much of your article to which you referred. But, be pointed out that in the recurrence theorem of the Frenet formulas occurs very frequently the ratio between curvature and torsion (parameter that we can call "lancretian", from Lancret's Theorem). It also occurs very frequently the root of the sum of the squares of curvature and torsion, which is exactly the Darboux vector module (which is why we call this important parameter as "darbuzian"). Now notice that in the study of complex numbers occurs very frequently the ratio between the real part and the imaginary part, and also the complex number module. For this reason, I think would be interesting to admit that to an any curve we can associate a complex number q that have the torsion on the real part and the curvature on the imaginary part, ie $$q=\tau+\textbf{i}\kappa$$, number that we can call it "complex torsion". Thereby, we introduce the complex numbers in the theory of curves and we can take the advantages of results obtained in complex analysis. Therewith, I also recommend the study of closed curves and especially of closed helices, because of the possibility that an elementary particle be just a luxon moving on a closed helix.