Generalized Helix: What Do You Think?

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Abel Cavaşi
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What do you think, might be generalized the helix in the manner that I propose in the attached material?
 

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The reccurence theorem can be found even https://www.physicsforums.com/showthread.php?t=612009. I would be glad if the problem could be studied in detail.
 
Unfortunately, I can not give you several sources. However, maybe someone else could help us in this regard.