Generalized Helix: What Do You Think?

In summary, the conversation is about the possibility of generalizing the helix and the request for references on differential geometry books that cover this topic. The recurrence theorem is mentioned as a possible source, but the other person requests a book reference instead of a forum post. The conversation ends with a reminder that personal research is not allowed on the forum.
  • #1
Abel Cavaşi
34
2
What do you think, might be generalized the helix in the manner that I propose in the attached material?
 

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  • #2
Can you give some references to differential geometry books that deal with these generalized frenet trihedrons and that recurrence theorem?
 
  • #3
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.
 
  • #4
Abel Cavaşi said:
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.

Please provide a reference such a book on differential geometry on this topic. Another forum post doesn't count.
 
  • #5
Unfortunately, I can not give you several sources. However, maybe someone else could help us in this regard.
 
  • #6
Then this is personal research. This is not allowed on this forum. Please do not post anything again without valid references.

Thread locked.
 

1. What is a generalized helix?

A generalized helix is a three-dimensional curve that follows a path of constant curvature and torsion. It can be thought of as a spiral that is twisted in multiple directions.

2. How is a generalized helix different from a regular helix?

A generalized helix has multiple centers of rotation, while a regular helix has only one. This means that a generalized helix can have varying curvatures and torsion along its length, while a regular helix maintains a constant curvature and torsion.

3. What are some real-life examples of generalized helices?

Generalized helices can be found in various biological structures, such as DNA molecules and protein structures. They can also be seen in man-made objects, such as springs and screws.

4. How is a generalized helix used in scientific research?

Generalized helices are used in various fields of science, including physics, chemistry, and biology. They are used to model and study complex structures and processes, such as molecular interactions and DNA folding.

5. What are the potential applications of generalized helices in technology?

Generalized helices have potential applications in fields such as robotics, materials science, and drug delivery. They can be used to create more efficient and versatile structures, as well as new technologies for targeted drug delivery in medicine.

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