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diffgeo4life
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- TL;DR Summary
- κ1,κ2,...,κn-1 is constant
What do we know of a curve(/what can it look like) in R^n if we know that κ1,κ2,...,κn-1 is constant?
Indeed. @diffgeo4life - a little bit of Googling will get you at least part way there even if your textbook isn't helpful.Orodruin said:your work/thoughts so far.
Sorry then, I guess then i will try posting in the Homework- Calculus and beyond forum, that looks most appropriateOrodruin said:So this is a homework type problem then. It should therefore be posted in the appropriate homework forum using the homework template - including the full problem statement, relevant equations, and your work/thoughts so far.
A generic curve in R^n is a mathematical concept that refers to a curve that exhibits certain properties that are true for most curves in n-dimensional space. These properties can include smoothness, non-self-intersection, and non-degeneracy.
A regular curve is a specific type of curve that is defined by a set of equations or parametric equations. A generic curve, on the other hand, is a broader concept that encompasses a larger set of curves that share certain properties. A regular curve can be considered a subset of a generic curve.
Studying generic curves in R^n allows us to gain a deeper understanding of the properties and behavior of curves in higher dimensions. This can have applications in fields such as geometry, physics, and computer science.
Yes, generic curves in R^n can be visualized in lower dimensions by projecting them onto a lower-dimensional space. For example, a 3-dimensional curve can be projected onto a 2-dimensional plane for visualization.
Yes, there are many real-world examples of generic curves in R^n. For instance, the path of a planet orbiting around a star can be approximated as a generic curve in 3-dimensional space. Similarly, the trajectory of a projectile can be modeled as a generic curve in 2-dimensional space.