Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

When one have a curve $\beta(s)$ which is parametrized by arc length (has natural parametrization) one is able to obtain the tangent, normal and binormal vectors by using Frenet-Serret frame equations:

$T = \beta'(s)$, $N=\frac{T'(s)}{|T'(s)|}$, $B = T \times N$

But are those formulas valid for non-regular parametrizations when one normalizes the tangent vector?

$T=\frac{\beta'(s)}{|\beta'(s)|}$, $N$ and $B$ are calculated as above.

share|cite|improve this question
up vote 3 down vote accepted

Yes, as the Wikipedia article says at the end.

share|cite|improve this answer
Oh, silly me. Did not see that, thank you! :) – MasterM Jun 24 '12 at 19:47

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.