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

Given $\alpha(s)$ a smooth arc-length parametrized curve, how can you write the equation for the surface $f(s,t) = \alpha(s) + t \alpha'(s)$ component-wise?

That is, I want to write $f = (f_x, f_y, f_z)$.

I can write $\alpha(s) = (x(s), y(s), z(s))$, but that doesn't give much. For instance, I don't think $f_x(s,t) = x(s) + t x'(s)$. Is that right?

share|cite|improve this question
up vote 2 down vote accepted

$f(s,t)=(x(s)+tx'(s),y(s)+ty'(s),z(s)+tz'(s))$ just as you're saying.

share|cite|improve this answer

Your Answer

 
discard

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.