Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

1 Answer 1

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


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.