1. Jan 21, 2012

### qinglong.1397

1. The problem statement, all variables and given/known data

This is the 1st problem in the section 1-5, do Carmo' Differential Geometry of Curves and Surfaces. It is in page 22.

We have a parametrized curve

$\alpha (s)=(a\cos \frac{s}{c}, a\sin \frac{s}{c}$,b$\frac{s}{c})$

with $c^2=a^2+b^2$.

The 4th problem is to show that the lines containing $n(s)$ and passing through $\alpha(s)$ meet the $z$ axis under a constant angle equal to $\pi /2$. What does this mean? What is the meaning of ''containing'' and ''passing through''? It sounds weird to me...

n(s) is the normal vector of the curve.

Last edited: Jan 21, 2012
2. Jan 21, 2012

### Staff: Mentor

First, tell us what n(s) is.

3. Jan 21, 2012

### qinglong.1397

Oh, n(s) is the normal vector of the curve.