Translate Differential Geometry of Curves and Surfaces Problem 1-5.4

[qinglong.1397]

Homework Statement

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.

 

[Mark44]

Homework Statement

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?

First, tell us what n(s) is.

 

[qinglong.1397]

First, tell us what n(s) is.

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