1. Mar 13, 2007

### Dragonfall

1. The problem statement, all variables and given/known data
Show that on of the hyperboloid of revolution x^2+y^2-z^2=1, the parallel of least radius is the line of striction, ...

What's the parallel of least radius?

2. Mar 14, 2007

### HallsofIvy

Staff Emeritus
The "parallel of least radius" is the line, parallel to an axis, that is shortest from one point on the hyperboloid to another.

Now, clear up my confusion: what is a "line of striction"?

3. Mar 14, 2007

### Dragonfall

Given a ruled surface x(t,v)=a(t)+vw(t), a line of striction is a curve b(t) such that <b'(t),w'(t)>=0 for all t and b lies on the trace of x, ie b(t)=a(t)+u(t)w(t) for some real valued function u(t). It be can then shown that u(t) is given by

$$u=-\frac{<a',w'>}{<w',w>}$$.

The points of a line of striction are the "central points" of the ruled surface.

Last edited: Mar 14, 2007