> I intended to clarify the idea.  Apparently, I failed.
> 
> I assumed, when creating the posting, that my audience could visualize
> tangent lines to curves and tangent planes to spheres/surfaces [NOT
> compute them!]... 
That much I can do.
> Do you want me to try again?  I think a more pictorial approach would
> have a better chance.  The concept can almost entirely be explained
> graphically.
> 
If you would.
Take care.  -KMO