Date:         Wed, 29 Jan 2003 16:22:45 -0600
Reply-To:     Blake Thornton <thornton@MATH.UTAH.EDU>
Sender:       Vanagon Mailing List <vanagon@gerry.vanagon.com>
From:         Blake Thornton <thornton@MATH.UTAH.EDU>
Subject:      Re: Curves (no Vanagon content)
Comments: To: John Rodgers <j_rodgers@CHARTER.NET>
In-Reply-To:  <3E381F61.3090703@charter.net>
Content-Type: TEXT/PLAIN; charset=US-ASCII

OK, having taught this stuff and having even done a fair amount of work
studying "hyperbolic geometry" I thought I had to comment on the answers
already given.

- First, what is a "hyperbolic" curve.  I know what a hyperbola is (its a
conic section), but I'm not entirely sure what is meant by a hyperbolic
curve.

- A cantenary is (as someone pointed out) the curve formed by a hanging
rope.  the equation of such a curve is a fairly easy derivation.  It
should be easy to either just do the derivation or find it in either a
calculus or differential equations book.

- The method for drawing an ellipse was correct.  An ellipse can be shown
to have this property: "Ellipse is the set of points whose sum of the
distance to the foci is a fixed constant."  A hyperbola can be shown to
have the similar property but you look at the difference of distances.

Well, I've got to run, but that is the summary.  I don't know a quick way
to draw a hyperbola, if thats what you want.

Blake


> Hello Vanagon Troops!!
>
> I need your help.
>
> I need to draw a hyperbolic curve as a line drawing that will look like
> a bowl. It has specific dimensions of 22" wide by 8 " deep. The curve
> must be true for the dimensions. There is a way to do this with string,
> pins, pencil, straight edge and triangle, but I don't know how. Can
> anyone tell me how do do this???
>
> Would appreciate it.
>
> Please reply off list.
>
> My thanks,
>
> John Rodgers
> 88 GL Driver
>