From: jons5451@telcel.net.ve
Newsgroups: sci.math
Subject: Re: Hyperbola Construction
Date: Sat, 04 Apr 1998 07:03:46 -0600

In article <3525B44C.30E4@sympatico.ca>,
  Ron Lewis <ronlewis@sympatico.ca> wrote:
>
> I am a high school math teacher.  I have been able to demonstrate the
> construction of an ellipse with thumbtacks and string.  But could anyone
> share a demonstrable construction of a hyperbola.  I once saw it done at
> a conference, but did not think that I would never come across it again
> for about twenty years.

A continuous drawing can be made as follows: let F, F' be the foci of
the hyperbola. Take a ruler, say of length m, with end points Q and R.
Attach one end of a string of length m - 2c to R and the other end to F.
Pin the extreme Q of the ruler to F', so that the ruler can pivot around F'.
Now tighten the string with the tip of a sharp pencil, touching the rule
at the same time say at a point P.


                /\ R
               / /
              / /
             / /
            / /
           / /\
          / / P\
         / /    \
        / /      \
       / /        \
       \/          \
      Q=F'          F


Since  F'P - FP = QP - (m - 2c - PR) = 2c  the point P will describe a
branch of the hyperbola (to draw the other branch interchange F and F').

There is a similar construction for parabolas, using a square which
slides on the directrix.

Greetings,
Jose H. Nieto


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From: Ken.Pledger@vuw.ac.nz (Ken Pledger)
Newsgroups: sci.math
Subject: Re: Hyperbola Construction
Date: Mon, 06 Apr 1998 09:03:51 +1300

In article <3525B44C.30E4@sympatico.ca>, Ron Lewis <ronlewis@sympatico.ca>
wrote:

> I am a high school math teacher.  I have been able to demonstrate the
> construction of an ellipse with thumbtacks and string.  But could anyone
> share a demonstrable construction of a hyperbola.  I once saw it done at
> a conference, but did not think that I would never come across it again
> for about twenty years.
> 
> Thanks.
> 
> R.L.


     Yes, there is such a construction.   It's in Robert C. Yates, "A
Handbook on Curves and their Properties," p.49.   I'm no good at ascii
art, but I'll try to explain it.


                                             P





                                A                B




                                Q



     Put pins at A and B.   Tie two strings to the pencil at P.   Lead one
string from P aroud A to Q;  and the other from P around B, then around A
(anticlockwise) to Q.   Hold the two ends of the string together at Q
while you pull, keeping the string taut.   That ensures that    PA - PB  
remains constant, giving you part of a hyperbola with foci at A and B.

          Ken Pledger.