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 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
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.