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 -----== Posted via Deja News, The Leader in Internet Discussion ==----- http://www.dejanews.com/ Now offering spam-free web-based newsreading 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.