RE: latitude with pegs and strings
Hello Arthur ! There is a simple and practical way to draw a hyperbola . I assume that these parameters are known: 2A = the constant difference between the distances of any point of the hyperbola from the two foci ; E = the eccentricity of the hyperbola ( 1 ). 1) Draw the two foci : two points whose distance is 2A*E 2) Take a sufficiently long bar or a straightedge and fix one end of this onto the focus of the other branch of the hyperbola you are going to draw , in such a way that the bar is free to rotate around this focus. 3) Connect by a string ( whose lenght is 2A) the other end of the bar to the other focus (the focus of the branch you are interested in ). 4) Keep the string taut with a pen and run alongside the bar (allow it to rotate ! ) 5) The resulting curve is the desired hyperbola . I hope this is sufficiently clear ... This the theory but I've never tried the practice ! Let me know Best regards Alberto Nicelli Italy ( 45,5N; 7,8E) -- From: Arthur Carlson[SMTP:[EMAIL PROTECTED] Sent: martedì 21 aprile 1998 14.02 To: sundial@rrz.uni-koeln.de Subject: latitude with pegs and strings In the course of these considerations, I also wished for an easy method to construct a hyperbola. You all know how to draw an ellipse with a loop of string around two pegs. There is another method to make an ellipse involving a stick or string of length a with a mark at distance b from one end. If one end is moved along one axis and the mark is moved along the perpendicular axis, then the other end traces out an ellipse. I have found a few ways to construct hyperbolae that are mathematically correct but not especially practical. Is there any way to construct a hyperbola which is of similar elegance and practicality to the methods for ellipses? Is there an easy way, given a hyperbola, to find its axes, asymptotes, or foci? Thanks for your help. Art Carlson
Re: latitude with pegs and strings
Art Carlson wrote: Is there any way to construct a hyperbola which is of similar elegance and practicality to the methods for ellipses? Is there an easy way, given a hyperbola, to find its axes, asymptotes, or foci? Hello Art, Do you have the geometrical construction using an axis, a perpendicular DIRECTRIX and a focus? You'll probably find it in any oldish book on Engineering Drawing e.g. Practical Geometry Engineering Graphics by W. Abbott Pub Blackie If you're relly stuck I'll send you a GIF of the construction involved. Tony Moss == \ ** *** \\ ** ** \\** *** *\\ ** ** *\\ ****** **\\ ***\\ Tony Moss, Lindisfarne Sundials *\\ 43, Windsor Gardens, Bedlington, ***\\Northumberland, England, NE22 5SY, **\\55° 07' 45 N1° 35' 38 W Tel/FAX +1670 823232 == Horizontal, Vertical, Declining, Analemmatic Capuchin Sundials individually made in solid engraving brass. Professional-quality Dialling Scales, 'engine-divided' meridian layout instrument with software. Analemmatic dial plots - any size for any latitude. ==
