Re: mystery curve

[Chris Lusby Taylor]

Road design uses cubic spline curves, which have the properties that they can be made to pass smoothly through any desired set of points, yet the radius of curvature has no discontinuities. This means that you never have to make a sudden change to the position of the steering wheel in order to stay precisely in lane. The same is true of the catenary, which is actually the curve formed by a dangling chain (with no stiffness). Bézier curves are parametric cubics - they are to be found in some drawing and CAD programs. But I'm afraid I can think of no application of parametric cubics to sundials. Sorry. Pity, because they are beautifully elegant. Regards Chris Lusby Taylor 51.4N, 1.3W J John Davis wrote: Hi all, While researching the BSS Glossary, I looked up the term "Lemniscate" in a mathematics dictionary.  This is the term used, I believe, for the analemma in the Latin countries, and originally meant "ribbon-like".  According to the dictionary, in English the lemniscate curve is similar to a spiral but differs from it principally because "... there is a slight falling off of the rate of increase of radial acceleration as the distance from the starting point increases" (!)  As a result of this, it is used in road design as a transition from a straight road into a circular arc. The diagram in the dictionary comparing the lemniscate, spiral and cubic parabola shows the first of these to look like one lobe of an analemma. So, there was a closer connection between Mike's original question and dialling than we might have originally thought! Best regards, John-------------------------------------Dr J R Davis Flowton, UK 52.08N, 1.043E email: [EMAIL PROTECTED] ----- Original Message ----- From: Peter Abrahams To: sundial@rrz.uni-koeln.de Sent: 11 February 2001 23:15 Subject: mystery curve  >There is a curve for which the transition from one radius of curvature to >another is as gradual as possible.  I too have forgotten its name however it >can be formed by bending a length of material of constant stiffness (such as >a garden hose) into a loop by holding only its ends. That's a catenary. >I don't think the occupants of a car would guide it through a path that >would cause them discomfort.  So even if a road did have a jump in radius of >curvature, the path traced out by a car wouldn't.  (Unlike a roller coaster, >a car doesn't have to travel out any particular path). No, but you do want to encourage drivers to stay in their lanes. --Peter _______________________________________ Peter Abrahams   [EMAIL PROTECTED]   The history of the telescope &    the binocular:   http://www.europa.com/~telscope/binotele.htm