Re: mystery curve

[John Davis]

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