"As far as I know, these days, this subject isn't taught ANYWHERE in the UK even in Universities.
Geometry is deemed a useless subject because 'you don't really need it'." Might be taught in geomatics programs in the U.K. We certainly teach it in our own courses as well as a bespoke course from the Math and Stats Department: http://www2.unb.ca/gge/Study/Undergraduate/CourseSequence.pdf http://www.unb.ca/academics/calendar/undergraduate/current/frederictoncourses/mathematics/math-3543.html -- Richard Langley ----------------------------------------------------------------------------- | Richard B. Langley E-mail: l...@unb.ca | | Geodetic Research Laboratory Web: http://gge.unb.ca/ | | Dept. of Geodesy and Geomatics Engineering Phone: +1 506 453-5142 | | University of New Brunswick Fax: +1 506 453-4943 | | Fredericton, N.B., Canada E3B 5A3 | | Fredericton? Where's that? See: http://www.fredericton.ca/ | ----------------------------------------------------------------------------- > On Oct 31, 2016, at 5:50 AM, Frank King <f...@cl.cam.ac.uk> wrote: > > Dear Karl, > > Your idea is not without merit: > >> Wrap the slate with a reflective strip ... >> Playing around with a laser should find the >> focii. > > This is sometimes referred to as the > "Elliptical Billiard Table Problem"... > > If you aim at a focus, the laser path will > reflect through the other focus and so on. > Eventually it will settle down into > running backwards and forwards along the > major axis BUT... > > If you aim the laser so that its path > passes OUTSIDE the line joining the > two foci, the path traced will, after > an indefinite number of reflections, > leave a dead area in the centre which > is ITSELF an ellipse. > > If you aim the laser so that its path > passes BETWEEN the two foci, the path > traced will, after an indefinite number > of bounces, leave two dead areas around > each end of the major axis. The inner > boundaries of these areas are the turning > points of a hyperbola. > > The real excitement comes if you aim > the laser so that you get a return to > the starting point after a finite > number of reflections. > > You then get a nice pretty pattern. I > have knocked up the attached example > where there are 46 reflections. > > You can prove all this using > Projective Geometry. This is a > delightful subject which includes > splendid concepts such as "The > Circular Points at Infinity". > > In the 1950's, Projective Geometry > was in the UK A-level Mathematics > syllabus and taught to 17- and > 18-year olds. > > As far as I know, these days, this > subject isn't taught ANYWHERE in > the UK even in Universities. > > Geometry is deemed a useless subject > because "you don't really need it". > > End of rant. > > Frank > > <Ellipse.pdf>--------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
