Dear Rudolph, Glad you enjoyed the puzzle or, at least, the solution...
> Brilliant! You add... > I never realized that the distance from > the focus to the end of the minor axis > equals the half major axis... Have you never tried drawing an ellipse with a Length of String and Two Pins? This is illustrated all over the web, for example here: http://bogan.ca/orbits/kepler.html This is a very bad way of drawing an ellipse but the theory is sound! In this illustration, the two ends of the string are each tied to one of the two pins. The pins are at the two foci. Now imagine the pencil point at one end of the major axis. It is then obvious that the total length of the string equals the major axis. Then imagine the pencil point at one end of the minor axis. It is then obvious that the total length of the string equals twice the distance from a focus to one end of the minor axis. If you try this in real life you will find you draw a potato shape! [Well that's what happens if I do it but there is nothing wrong with the idea!] Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
