Dear Dave and Donald, This puzzle actually has serious practical sundial applications as I shall illustrate. First:
Good try Dave... > Personally, I'd fold the paper, > superimposing the reflected > half-ellipse, crease it, unfold, > rotate ~90 degrees and repeat! Although this is not what I had in mind, it is undoubtedly a practical method. I wonder whether you have actually tried it? The clue to the difficulty lies in the approximation sign you have wisely written before the "90"! A fair proportion of my sundials are hand-cut into elliptical slabs of slate. These days, some stone-yards will simply accept the major and minor axes of the ellipse and, somehow, (water-jet?) cut a slate which is a close-to-perfect ellipse. Almost the first task is to find the centre and the axes. Clearly you cannot fold a slate in half and the traditional way to proceed is to put a large sheet of paper over the slate and crease it down all round the rim. You then cut round the crease and attempt to follow your procedure! No doubt in practised hands this can give a good result but I find that, no matter how carefully I work, the two axes are invariably not (quite) at 90 degrees. It is quite hopeless to refold the paper; the folds are too close together. You have to start again. I usually get it to my satisfaction at second attempt but occasionally I have had to have three tries. It is especially hard if the ellipse is not too far off being a circle, say 1200mm x 1050mm. This is a big sheet of paper. Just try it for yourself and see the challenges! Donald pointed to a link which gives the answer I was aiming at. Alas, although I find the geometry a delight, the practicalities are just as challenging as the folding method! You can get the axes at right-angles fairly easily but you find the "centre" is nearer one end of the major axis than the other, ditto the minor axis. As so often with sundials, the theory may be elegant and straightforward but real life has a way of making implementation a struggle! Frank --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
