Yes, you did understand the problem correctly. A shadow point is not be that "interesting" because it would be unique for only one instant of time during the year. But I think there are unique observations that can be made about any plane for a sun "setting" beyond the plane. For example, I can say there are Y hours of sunshine that remain in the day for a location X whenever (any day of the year) the sun "sets" beyond the roof of my house. I just need a way to calculate X and Y for and latitude and direction of plane. But X and Y are the same every time the sun "passed" that plane.
Jack Aubert wrote: > Ah, but the problem specifies "flat" surface. I took this to rule out > convex-polygonal or elliptical/circular. > I believe that every truly flat surface with no other obstructions in the > way would get some glimmer of sunlight. If the surface is facing north and > is predominantly in the shade, it will still be illuminated during morning > and evening hours of the summer when the sun rises in the northeast and > sets in the northwest. Even if the surface is facing down (!) it will > catch rays at sunrise and sunset, assuming that it is high enough to clear > any surrounding obstructions including mountains, foliage, etc. > > > At 09:39 AM 7/19/99 -0500, William P Thayer wrote: > >Big enough of course to fit every dialist that deserved it; but what I mean > >is this: > > > >>1. Is there any flat surface anywhere that never gets sunshine at some > >>moment during the year? > > > >If you mean direct sunlight, yes, lots of them. Trivially, any point > >adjacent to, and away from the equator from, a vertical wall, > >convex-polygonal or elliptical/circular in plan, the ends of which cast > >shadows on it even at summer sunrise and sunset. Tof produce a minimum > >single point, the arc traced by such a wall would not have to be great, > >although it increases with latitude. > > Extending that, there must be a zone of perennial shade -- you guys with > >computers can calculate the general formula for its shape and extent based > >on the latitude and the height of the wall -- including points not > >immediately adjacent to the wall. > > > >Practically speaking, this is the principle behind the urban layout of many > >old Mediterranean towns: narrow streets make for constant shade in the > >summer; if in addition they are not straight, they also temper winter > >conditions. I noticed this in several towns of central Italy; one of which > >-- Pitigliano, in Tuscany -- has a sundial in about the only place it can > >have one near ground level: in a piazza where the streets widen out. > > > >Geographically, there must be plenty of deep non-N-S valleys, and surely > >steep enough mountains act as my walls, above, for places on their > >"leeward" side so to speak. > > > >The question then becomes: "Where is the *largest* such surface on Earth? > >(Now there's a project...!) A similar question would be "Where is the > >largest *volume* of air on Earth never to see direct sunlight?" > > > >*** > >BTW, did anyone see the special on Noah's Ark last night? in which God's > >rainbow was shown with the colors backward... A miracle indeed! > > > > > >Bill Thayer > > LacusCurtius > >http://www.ukans.edu/history/index/europe/ancient_rome/E/Roman > > > >
