Dear Membership, Here is more help for Emergency Sundial Makers.
Trigon - Folding When you need 15, 30, 45, 60, 75 degree angles to lay out radially from a gnomon to create hour lines and don't even have a pencil, but do have something foldable; paper, foil, starched linen, etc., here is how to fold these angles. There turns out to be a number of ways to do this, but I'll describe only one. It involves trisecting an angle. I found the method on http://chasm.merrimack.edu/~thull/geoconst.html Starting from a scruffy piece of fom (foldable material) with no straight lines in it's shape. A. Fold up from the bottom a short distance and crease a straight line ( line 1). Reopen. B. Fold this line back on itself a short distance from the left side and crease a straight line (line 2) which is now forms a right angle of 90 degrees with line 1. Reopen. C. Fold lines 1 and 2 over onto themselves and through the point they cross each other forming a 45 degree line and crease it (line3). Reopen. D. Fold line 2 up along itself for a fair distance and crease a line parallel to line 1 (line 4). Reopen. E. Bisect the distance between line 4 and line 1 by laying line 1 on line 4 and creasing (line 5). Reopen. Let's review what you have. You have line one zooming across the lower portion of the sheet. Crossing it at right angles and zooming up the sheet you have line 2. Through the point where they meet a 45 degree angled line zooms up and to the right as line 3. We also have a couple of lines parallel and equally spaced from line 1, lines 5 and 4 going up the page from the bottom. F. Looking along line 2 there are now two critical points. a. Where line 1 and 2 cross (point p1) and where line 4 crosses line 2 ( point p2). We want to take point p2 and place it on our 45 degree line (line 3) while we take point p1 and have it on line 5, hold it in place and crease it. Don't reopen. It is now folded flat with p1 on the 45 degree line 3 and p2 on line 5 the line just up from line 1. G. Now, where line 5 hits this fold we want to re-crease line 5 where it extends up to the right on the top sheet of the fold. Continue this fold right on across the fom. Open it up and continue this line right back the other way. It should cross right through point p1. This is line 6 Going clockwise now starting from line 2 we have a 45 degree angle, then a 15 degree angle followed by a 30 degree angle. Combining the 45 degree angle and the 15 we also have a 60 degree angle. Arranging this trigon as a sheet perpendicular to our gnomon which is parallel to the earth's axis and with line 2 pointing vertically we can see where to mark 15 degrees to either side of our north south line which when drawn through the base of the gnomon make 11 and 1 o'clock lines. The 30 degree angle makes 10 and 2 o'clock lines, the 45 the 9 and 3, the 60 the 8 and 4. Sighting from these last two lines we can make the 7 and 5 with the 15 degree angle. And more if we need them. These hour lines can be scratched with a rock, or laid out with strings , painted, or however we wish. I've been asked about how to make a sundial where one only has a shoelace and rocks. When I get around to it, I'll write it up ( if there is some interest in it. ). Enjoy! Edley McKnight [43.126N 123.357W]
