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7 POINT STAR This piece evolved from two things- one was seeing something similar made of cardboard, and a need to figure out how to work with compound angles. I have encountered this second problem a few times at work as well.    A good example would be two roof planes meeting at the hip. If both roof peaks are 90 degrees to each other in plan view, and both roof planes are 45 degree slope, what is the angle formed by the hip line from horizontal, and what is its length from eave to roof peak? I can't tell you off hand, but I can tell you that the solution gets more difficult if the roof peak angle is other than 90 degrees, and especially if the two slopes differ!

I have a couple solutions in my machinist's handbook, but they involve some cumbersome algebra as well as trigonometry. I felt that for this star, anyway, I ought to be able to use straight-forward triangulation, using trig to figure out the angles and lengths of each panel.   When all was said and done, I was pleased to see that my math had proved out. I did cheat and I used a little program I found called kwiktrig, but I still had to think out all the steps to arrive at a solution. Each step involves using known angles and line lengths to construct triangles with an unknown value, and use kwiktrig to crunch the numbers and solve for the unknown. I like my kwik trig!       I first chose the number of points. I picked 7, because it was such an odd number. I had seen a lot of 5 points, 6 points seemed just too easy, same with 8. I found out later that sheriff's badges have seven.    Now,  if you look close, the line formed from one point to a farside point is bowed slightly away from center. This wasn't intentional, What I set out to do was pick a point on the radius that was the same ratio as the golden ratio, expressed as 1:1.618, or .618, or a bit less than 5/8 of the length of the radius, and make the star points join up along this point.     I also went out of the plane of the star to locate the center points, which causes each apex line of the star to rise up vertically, both up and down.    Armed with some starting numbers, I went through quite a series of trig calculations, and found all the info I needed to build. I had an early set back when I discovered I did not build my gluing  jig at the proper angle to glue up a face panel set, containing the apex line!   After sawing the parts apart on the scroll saw, I rebuilt the jig, and went forward with my project.