A highway and a country road intersect at an arbitrary angle. We wish to pave an arc connecting them with as large a turning radius as possible and going around the corner of a farmer's field. Because the highway has a wider right of way than the country road, the corner of the field is closer to the country road than it is to the highway.
In the attached paper, Geometry-Do: Geometry without Multiplication, I present a heuristic method on pages 63-64. Within the accuracy that can be achieved on U.S. letter-size paper, it converges in three or four iterations.
But I would prefer an algorithmic solution that just constructs the needed arc or, at worst, constructs an arc that is wrong but then shows exactly how to redraw it so it is correct.
I would very much appreciate it if someone could help me with this problem!
Article Volume One: Geometry without Multiplication
I now have four independent solutions to this problem, which will be used in my book to tie the several chapters together by repeatedly solving the same problem with different techniques.
If you have another, though, I would very much appreciate hearing about it. This is an interesting problem and there may well be other solutions that illustrate problem-solving techniques unknown to me.
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