The number of triangles in arrangements of lines and pseudolines has been object of some research. Most results, however, concern arrangements in the projective plane. In this arti...
We present a simple but powerful new probabilistic technique for analyzing the combinatorial complexity of various substructures in arrangements of piecewise-linear surfaces in hig...
Though arrangement knowledge is well suited for qualitative representations of spatial situations, if we only use this kind of knowledge, we cannot do interesting inferences about...
Consider an arrangement of equilateral non-overlapping translated triangles in the plane and two points S and T so that the segment ST is parallel to a side of each of the triangl...
This paper gives a brief overview of FG, a formal system for doing Euclidean geometry whose basic syntactic elements are geometric diagrams, and which has been implimentented as th...