ARE THESE FIGURES OXYMORA

The century-old topic of point and line configurations straddles the fence between projective geometry and combinatorics. In this article we shall be concerned mainly with the geometric approach and will attempt to highlight certain aspects of such configurations that we find very interesting. We hope the reader will agree. These aspects seem not to be widely known, possibly because of the confusing nature of the usual terminology, and-even more-due to the general decline in familiarity with geometric facts. Also, although there is a great amount of known material, it is scattered in many papers, a large fraction of which appeared in rather inaccessible journals. Unfortunately, there is no book that would present a reasonable account of such material. It is remarkable that in an elementary topic such as configurations, there are still many unsolved questions, and that fruitful connections to other branches of mathematics and its applications are fueling a renewed interest. The reason for the following pages is the hope that they may help awaken in our students (and in other readers) an interest in geometry. The paper may also afford them a chance to “try their wings” in independently developing a nontrivial but easily accessible topic, and to experience the fact that “elementary” questions may be hard enough to have resisted solution even to this day. Although the material of this note traditiofally would appear in the context of projective geometry, the reader may consider that all the points and lines are in the ordinary Euclidean plane. Many of the references are given for the sake of historical interest and understanding of the development, and we do not expect the reader to spend much time looking for them.