Chapter 6 - The meet operation

Abstract

This chapter focuses on the meet operation in classical geometry. In classical (unoriented) geometry, flats are considered to be sets of points, and therefore their intersection does not have to be defined explicitly: it is plain set intersection. In the oriented version, however, this simple definition is not enough, because the meet operation must also choose an orientation for the resulting set. The meet operation thus defined has properties quite similar to those of join. Two lines of T2 generally intersect on a pair of antipodal points. The meet of two lines as defined above depends strongly on the orientation of the whole plane. This dependency is not a matter of choice, but rather an essential property of oriented intersections. It turns out that it is not possible to consistently select one of the intersection points without a reference orientation for the whole plane.