Elementary Surprises in Projective Geometry

The classical theorems in projective geometry involve constructions based on points and straight lines. A general feature of these theorems is that a surprising coincidence awaits the reader who makes the construction. One example of this is Pappus’s theorem. One starts with 6 points, 3 of which are contained on one line and 3 of which are contained on another. Drawing the additional lines shown in Figure 1, one sees that the 3 middle (blue) points are also contained on a line