Elementary Surprises in Projective Geometry Richard EvanSchwartz ...

• exposé - matière potentielle : to statement
• exposé

Elementary Surprises in Projective Geometry Richard Evan Schwartz∗ and Serge Tabachnikov† 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. A classical 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 (black) points are also contained on a line.

• planes through the origin
• pentagram map
• odd vertices
• projective duality
• curve dual to a conic section
• pn
• polygon
• statement
• dual
• lines