I2

YOUNG'S GEOMETRY Undefined Terms: point, line, incidence Defined Term: Lines not incident with a common point are said to be parallel. Axioms Yl There exists at least one line. Y2 Each line is incident with exactly three points. Y3 Not all points are incident with the same line. Y4 Each two distinct points are incident with exactly one line. Y5 Given a line / and a point P not incident with /, there exists exactly one line incident with P that is parallel to l. Problems 1. Prove that Young's geometry there are exactly 12 lines. 2. Prove that Young's geometry has at least nine points. 3. Prove that two lines parallel to a third line are parallel to each other. 4. Sketch a model of the geometry