MATH 335 Class Exercise on Axiom Systems

Names____________________________________________________

1. Using the model for Fano’s Geometry pictured below, add a point Q to the model and show that this leads to a violation of the axioms. This shows that Fano has exactly seven points. (Note. E – B – F is a line.)

2. Using the data on the Axiom page draw a model of Young’s Geometry using the points A through G below. You will have to draw some lines that are not straight. Then answer the questions below.

A B C

D E F

G H I

a) Which lines are parallel to L10? ______________

b) Which lines intersect L10 at point H? ____________

c) Find the line that is on G and has no points in common with L5. ____________

d) How many lines are on point F?

3. a) Devise a model for Axioms 2-4 in Incidence Geometry that shows that Axiom 1 is independent of the rest.

b) Repeat part a) except show that Axiom 4 is independent.

c) Repeat part a) except show that Axiom 3 is independent.