Fundamentals of Projective Geometry, Basic Objects FRP1

*SEE IF YOU CAN DO THE EXERCISES WRITTEN @ BOTTOM *

We begin this more rigorous treatment of projective geometry by defining the basic objects algebraically. In particular, we define the join, the meet, the complete quadrangle and the complete quadrilateral. The notation defined here will allow us to describe an axiomatic framework later on.

Projective geometry is more basic and important than Euclidean geometry, because it uses less assumptions, and in concerned with statements which remain true for a much wider range of different geometric setups. In fact, with this algebraic approach, we do not even define a metric. We shall see how such ideas, as well as those of polarity, harmony and conic curves arise as natural consequences of our small set of initial axioms.

I also created a less algebraic more visual, course in projective geometry, which begins with the video:

   • Projective Geometry 1 Without Equations, C...  


There are the FPG1 problems:

1: Set up a one to one correspondence from the positive whole numbers 1,2,3,.,
to the sequence of positive even numbers 2,4,6,...
Is it fair to say `there are as many positive whole numbers as there are even positive whole numbers ?

2: A complete quadrangle, also known as a complete 4 point, is constructed by starting off with four vertices, and then adding extra structure. In a similar way, describe the structure of a complete n-point, for any n greater than 2