I'm attempting to solve a little exercise that my maths lecturer has given me relating to projective planes. Basically, she has asked me to show that a projective plane contains a set of 7 points and 6 lines. I was wondering how this can be done, as using the axioms that define a projective plane, I can only achieve a Fano plane which contains 7 points and 7 lines as a circular line has to be included to satisfy the axioms.
The axioms in question are:
- Any two distinct points lie on a unique line.
- Any two distinct lines meet in a unique point.
- There exist at least three non-collinear points.
- There exist at least three points on every line.
Any tips or help will be greatly appreciated!