Miami University Incidence Geometry Questions
I’m working on a geometry discussion question and need a sample draft to help me learn.
- Give a model of an incidence geometry (i.e. all of IA1, IA2, IA3 are satisfied) which does
not satisfy any of the parallel postulates. (Hint: I came up with an example on five points.) - Give a model of an incidence geometry with a finite number of points which satisfies the
Hyperbolic Parallel Postulate and not every line has the same number of points. (Hint: I
came up with an example on six points.) - Give a model of an incidence geometry with a finite number of points which satisfies the
Elliptic Parallel Postulate and not every line has the same number of points. (Hint: I came
up with an example on four points. - (i) Is it possible for there to exist a model of incidence geometry on 6 points such that every line
contains exactly 3 points. (ii) Create a version of “Spot-it” in which each card has three symbols. It must have the property
that every pair of cards has exactly one symbol in common and the number of cards must be
equal to the total number of symbols.
