I am looking for a book that goes deep into the geometry where points have area preferably were points are hexagons but a good introduction of the geometry where points are squares is also welcome.
I would like to learn what he consequences of such an geometry are.
Some I can think of:
A segment contains only a limited number of points.
Segments have an area.
Some parallel lines are indistinguisable (because they are the same point sets)
And I guess many more curious concequences.
I would like te learn about the euclidean case and after that develop my own ideas in the hyperbolic geometry case, but i need a good footing :)
The geometry of hexagons was bij a commenter in an early version of this question refered to as the beehive geometry but a google seach did not give interesting result
I found some pages on hexagonal geometry:
But i would like much more :)