There are 5: en.wikipedia.org/w/index.php?title=Euclidean_geometry&oldid=1036511366#Axioms, the parallel postulate being the most controversial/interesting.
Analects translation by Robert Eno (2015) 16.7:
To see that the real projective plane is not simply connected space, considering the lines through origin model of the real projective plane, take a loop that starts at and moves along the great circle ends at .
Now try to shrink it to a point.
There's just no way!
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