"We'd then argue over what shape a circle looked like, but my maths would certainly be easier than yours due to lack of irrationality."
Actually that argument was had and ended a long time ago; you can set pi to 3 and you get a thing called a spherical geometry. See, for instance, http://mathforum.org/library/drmath/view/55021.html . Between the word "spherical geometry" and what you find in that link you'll have the keywords to continue digging if you want to.
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"We'd then argue over what shape a circle looked like, but my maths would certainly be easier than yours due to lack of irrationality."
Actually that argument was had and ended a long time ago; you can set pi to 3 and you get a thing called a spherical geometry. See, for instance, http://mathforum.org/library/drmath/view/55021.html . Between the word "spherical geometry" and what you find in that link you'll have the keywords to continue digging if you want to.
Thanks for the link. Perhaps the higher order sequel to flatland is looking for an author?