1) Abbott at one point states, "a Line, if I may so say, has 2 sides (for the points of a Line may be called by courtesy, its sides)"
How is it that a line is said to have 2 sides? I realize that Abbott here is talking of "sides" in a different sense.. referring instead to a two-dimensional definiton of sides I suppose. But this concept becomes even more confusing to me as I consider it in higher dimensions. What exactly are the two-dimensional "sides" of a hypercube?
2) Another mathematical question: Abbott often uses "slice shapes" to attempt to explain three dimensions to a flatlander, or two dimensions to a one-dimensional being. Yet he limits his explanations to consecutive dimensions. What would happen if a fourth dimensional solid were to intersect a two-dimensional world, for instance?
3) I noticed also while reading Flatland that Abbott seems nearly obsessed with the social setting of his world. In many ways the rigid class distinctions he describes reminded me of the caste system in India. Yet at various points Abbott makes not-so-subtle references to "Revolution," perhaps likening an isosceles revolt to a Marxist revolution. What were Abbott's political views? Was he a supporter of Marxist ideology?