From a tangentially related discussion: "And how the heck would [sex] work, anyway? Seeing as women are good for nothing but killing polygons with their pointy, pointy ends."
For that matter, pregnancy. Do the males carry the child to term, or something?
Maybe the children are points.
But they have measurable angles at birth. Nothing with a measurable angle will fit inside a line. Unless there's something I'm missing in the parody of Victorian society, but this looks to me like mister seahorse.
Maybe they bud instead of having internal gestation.
Now you've all got me wondering how Lineland pregnancy happens. If I recall correctly, they explain the process of marriage and, uhh, mating, but not how a point can gestate anything...
Given that they can't obtain food unless it just... appears, presumably the mass needed is created through spontaneous generation. Mediated by sound. Think serious Mundane Utility, as that would imply that they have all children by Functional Magic. That's sort of like needing to focus one's chakra in order to eat.
This troper thought that the children could be a bit of the line folded (around?) the polygon and cut off by its own end. He just realized that females could be lines whose ends don't "take", and unfold back into a line segment.
I always thought that the whole point of the system is a kind of simplistic innuendo — a Square plus one more Line equals a Pentagon, after all, so the Square and the Line are literally putting themselves together to make a new shape. It can't be that literal because the Square and Line still exist afterwards, of course. Probably there is no pregnancy, just the two of them combining into one big squiggle and the offspring budding off.
As far as how Flatlanders eat, you're being too literal about accepting A. Square's view of the world as objective truth. Remember Flatland *isn't* a truly self-contained universe, and the Flatlanders aren't truly "flat". It seems pretty clear, actually, that the way Flatlanders live is kind of akin to a bunch of single-celled organisms floating in a watery film in a petri dish. It's entirely possible that Flatlanders are some kind of photosynthetic organism that live in a thin film of water or live on the surface of a body of water — remember that A. Square states clearly that his "world" has no sun or other source of light and that light is "everywhere" (i.e. that they're on a surface that has a light source constantly hovering overhead, most likely). I picture Flatland as some kind of pond or pool. (The Sphere himself kind of defeats this real-world vision of Flatland, but hey.)
In Chapter 16, the Sphere says "What you style Flatland is the vast level surface of what I may call a fluid, on, or in, the top of which you and your countrymen move about."
On that note, I have always suspected that the Flatlanders accomplish the task of eating by folding in pockets of an outer membrane around the food, as amoebas do; that removes the problem of having a "gut" that would split the body in two.
That would also solve the problem of how they move, they would move similar to amobeas
It would seem that geometry provides a more interesting answer here than biology. When a line bisects a polygon, the result is two polygons, with the number of sides depending on whether the line intersects any vertices or not. From the perspective of the shape, he has to be careful when being bisected in this way, and loses some 'area' to the newly created polygon. In accordance with the Victorian society parallels, the initial polygon determines how many sides the offspring may have, and it would take a great many 'generations' to produce anything resembling a circle. Creating a new line is possible by the same process, if the original one overlaps one of the the polygon's sides, rather than bisecting it.
If Flatland is in the surface of a pool of fluid, why does the sphere not cause damage to it every time it passes through? It should be causing ripples, which might simply change the space and not the shape inside the space if the surface itself stays in place, but why does it not constantly destroy things as it disturbs the surface of the fluid in other ways? Was the fluid and surface only a metaphor, and the Sphere never really displaces anything?
If the fluid is very light, it could be similar to how one moves through air.
If Lord Sphere moved into and out of the fluid slow enough, it wouldn't cause a ripple. Since Flatland just rests on the surface, it could flex to accommodate the displacement.
Perhaps a useful metaphor for attempting to think about 'deforming' the (likely metaphorical) fluid would be time dilation. A body moving sufficiently fast does perceive some 'disturbance of the fluid' (in this case spacetime). However, the effect is only significant at very high speeds. If this metaphor is used, then a polyhedron intruding into the flatland plane would produce minute distortions as described above, but too slight to have any effect in most cases. And if a polyhedron attempts to enter a region of the plane occupied by a two-dimensional shape, the two simply interact. Presumably this is exactly how Lord Sphere caused A. Square to leave the plane, after all.
When the Sphere takes A. Square to see his dimension, presumably he has to pick Square up to do so. Why don't all of A Square's organs fall out of his body into a globby mess? Also, where do the females keep their guts? Can they even eat?
We know for a fact that Flatlanders have a minor presence in the third dimension, so they're very probably sealed like any reasonable organism. Doesn't explain the women, though.
If we go by the movie, A. Square explicitly says that the "lines" are actually very thin rectangles.
In fact, in the book the women were described as thin parallelograms.
Why do all the creatures in Flatland only have one eye? Why are there no shapes with two eyes, side by side? Stereoscopic vision, so that one could see the edge-on silhouette of another shape from two different vantage points, would offer a tremendous advantage — you could tell whether or not another shape was a circle without you or he needing to move, for starters. (You'd have to wear special glasses to be able to see movies in 2-D, though.)