Flatland

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard with luminous edges—and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe:" but now my mind has been opened to higher views...

 Geometry Divides the World

This meant, then, that the Greeks, in attempting to communicate their mathematical conceptioning, defined the circle as "an area bound by a closed line of equal radius from one point," the triangle as "an area bo)ound by a closed line of three angles, three edges, and three vertices." The Greeks talked only of the area that was "bound" as having validity and identity, while outside (on the other side of the boundary) existed only treachenerous terrain leading outward to boundless infinity—a...