The Academy (November 8, 1884), p. 302.
Flatland is a world inhabited by beings whose experience of space is limited to two dimensions. In this book a native of this strange region has undertaken to describe its peculiarities to us dwellers in `Spaceland.' It seems the male Flatlanders are plane rectilineal figures, varying in shape according to their position in the social scale, or, what in Flatland is the same thing, to their degree of intellectual development; the lowest class being isosceles triangles, and the highest class, or priesthood, being polygons which have so many sides that they are accounted circles. The Flatland women, being deplorably lacking in intellect, are not figures at
all, but merely straight lines. Of course, the inhabitants of two-dimensional space cannot see each other as figures, but only as straight lines. For the means by which they can infer one another's true shape, and for the manners and institutions of Flatland, the reader must be referred to the book itself. The historian of Flatland is by rank and figure `a square,' and he has a grandson, a clever hexagon, who one day startles him with a suggestion that space may have a third dimension, and that beings may exist who are capable of seeing the inside of a closed figure. The notion is angrily rejected as absurd; but the `Square' afterwards undergoes a miraculous experience that introduces him to the threefold space which he was previously
unable to imagine. Guided by the analogy of his own experience, he ventures to suggest to the inhabitants of `Spaceland' that a fourth dimension may have real existence, though it is to them as inconceivable as the third dimension once was to himself. The `Square' has forgotten to tell us by what means he has managed to make himself intelligible to tri-dimensional mankind, and one or two other weak points might easily be found in his story; but, on the whole, the idea is very cleverly worked out, with many happy satiric touches, and the book is much more entertaining than this account of it will lead the reader to suppose.