all places, whence we know not. It was in old days, with our learned men, an interesting and oft-investigated question, “What is the origin of light?” and the solution of it has been repeatedly attempted, with no other result than to crowd our lunatic asylums with the would-be solvers. Hence, after fruitless attempts to suppress such investigations indirectly by making them liable to a heavy tax, the Legislature, in comparatively recent times, absolutely prohibited them. I—alas, I alone in Flatland—know now only too well the true solution of this mysterious problem; but my knowledge cannot be made intelligible to a single one of my countrymen; and I am mocked at—I, the sole possessor of the truths of Space and of the theory of the introduction of Light from the world of three Dimensions—as if I were the maddest of the mad! But a truce to these painful digressions: let me return to our houses.
The most common form for the construction of a house is five-sided or pentagonal, as in the annexed Figure. The two Northern sides RO, OF, constitute the roof, and for the most part have no doors; on the East is a small door for the women; on the West a much larger one for the men; the South side or floor is usually doorless.
Square and triangular houses are not allowed, and for this reason. The angles of a Square (and still more those of an equilateral Triangle), being much more pointed than those of a Pentagon, and the lines of inanimate objects (such as houses) being dimmer than the lines of men and women, it follows that there is no little danger lest the points of a square or triangular house residence might do serious injury to an inconsiderate or perhaps absentminded traveller suddenly therefore, running against them: and as early as the eleventh century of our era, triangular houses were universally forbidden by law, the only exceptions being fortifications, powder-magazines, barracks, and other state buildings, which it is not desirable that the general public should approach without circumspection.
At this period, square houses were still everywhere permitted, though discouraged by a special tax. But, about three centuries afterwards, the law decided that in all towns containing a population above ten thousand, the angle of a Pentagon was the smallest house-angle that could be allowed consistently with the public safety. The good sense of the community has seconded the efforts of the Legislature; and now, even in the country, the pentagonal construction has superseded every other. It is only now and then in some very remote and backward agricultural district that an antiquarian may still discover a square house.
III
Concerning the Inhabitants of Flatland
The greatest length or breadth of a full grown inhabitant of Flatland may be estimated at about eleven of your inches. Twelve inches may be regarded as a maximum.
Our women are Straight Lines.
Our soldiers and lowest classes of workmen are Triangles with two equal sides, each about eleven inches long, and a base or third side so short (often not exceeding half an inch) that they form at their vertices a very sharp and formidable angle. Indeed when their bases are of the most degraded type (not more than the eighth part of an inch in size), they can hardly be distinguished from Straight Lines or women; so extremely pointed are their vertices. With us, as with you, these Triangles are distinguished from others by being called “Isosceles”; and by this name I shall refer to them in the following pages.
Our middle class consists of Equilateral or Equal-Sided Triangles.
Our professional men and gentlemen are Squares (to which class I myself belong) and Five-Sided Figures or Pentagons.
Next above these come the nobility, of whom there are several degrees, beginning at Six-Sided Figures, or Hexagons, and from thence rising in the number of their sides till they receive the honourable title of Polygonal, or many-sided. Finally when the number of the sides becomes so numerous, and the sides themselves so small, that the Figure cannot be distinguished from a Circle, he is included in the Circular or Priestly order; and this is the highest class of all.
It is a law of Nature with us that a male child shall have one more side than his father, so that each generation shall rise (as a rule) one step in the scale of development and nobility. Thus the son of a Square is a Pentagon; the son of a Pentagon, a Hexagon; and so on.
But this rule applies not always to the tradesmen, and still less often to the soldiers, and to the workmen; who indeed can hardly be said to deserve the name of human Figures, since they have not all their sides equal. With them therefore the law of Nature does not hold; and the son of an Isosceles ( i.e. a Triangle with two sides equal) remains Isosceles still. Nevertheless, all hope is not shut out, even from the Isosceles, that his posterity may ultimately rise above his degraded condition. For, after a long series of military successes, or diligent and skilful labours, it is generally found that the more intelligent among the artisan and soldier classes manifest a slight increase of their third side or base, and a shrinkage of the two other sides. Intermarriages (arranged by the Priests) between the sons and daughters of these more intellectual members of the lower classes generally result in an offspring approximating still more to the type of the Equal-Sided Triangle.
Rarely—in proportion to the vast numbers of Isosceles births—is a genuine and certifiable Equal-Sided Triangle produced from Isosceles parents. 2 Such a birth requires, as its antecedents, not only a series of carefully arranged intermarriages, but also a long, continued
