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 fo 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 homes.
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 of triangular house residence might do serious
injury to an inconsiderate or perhaps absentminded traveller suddenly
running against them: and therefore, 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 is not desirable that the general public
should approach without circumspection.
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