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In this situation, they generally assume the shape of irregular polygons, with angles somewhat rounded; a form apparently caused by the lateral pressure of the contiguous pieces. On the river Wharfe, near Otley, in the West Riding of Yorkshire, is a weir or milldam where this phenomenon is sometimes manifested in a striking manner.
We cannot flatter ourselves, therefore, that under equal laws and opportunities we have rubbed out the saliencies of human nature. At a distance the mass of the Russian people seem as monotonous as their steppes and their commune villages, but the Russian novelists find characters in this mass perfectly individualized, and, indeed, give us the impression that all Russians are irregular polygons.
At last she said abruptly: "I don't see what harm there is in my wishing not to tie myself. I don't want to begin life by marrying. There are other things a woman can do." "There's nothing she can do so well. But you're of course so many-sided." "If one's two-sided it's enough," said Isabel. "You're the most charming of polygons!" her companion broke out.
We cannot flatter ourselves, therefore, that under equal laws and opportunities we have rubbed out the saliencies of human nature. At a distance the mass of the Russian people seem as monotonous as their steppes and their commune villages, but the Russian novelists find characters in this mass perfectly individualized, and, indeed, give us the impression that all Russians are irregular polygons.
Antiphon the Sophist, in connexion with attempts to square the circle, had asserted that, if we inscribe successive regular polygons in a circle, continually doubling the number of sides, we shall sometime arrive at a polygon the sides of which will coincide with the circumference of the circle.
And how perfect a proof of the natural fitness and, I may almost say, the divine origin of the aristocratic constitution of the States of Flatland! By a judicious use of this Law of Nature, the Polygons and Circles are almost always able to stifle sedition in its very cradle, taking advantage of the irrepressible and boundless hopefulness of the human mind.
Colonel Philibert and Master Pothier rode up the broad avenue that led to the Chateau, and halted at the main gate set in a lofty hedge of evergreens cut into fantastic shapes, after the fashion of the Luxembourg. Within the gate a vast and glowing garden was seen all squares, circles, and polygons.
Fixed in the floor of the tank are 144 posts, 9 inches thick at the bottom and 6 inches thick at the top, to support the crown of the holder in such a way that the tops are fixed in a kind of socket, each of them being provided with four horizontal bars, which decrease in thickness from 305 by 100 mm. to 150 by 50 mm., and represent 16 parallel polygons, which in their turn are fastened diagonally by means of iron rails 63 by 100 mm. thick, arranged crosswise.
Even to me, a Mathematician of no mean standing, and the Grandfather of two most hopeful and perfectly regular Hexagons, to find myself in the midst of a crowd of rotating Polygons of the higher classes, is occasionally very perplexing.
Indeed, is it by the will of God, for example, or is it not rather by the nature of numbers, that certain numbers allow more than others of various exact divisions? that some are more fitted than others for forming battalions, composing polygons and other regular figures? that the number six has the advantage of being the least of all the numbers that are called perfect? that in a plane six equal circles may touch a seventh? that of all equal bodies, the sphere has the least surface? that certain lines are incommensurable, and consequently ill-adapted for harmony?
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