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Updated: May 15, 2025
If a number of planets were revolving around the sun, then supposing the materials of all these bodies were equally affected by gravitation, it can be demonstrated that the square of the periodic time in which each planet completes its orbit is proportional to the cube of the greatest diameter in that orbit.
Hence the relation in volume between them is that of the cubes of the series of numbers from one to ten, i.e., 1 : 8: 27 : 64: 125 : 216 : 343 : 512 : 729 : 1000. In fact, to make up the volume of the second pink cube, eight of the first little cubes would be required; to make up the volume of the third, twenty-seven would be required, and so on.
But surely it was only this morning oh, beautiful, star-eyed Harry, that you and I, wearied with the frantic vain attempts of the unmathematical professor to elucidate by appalling triangles and hieroglyphics on the blackboard the perplexities of cube root, ousted each other from the seat, sprawling upon the floor, and were chased by the LL.D. out of doors, never to return until we apologized and promised "to do so no more."
The transition may be made very easy. Let the cube, for instance, be cut into thin divisions, and placed on paper; he will then see as many plane rectangles as he has divisions; so with all the others. Globes may be treated in the same manner; he will thus see how surfaces really are generated, and be enabled to abstract them with facility in every solid.
He had seen no more than a tiny fraction of Godhome and felt only the lightest touch of its power, until now. The computer was a fifteen-n'liu cube, yet his newly stretched mind enabled him to comprehend it. So that was a psionic computer! He had plenty of time to study it in detail several minutes before Godhome began the last part of its work, with Kranath's cooperation.
The squaring of a number the raising of it to its second power finds graphic expression in the plane figure of the square; and the cubing of a number the raising of it to its third power in the solid figure of the cube. Now squares and cubes have been recognized from time immemorial as useful ornamental motifs.
It is a well known fact that in the microscopically minute of nature, units everywhere tend to arrange themselves with relation to certain simple geometrical solids, among which are the tetrahedron, the cube, and the sphere.
The former architect was not able to inspect it minutely; but she afterwards said that it impressed her as being entirely plain, and almost a perfect cube. Its walls were white and quite without ornament; there was only one entrance, an extremely low and broad, flat archway, extending across one whole side. The structure was about a hundred yards each way.
It was in the form of a cube, and must have measured nine or ten feet in all directions. Its contents I never ascertained, but the difficulty with which the boatmen got it rested on the side of the boat proved its weight to be worthy of its size. To get it on the shoulders of the Kafirs was the next difficulty. It was done by degrees.
I felt myself as fragile as a doll of glass in the hands of careless children. I was tossed to a waiting cube. On the ground, not ten feet from me, was Drake, swaying dizzily. Suddenly the cube that held me tightened its grip; tightened it so that it drew me irresistibly flat down upon its surface. Before I dropped, Drake's body leaped toward me as though drawn by a lasso. He fell at my side.
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