Mathematical Essays And Recreations
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Cut two figures, exactly like that of Fig. 38, out of a piece of paper, and turn the triangle ABJ^ about the side A£, ACE about the side AC, BCD about the side BC, and in one figure above and in the other below; then in both cases the points D,E, P will meet at a point, because AE is equal to AF, BF is equal to BD, CD is equal to CE. In this manner we obtain two pyramids which in all lengths and all angles are congruent, yet which cannot, THE FOURTH DIMENSION. Ql no matter how we try, be made t...o coincide, that is, be so fitted the one into the other that they shall both stand as one pyramid. But the reflected image of the one could be brought into coincidence with the other. Two spatial structures whose sides and angles are thus equal to each other, and of which each may be viewed as the reflected image of the other, are called synnnetrical. For instance, the right and the left hand are symmetrical ; or, a right and a left glove. Now just as in tv/o dimensions it is impossible by simple displacement to bring into congruence triangles which like those above mentioned can only be made to coincide by circumversion, so also in three dimensions it is impossible to bring into congruence two symmetrical pyramids.
What to read after Mathematical Essays And Recreations?
You can find similar books in the "Read Also" column, or choose other free books by Thomas J Thomas Joseph Mccormack to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Cut two figures, exactly like that of Fig. 38, out of a piece of paper, and turn the triangle ABJ^ about the side A£, ACE about the side AC, BCD about the side BC, and in one figure above and in the other below; then in both cases the points D,E, P will meet at a point, because AE is equal to AF, BF is equal to BD, CD is equal to CE. In this manner we obtain two pyramids which in all lengths and all angles are congruent, yet which cannot, THE FOURTH DIMENSION. Ql no matter how we try, be made t...o coincide, that is, be so fitted the one into the other that they shall both stand as one pyramid. But the reflected image of the one could be brought into coincidence with the other. Two spatial structures whose sides and angles are thus equal to each other, and of which each may be viewed as the reflected image of the other, are called synnnetrical. For instance, the right and the left hand are symmetrical ; or, a right and a left glove. Now just as in tv/o dimensions it is impossible by simple displacement to bring into congruence triangles which like those above mentioned can only be made to coincide by circumversion, so also in three dimensions it is impossible to bring into congruence two symmetrical pyramids.
What to read after Mathematical Essays And Recreations?
You can find similar books in the "Read Also" column, or choose other free books by Thomas J Thomas Joseph Mccormack to read onlineMoreLess
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