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Mathematical essays and recreations (1903)

Schubert, Hermann, 1848-1911, McCormack, Thomas J. (Thomas Joseph), 1865-1932 · Chicago : Open Court Publishing · leaf 101

An illustration from Mathematical essays and recreations, 1903, leaf 101
space which may bedenoted by the numbers i, 2, 3, 4, 5 ; then imagine all the possibleten straight lines of junction drawn between each two of these points,namely, 1-2, 1-3 ... . 4-5 ; and finally, also, all the ten planes ofjunction of every three points described, namely, the plane 1-2-3,1-2-4, •… … Fig. 36. THE FOURTH DIMENSION. 87 Thus, for example, on this plane the points 1-2, 1-3, and 2-3 will lie ina straight line, for through the three spatial points i, 2, 3, a plane canbe drawn which will cut the plane of a drawing in a straight line.The reason, therefore, that the three points 3-4,…

Mathematics · Magic squares · Hyperspace · Circle-squaring

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