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The Fourth Dimension

Nature volume 70, page 268 (21 July 1904) | Download Citation



A BOOK bearing the present title may be reasonably expected to contain certain things. In the first place it should have a clear exposition of Descartes's applications of algebra to geometry, and conversely of geometry to algebra, the logical conclusion of which consists in the removal of all restrictions as to the conceivable number of dimensions of space. In the second place it should contain clear, concise, and exactly worded statements of the peculiar and distinctive geometrical properties which are characteristic of spaces of two, three, four, or more dimensions respectively. Among these peculiarities might be cited, as examples, the number of possible regular figures corresponding to the five regular polyhedra of three-dimensional space, the number of independent motions of a rigid body, the properties analogous to those of the shortest distance between two lines, the symmetry of crystals, and, in short, any results calculated to convince the reader that the study of space not only of four, but of five, six, and generally n dimensions leads to the discovery of geometrical theorems no less interesting than those of ordinary plane and solid geometry.

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