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Geometry |
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Authors: Vladislav Koshchakov
The non-obvious possibility of decomposing any n-cube consisting of n-cubes (includingvisually perceptible 2D and 3D) into layers of these cubes sequentially placed along the maindiagonal of this n-cube is presented. At the same time, the number of n-cubes in each layerturned out to be closely related to the numbers of Pascal's triangle. The coefficients of cutting each n-cube from the last (n-1) layers of them with a section of dimension (n-1)D are calculated. Examples are given that allow us to outline some ways to further explore this possibility. In Addition, the possibility of using this method to prove the tetrahedron volume formula without using infinitesimal methods is shown.
Comments: 9 Pages. In Russian
Download: PDF
[v1] 2024-05-20 20:35:21
[v2] 2024-06-28 21:00:51
Unique-IP document downloads: 1418 times
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