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arXiv · 2010.05758

Shadows of Cube Vertices

Yossi Lonke
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Abstract

Suppose that a finite-dimensional cube is orthogonally projected onto a central section of itself by a subspace of one dimension less. Up to dimension $9$, at least one vertex is projected onto the section, but for dimension $10$ or larger, there are orthogonal projections for which all the vertices are projected outside the section. In fact, this is the case for "most" orthogonal projections, as the dimension tends to infinity.

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Yossi Lonke. 2020-10-08. Shadows of Cube Vertices. https://doi.org/10.1080/00029890.2019.1606576

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