论文标题
立方顶点的阴影
Shadows of Cube Vertices
论文作者
论文摘要
假设有限维立方体通过一个维度的子空间较小地投射到自身的中心部分上。最多达到$ 9 $,将至少一个顶点投影到该部分,但是对于尺寸$ 10 $或更大的尺寸,有一些正交预测,所有顶点都在本节之外投影。实际上,“大多数”正交预测就是这种情况,因为维度趋于无限。
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.