# A Surprise from Geometry

by Ross Honsberger (University of Waterloo)

Mathematics Magazine
February, 1986

Subject classification(s): Algebra and Number Theory | Linear Algebra | Vector Spaces
Applicable Course(s): 3.8 Linear/Matrix Algebra

Consider $n$ vectors issuing from the origin in $n$-dimensional space.  The author shows that the statement “any set of $n$ vectors in $n$-space, no two of which meet at greater than right angles, can be rotated into the non-negative orthant” is true for $n \leq 4$, but false for $n>4$.

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