How to Tee a Hyperplane

Abstract

A letter tee ($\mathsf{T}$) is a geometric figure consisting of two line segments meeting at a right angle. We construct a covering of a hyperplane by a disjoint family of tees.

MSC::

• Primary 97G99
• Secondary 03E10

Acknowledgments

We thank Jeffrey Lagarias, Andrey Mishchenko, Ben Schmidt, Karen Smith, Juan Souto, and Jordan Watkins for helpful discussions and feedback. We thank the anonymous referees and editorial board member for suggesting several improvements.

Notes

1 Among the possible choices for a_p and b_p, we can choose those with minimal denominator, breaking ties by minimizing the numerator. So this step does not involve the axiom of choice.