PreprintCC BY 4.0arXiv
The Quarter-Turn and the Ball
Abstract
In his Tau Manifesto, Michael Hartl presents a formula, credited to Jeff Cornell, for the volume of the unit n-ball in terms of the quarter-turn constant η=π/2. We read the formula as a set of clues to a geometric proof, leading through orthant geometry and a higher-dimensional version of Lambert's equal-area projection. We conclude with some additional thoughts on the circle constant.
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BibTeX
@misc{steinberger2026quarterturn,
title = {{The Quarter-Turn and the Ball}},
author = {John Paul Steinberger},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06303},
eprint = {2610.06303},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06303},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Quarter-Turn and the Ball
AU - John Paul Steinberger
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06303
UR - https://arxiv.org/abs/2610.06303
AB - In his Tau Manifesto, Michael Hartl presents a formula, credited to Jeff Cornell, for the volume of the unit n-ball in terms of the quarter-turn constant η=π/2. We read the formula as a set of clues to a geometric proof, leading through orthant geometry and a higher-dimensional version of Lambert's equal-area projection. We conclude with some additional thoughts on the circle constant.
ER -