The Quarter-Turn and the Ball

John Paul Steinberger

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arXiv · 2610.06303

The Quarter-Turn and the Ball

John Paul Steinberger

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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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John Paul Steinberger. 2026-10-05. The Quarter-Turn and the Ball. https://arxiv.org/abs/2610.06303

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