The Quarter-Turn and the Ball
John Paul Steinberger
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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