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The Spiral of Theodorus and Sums of Zeta-values at the Half-integers

David Brink
The American Mathematical Monthly
Vol. 119, No. 9 (November 2012), pp. 779-786
DOI: 10.4169/amer.math.monthly.119.09.779
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.119.09.779
Page Count: 8
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The Spiral of Theodorus and Sums of Zeta-values at the Half-integers
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Abstract

Abstract The total angular distance traversed by the spiral of Theodorus is governed by the Schneckenkonstante K introduced by Hlawka. The only published estimate of K is the bound K ≤ 0:75. We express K as a sum of Riemann zeta-values at the half-integers and compute it to 100 decimal places. We find similar formulas involving the Hurwitz zeta-function for the analytic Theodorus spiral and the Theodorus constant introduced by Davis.

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