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The Fastest Way Not to Run a Four-Minute Mile

Michael Bolt, Anthony Meyer and Nicholas Visser
The College Mathematics Journal
Vol. 45, No. 2 (March 2014), pp. 101-107
DOI: 10.4169/college.math.j.45.2.101
Stable URL: http://www.jstor.org/stable/10.4169/college.math.j.45.2.101
Page Count: 7
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The Fastest Way Not to Run a Four-Minute Mile
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Abstract

Summary In this manuscript we present the mathematics that is needed to answer three counterintuitive problems related to the averaging of functions. The problems are manifestations of the question, “Is the average rate of change on a given interval determined by the average rate of change on subintervals of a fixed length?” We also ask questions in higher dimensions that may have interesting geometric significance.

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