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Let π Be a Function

Justin T. Schultz and Catherine Stenson
Mathematics Magazine
Vol. 86, No. 3 (June 2013), pp. 177-188
DOI: 10.4169/math.mag.86.3.177
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Page Count: 12
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Let π Be a Function
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Summary In the plane, the ratio of the circumference of a circle to its diameter is always π. On a sphere, however, this ratio (which we denote Π) takes on other values, provided the diameter is measured along a great circle on the sphere. In this article, we explore Π as a function of radius on surfaces of revolution. We also consider the inverse problem—we begin with a function and, under certain conditions, find a surface or Riemannian manifold with Π equal to that function.

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