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Estimating pi using geoscience

Nature Geoscience volume 15, pages 246–247 (2022)Cite this article

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Let us assume that the Earth is a smooth sphere with radius R. An intersecting plane that passes through the Earth’s centre traces a great circle on the Earth’s surface with circumference C. Using this spherical assumption, we can find π by π = C/(2R). NASA provides determinations of both R and C for an average plane through the equator (Re = 6,378.1 km; Ce = 40,030.2 km) and through a meridian (Rp = 6,356 km; Cp = 40,008 km). These yield an equatorial πe ≈ 3.1381 and a polar πp ≈ 3.1473, within 0.11% and 0.18% of the true value of π, respectively.

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Fig. 1: 03.14 by Lucía Pérez-Díaz.

Lucía Pérez-Díaz

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Acknowledgements

The authors thank J. van Hunen, M. Allen and J. Jenkins for discussions.

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Authors and Affiliations

  1. Durham University, Durham, UK

    Fabian B. Wadsworth

  2. Ludwig-Maximilians-Universität, Munich, Germany

    Jérémie Vasseur & Iphigenia Anagnostopoulos

  3. Neftex, Halliburton, Abingdon, UK

    Lucía Pérez-Díaz

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  1. Fabian B. Wadsworth
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  2. Jérémie Vasseur
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  3. Iphigenia Anagnostopoulos
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  4. Lucía Pérez-Díaz
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Correspondence to Fabian B. Wadsworth.

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The authors declare no competing interests.

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Wadsworth, F.B., Vasseur, J., Anagnostopoulos, I. et al. Estimating pi using geoscience. Nat. Geosci. 15, 246–247 (2022). https://doi.org/10.1038/s41561-022-00928-z

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