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Making π Accessible

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Abstract

The expression C = π D, which gives the relationship between the circumference C and the diameter D of a circle, is one of the few formulas known to almost all children and adults, regardless of how long they have been out of school. School-going children are introduced to this relation in their 7th grade. How this is done in India is illustrated by a snapshot from a textbook (NCERT, Mathematics, Grade 7, Chapter 11, [1].)

There is no reference as to who proved it first, leave aside any proof of this fact. More so at no stage in the school curriculum, there is a reference to a proof of this for self-study. The aim of this article is to provide arguments that are rigorous and accessible to upper middle-grade students to illustrate the fact that C/D is constant for every circle.

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References

  1. https://ncert.nic.in/textbook.php?gemh1=11-15

  2. http://aleph0.clarku.edu/djoyce/java/elements/elements.html

  3. Bill Casselman, Archimedes on the circumference and area of a circle, http://www.ams.org/publicoutreach/feature-column/fc-2012-02 1 of 8 06-04-2019, 09:41

  4. David Richeson, Circular reasoning: Who first proved that C/d is a constant?, https://arxiv.org/abs/1303.0904

  5. Lee, J.M., Axiomatic Geometry, American Mathematical Society, 2013.

  6. Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, 1990.

  7. Körner, Thomas, A Companion to Analysis: A Second First and First second course in analysis, AMS Chelsea, 2004.

  8. Rana, Inder K., From Numbers to Analysis, World Scientific, 1998.

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Acknowledgement

• Part of this note was prepared during my engagement as an Adjunct Faculty at SGT University, Gurugram. I would like to thank the authorities at SGT University for the opportunity.

• I would like to thank the referee for the corrections and suggestions in preparing this note.

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Authors and Affiliations

  1. Indian Institute of Technology, 1003, 20A, MHADA, Powai, Mumbai, 400076, India

    Inder K. Rana

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  1. Inder K. Rana
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Correspondence to Inder K. Rana.

Additional information

Inder K. Rana is retired from IIT Bombay as Emeritus Fellow in June 2022.

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Rana, I.K. Making π Accessible. Reson 28, 1075–1091 (2023). https://doi.org/10.1007/s12045-023-1638-9

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  • DOI: https://doi.org/10.1007/s12045-023-1638-9

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