Harmonic mean iteration

We consider a method akin to the Babylonian method for approximating 2, but using the Harmonic mean instead of the Arithmetic mean. This yields a sequence which increases to 2. Then we compare this method to the Babylonians' method and see how they might be used in conjunction.

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Publication Details

Journal
International Journal of Mathematical Education in Science and Technology
Published
2026-08-03
DOI
https://doi.org/10.1080/0020739x.2026.2703175
Primary Topic
Approximation Theory and Sequence Spaces
Type
article
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article

Harmonic mean iteration

Peter R. Mercer
International Journal of Mathematical Education in Science and Technology
Approximation Theory and Sequence Spaces
article

Harmonic mean iteration

Peter R. Mercer
article en

Abstract

We consider a method akin to the Babylonian method for approximating 2, but using the Harmonic mean instead of the Arithmetic mean. This yields a sequence which increases to 2. Then we compare this method to the Babylonians' method and see how they might be used in conjunction.

International Journal of Mathematical Education in Science and Technology
Buffalo State University (US)
Openalex Percentile: Top 6%
Approximation Theory and Sequence Spaces
DOISourceOpenAlex
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