Far East Journal of Mathematical Education

The Far East Journal of Mathematical Education is a peer-reviewed journal focused on mathematical education. It publishes research papers that enhance understanding of mathematical concepts and encourages the use of technology, statistics, algorithms, and simulations in mathematics learning.

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PROOF WITHOUT WORDS: EISENSTEIN’S DUPLICATION FORMULA

Authors

  • Guojun Fang

Keywords:

Eisenstein’s duplication formula, proof without words

DOI:

https://doi.org/10.17654/0973563126002

Abstract

We provide a proof without words about Eisenstein’s duplication formula.

Received: September 27, 2025
Accepted: October 16, 2025

References

[1] L. Tan, Proof without words: Eisenstein’s duplication formula 2csc (2θ) = tan θ+ cot θ, Math. Mag. 71(3) (1998), 207. DOI: 10.2307/2691206.

[2] Roger B. Nelson, Proof without words: A trigonometric proof of the arithmetic mean-geometric mean inequality, The College Mathematics Journal 46(1) (2015), 42. DOI: 10.4169/college.math.j.46.1.42.

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Published

27-11-2025

Issue

Vol. 28 No. 1 (2026)

Section

Articles

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Copyright (c) 2025 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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How to Cite

PROOF WITHOUT WORDS: EISENSTEIN’S DUPLICATION FORMULA. (2025). Far East Journal of Mathematical Education, 28(1), 3-4. https://doi.org/10.17654/0973563126002

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