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.

Submit Article

ON SOME RELATIONS BETWEEN BINOMIAL COEFFICIENTS AND TANGENT VALUES

Authors

  • Atsushi Yamagami

Keywords:

binomial coefficients, tangent values, Euler’s formula

DOI:

https://doi.org/10.17654/0973563125009

Abstract

Let $n \geq 3$ and $0 \leq r \leq \frac{n-1}{2}$ be any integers. In this article, we see some formulas which calculate the binomial coefficients ${ }_n C_{2 r+1}$ using the values of $\tan \frac{k \pi}{n}$ for integers $1 \leq k \leq n-1$ as applications of Euler's formula " $e^{\sqrt{-1} \theta}=\cos \theta+\sqrt{-1} \sin \theta$ ".

Received: February 20, 2025
Accepted: March 29, 2025

References

L. Euler, Introductio in analysin infinitorum, 1748.

Downloads

Published

05-06-2025

Issue

Vol. 27 No. 1 (2025)

Section

Articles

License

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

Creative Commons License

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

_________________________

Licensing Terms:

Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.

No Derivatives: Modifying or creating derivative works not allowed without written permission.

Contact Puspha Publishing House for more info or permissions.

How to Cite

ON SOME RELATIONS BETWEEN BINOMIAL COEFFICIENTS AND TANGENT VALUES. (2025). Far East Journal of Mathematical Education, 27(1), 71-81. https://doi.org/10.17654/0973563125009