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

SEMI-CIRCLES, ELLIPSES AND SUPER ELLIPSES DISTINGUISHED BY INSCRIBED RIGHT ANGLE

Authors

  • Isabelle N. Awai
  • Sweta Sharma
  • Beverly Ukoha
  • Ramesh Sharma

Keywords:

Thales’ theorem, inscribed right angle, semi circle, semi-ellipse, semi- super ellipse

DOI:

https://doi.org/10.17654/0973563125018

Abstract

Thales’ theorem says that the angle subtended by the base at any point of the upper half of a circle is a right angle. We derive a formula that proves Thales’ theorem and its converse, and apply it to seek points on the upper half an ellipse and more generally on the upper half of a super ellipse, where the angle subtended by the base diameter makes a right angle. Our results show a way of distinguishing among a semi-circle, ellipse and super ellipse. The contents of this paper can be understood by undergraduate students with calculus background.

Received: October 1, 2025
Accepted: November 1, 2025

References

[1] S. Ceribasi and G. Altay, Free vibration of super elliptical plates with constant and variable thickness by Ritz method, J. Sound. Vib. 319 (2009), 668-680.

[2] N. T. Gridgeman, Lamé ovals, The Math. Gazette 54 (387) (1970), 31-37.

[3] Thomas L. Heath, The Thirteen Books of Euclid’s Elements, Vol. 2 (Books 3-9), 2nd ed., Dover, 1956, p. 61, Originally published by Cambridge University Press, 2nd ed., 1926.

[4] T. Patronis and D. Patsopoulos, The theorem of Thales: a study of the naming of theorems in school geometry textbooks, The International Journal for the History of Mathematics Education 1 (2006), 57-68.

[5] R. D. Poodiack, Squigonometry, hyperellipses and supereggs, Math. Mag. 89(2) (2016), 92-100.

Downloads

Published

20-11-2025

Issue

Vol. 27 No. 2 (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

SEMI-CIRCLES, ELLIPSES AND SUPER ELLIPSES DISTINGUISHED BY INSCRIBED RIGHT ANGLE. (2025). Far East Journal of Mathematical Education, 27(2), 145-153. https://doi.org/10.17654/0973563125018

Similar Articles

You may also start an advanced similarity search for this article.