Cuadriláteros Perfectos

Alicia M. Delgado de Brandao; Yanina del Carmen Rodríguez Reyes; Ubaldino Sandoval Moreno; Temístocles Zeballos Mitre; Ángela Y. Franco

doi:10.48204/j.vian.v9n1.a7537

Submitted June 26, 2025

Published 2025-06-25

Artículos

Vol. 9 No. 1 (2025): Visión Antataura

Perfect Quadrilaterals

Alicia M. Delgado de Brandao⁺⁻
Yanina del Carmen Rodríguez Reyes⁺⁻
Ubaldino Sandoval Moreno⁺⁻
Temístocles Zeballos Mitre⁺⁻
Ángela Y. Franco⁺⁻

DOI https://doi.org/10.48204/j.vian.v9n1.a7537

PDF (Español (España))

References

DOI: 10.48204/j.vian.v9n1.a7537

Published: 2025-06-25

How to Cite

Delgado de Brandao, A. M., Rodríguez Reyes, Y. del C., Sandoval Moreno, U., Zeballos Mitre, T., & Franco, Ángela Y. (2025). Perfect Quadrilaterals. Visión Antataura, 9(1), 48–70. https://doi.org/10.48204/j.vian.v9n1.a7537

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

Abstract

This article explores the existence of perfect quadrilaterals as a generalization of perfect triangles. We define the concepts of rational quadrilaterals and cyclic quadrilaterals, illustrating and proving several of their properties. Subsequently, we present the significant contributions of Brahmagupta and Kummer related to the study of rational quadrilaterals. Finally, we introduce the concept of perfect quadrilaterals and demonstrate, with the aid of computational algebra, the existence of only eleven perfect cyclic quadrilaterals.

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References

Colebrooke, H.T. (1817). Algebra, Arithmetic and Mensuration from the Sanskrit of Brahmagupta and Bhaskara. London.
Delgado de Brandao, A. M., Rodríguez Reyes, Y. del C., Sandoval Moreno, U., & Zeballos Mitre, T. (2023). Triángulos Perfectos. Visión Antataura, 7(2), 52–65. https://doi.org/10.48204/j.vian.v7n2.a4562
Dickson, L. E. (1971). History of the Theory of Numbers. Volume II. Chelsea Publishing Company, New York.
Pamfilos, P. (2024). Lectures on Euclidean Geometry 1. Springer Nature Switzerland AG. Switzerland.
R. D. Nelson (1979) Perfect Quadrilaterals. The American Mathematical Monthly, 86:10, 845-847, https://doi.org/10.1080/00029890.1979.11994927
Sujatha et al. (2011). Math Unlimited. Essays in Mathematics. Taylor & Francis Group, New York.