Triangles with arithmetic, geometric and harmonic progressions

Geovane Pereira do Nascimento ^[1] ; Douglas Azevedo ^[2] ; Thiago Pinguello de Andrade ^[2] ; Michele Cristina Valentino ^[2]
1. [1] Master in Mathematics through PROFMAT and Mathematics teacher at E.E. Dr. Ernesto Fonseca
2. [2] DAMAT (Departamento Acadêmico de Matemática), PROFMAT -- DAMAT-Universidade Tecnólogica Federal do Paraná, Cornélio Procópio, Paraná, Brasil
Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 56, Nº. 10, 2025, págs. 2050-2060
Idioma: inglés
DOI: 10.1080/0020739X.2024.2363348
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Resumen
- This article explores the fascinating world of triangles with angle and side sequences in arithmetic, geometric and harmonic progressions. The properties and relationships between these progressions and the corresponding triangle parameters are investigated. The main focus is on proving a series of theorems that provide insights into the conditions under which triangles exhibit these progressions. The proofs are presented with meticulous attention to detail, offering a deep understanding of the results. The presented findings contribute to the field of mathematical education by providing rich material for classroom activities and discussions.