A Computational Approach to the Perimeter-Area Inequality in a Triangle
This paper explores the application of automated reasoning tools, specifically those implemented in GeoGebra Discovery, to the perimeter-area inequality in triangles. Focusing on the computational complex and real algebraic geometry methods behind these tools, this study analyzes a geometric constru...
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| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/14/1/40 |
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| author | Tomás Recio Carlos Ueno María Pilar Vélez |
| author_facet | Tomás Recio Carlos Ueno María Pilar Vélez |
| author_sort | Tomás Recio |
| collection | DOAJ |
| description | This paper explores the application of automated reasoning tools, specifically those implemented in GeoGebra Discovery, to the perimeter-area inequality in triangles. Focusing on the computational complex and real algebraic geometry methods behind these tools, this study analyzes a geometric construction involving a triangle with arbitrary side lengths and area, investigating the automated derivation of the relationship between the area and perimeter of a triangle, and showing that only equilateral triangles satisfy the exact perimeter-area equality. The main contribution of this work is to describe the challenges, and potential ways to approach their solutions, still posed by the use of such automated, symbolic computation, methods in dynamic geometry, in particular concerning the discovery of loci of points that satisfy specific geometric conditions, suggesting relevant improvements for the future development of these symbolic AI-based educational tools in geometry. |
| format | Article |
| id | doaj-art-f01b0e7d261d49eb97d3683bf6940f9c |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-f01b0e7d261d49eb97d3683bf6940f9c2025-01-24T13:22:14ZengMDPI AGAxioms2075-16802025-01-011414010.3390/axioms14010040A Computational Approach to the Perimeter-Area Inequality in a TriangleTomás Recio0Carlos Ueno1María Pilar Vélez2Departamento de Matemáticas y Física, Escuela Politécnica Superior, Universidad Antonio de Nebrija, 28015 Madrid, SpainCentro de Educación a Distancia Profesor Félix Pérez Parrilla, 35005 Las Palmas de Gran Canaria, SpainDepartamento de Matemáticas y Física, Escuela Politécnica Superior, Universidad Antonio de Nebrija, 28015 Madrid, SpainThis paper explores the application of automated reasoning tools, specifically those implemented in GeoGebra Discovery, to the perimeter-area inequality in triangles. Focusing on the computational complex and real algebraic geometry methods behind these tools, this study analyzes a geometric construction involving a triangle with arbitrary side lengths and area, investigating the automated derivation of the relationship between the area and perimeter of a triangle, and showing that only equilateral triangles satisfy the exact perimeter-area equality. The main contribution of this work is to describe the challenges, and potential ways to approach their solutions, still posed by the use of such automated, symbolic computation, methods in dynamic geometry, in particular concerning the discovery of loci of points that satisfy specific geometric conditions, suggesting relevant improvements for the future development of these symbolic AI-based educational tools in geometry.https://www.mdpi.com/2075-1680/14/1/40perimeter-area inequalitytriangle inequalityGeoGebra DiscoveryMaplecomputer algebra systemautomatic reasoning tools |
| spellingShingle | Tomás Recio Carlos Ueno María Pilar Vélez A Computational Approach to the Perimeter-Area Inequality in a Triangle Axioms perimeter-area inequality triangle inequality GeoGebra Discovery Maple computer algebra system automatic reasoning tools |
| title | A Computational Approach to the Perimeter-Area Inequality in a Triangle |
| title_full | A Computational Approach to the Perimeter-Area Inequality in a Triangle |
| title_fullStr | A Computational Approach to the Perimeter-Area Inequality in a Triangle |
| title_full_unstemmed | A Computational Approach to the Perimeter-Area Inequality in a Triangle |
| title_short | A Computational Approach to the Perimeter-Area Inequality in a Triangle |
| title_sort | computational approach to the perimeter area inequality in a triangle |
| topic | perimeter-area inequality triangle inequality GeoGebra Discovery Maple computer algebra system automatic reasoning tools |
| url | https://www.mdpi.com/2075-1680/14/1/40 |
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