Flores, Pablo; Ramírez, Rafael (2021). Note for the Third Hilbert Problem: a Fractal Construction. The Mathematics Student, 90(3-4), pp. 173-182 .
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Resumen
Hilbert’s Third problem questioned whether, given two polyhedrons with the same volume, it is possible to decompose the first one into a finite number of polyhedral parts that can be put together to yield the second one. This finite equidecomposition process had already been shown to be possible between polygons of the same area. Dehn solved the problem by showing that a regular tetrahedron and a cube with equal volume were not equidecomposable. In this paper, we present an infinite fractal process that allows the cube to be visually reconstructed from a tetrahedron with equal volume. We have proved that, given two tetrahedrons with the same volume, the first one can be decomposed into an infinite number of polyhedral parts that can be put together to yield the second one. This process makes it possible to obtain the volume of a tetrahedron from the volume of the parallelepiped, without the use of formulas or the Cavallieri Principle
Tipo de Registro: | Artículo |
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Términos clave: | 14. Matemáticas superiores > Geometría (matemáticas superiores) 03. Aula > Recursos didácticos > Materiales manipulativos 07. Enseñanza > Planificación del profesor > Metodología de enseñanza > Preparación de clases 13. Matemáticas escolares > Geometría > Geometría en tres dimensiones |
Nivel Educativo: | Educación Secundaria Básica (13-16 años) |
Código ID: | 23798 |
Depositado Por: | Rafael Ramírez |
Depositado En: | 05 Ene 2022 07:18 |
Fecha de Modificación Más Reciente: | 05 Ene 2022 07:18 |
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