Mémoire de Maîtrise
DOI
10.11606/D.55.2017.tde-11042017-095821
Document
Auteur
Nom complet
Reginaldo Alexandre da Silva
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2017
Directeur
Jury
Zani, Sergio Luis (Président)
Manzoli Neto, Oziride
Paterlini, Roberto Ribeiro
Sampaio, Joao Carlos Vieira
Titre en portugais
Caleidociclos
Mots-clés en portugais
Aplicação da lei dos cossenos
Aplicação da relação fundamental da trigonometria
Caleidociclo
Poliedros
Polígonos
Simetria axial
Simetria rotacional
Teorema de Pitágoras
Resumé en portugais
Titre en anglais
Kaleidocycles
Mots-clés en anglais
Application of the fundamental relation of trigonometry
Application of the law of cosines
Kaleidocycles
Polygon
Polyhedron
Pythagorean theorem
Rotational symmetry
Symmetry of reflection
Resumé en anglais
Kaleidocycles have been used asan artistic formof presentation of pictures, paintings or a part of artworks, especially images with symmetries; perhaps the best known works are M. C. Eschers. The few finded publications of the mathematical theory related to these three-dimensional rings give rise to imagine and create applications for developing skills to be worked in classroom. In order to increase the possibility of applications of concepts, theorems and mathematical relations, the present work proposes some activities dealing with kaleidocycles. The proposals were prepared in accordance with the students level of education, i.e., symmetries for the7th grade, the Pythagorean theorem for the 8th and 9th grades, law of cosines and the fundamental relation of trigonometry, volume and surface area of geometric solids for high school students; some of the proposals have variations to suit the level of development in which the class is at. All the molds used and other possibilities of kaleidocycles, including solids which fit into kaleidocycles, were organized at the end of this dissertation in one of the appendices. There is also an appendix with other types of mobile geometric solids that can be used in the same purpose in different applications of spatial geometry.

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Date de Publication
2017-04-12

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