Groups of Transformations with a Finite Number of Isometries: the Cases of Tetrahedron and Cube

Authors

  • Ferdinando Casolaro Department di Architecture University “Federico II” of Naples
  • Luca Cirillo University of Sannio in Benevento
  • Raffaele Prosperi DISUFF University of Salerno

DOI:

https://doi.org/10.23755/rm.v31i0.322

Keywords:

Geometric transformations, isometries, symmetry

Abstract

This paper deals with groups of transformations with finite number of isometrics and, therefore, appears as the completion of previous and published works (Casolaro, F. L. Cirillo and R. Prosperi 2015) related only to endless groups of transformations with isometrics. In particular isometries of the tetrahedron and the cube are presented which turn these figures in itself.

References

Casolaro, F. L. Cirillo and R. Prosperi (2015). “Le Trasformazioni Geometriche nello Spazio: Isometrie”. Science&Philosophy n. 1, 2015.

Casolaro, F. and Eugeni, F. (1996). “Trasformazioni geometriche che conservano la norma nelle algebra reali doppie”. Ratio Matematica n. 1, 1996.

Casolaro, F. and Prosperi, R. (2011). “La Matematica per la Scuola Secondaria di secondo grado: un contributo per il docente di Matematica". Atti della “Scuola estiva Mathesis” 26-30 luglio 2011. Terni: Editore 2C Contact.

Casolaro, F. and Paladino L. (2012). “Evolution of the geometry through the Arts”. 11th International Conference APLIMAT 2012 in the Faculty of Mechanical Engineering - Slovak University of Tecnology in Bratislava, febbraio 2012.

Casolaro, F. (2014). “L'evoluzione della geometria negli ultimi 150 anni ha modificato la nostra cultura. Lo sa la Scuola?”. “Science&Philosophy Journal of Epistemology", Volume 2, Numero 1, 2014.

Cundari, C. (1992). “Disegno e Matematica per una didattica finalizzata alle nuove tecnologie”. Progetto del M.P.I. e del Dipartimento di Progettazione e Rilievo dell’Università “La Sapienza” di Roma, 11-15 dicembre 1990; 6-10 maggio 1991; 8-12 dicembre 1991.

Casolaro, F. (1992). “Gruppo delle Affinità, Gruppo delle Similitudini, Gruppo delle Isometrie”. Da C. Cundari, Progetto del M.P.I. e del Dipartimento di Progettazione e Rilievo dell’Università “La Sapienza” di Roma (1992).

Morelli, A. (1989). Geometria per il biennio delle scuole medie superiori. Napoli: Edizione Loffredo.

Impedovo, M. (1998). “Matrici e isometrie nello spazio”. Un utilizzo didattico di MAPLE. L’insegnamento della matematica e delle scienze integrate, vol. 21 B, n° 1, febbraio 1998.

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Published

2016-12-30

Issue

Vol. 31 (2016)

Section

Volume 31-2016

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