The subject of this paper is the Penrose kite and dart tiling of the plane: an aperiodic tiling where, in his own words, “the tiles may be used to form an instructive game ... the virtue of the game lies in the very surprising variety which arises in the fitting together of pieces of only two kinds”. We deal with a teaching experience in collaboration with a lab technician, a high school teacher and a graduating student: how to let high school students project and produce the kite and dart tiles using a Computer Numerical Control (CNC) machine. It is a project of work-related learning with 110 students coming from seven different high schools, in collaboration with the Model and Prototype Laboratory of the Department of Architecture at Roma Tre University. We discuss the effect of this activity on the learning process of the students, the methodology applied, the technical and organizational problems we faced in a Covid related period. Using the software GeoGebra, we will also show the geometric construction of Penrose tiles and how to produce an application to simulate the tessellation making.

Falcolini, C., Mauti, B.L., Siccardi, M., D'Angeli, A. (2023). Penrose Tiling: a Math-related Learning Interaction between HighSchool Students and a University Lab. PALESTINE JOURNAL OF MATHEMATICS, 12, 155-166.

Penrose Tiling: a Math-related Learning Interaction between HighSchool Students and a University Lab

Corrado Falcolini
Membro del Collaboration Group
;
Barbara Licia Mauti
Membro del Collaboration Group
;
Matteo Siccardi
Membro del Collaboration Group
;
Antonello D’Angeli
Membro del Collaboration Group
2023-01-01

Abstract

The subject of this paper is the Penrose kite and dart tiling of the plane: an aperiodic tiling where, in his own words, “the tiles may be used to form an instructive game ... the virtue of the game lies in the very surprising variety which arises in the fitting together of pieces of only two kinds”. We deal with a teaching experience in collaboration with a lab technician, a high school teacher and a graduating student: how to let high school students project and produce the kite and dart tiles using a Computer Numerical Control (CNC) machine. It is a project of work-related learning with 110 students coming from seven different high schools, in collaboration with the Model and Prototype Laboratory of the Department of Architecture at Roma Tre University. We discuss the effect of this activity on the learning process of the students, the methodology applied, the technical and organizational problems we faced in a Covid related period. Using the software GeoGebra, we will also show the geometric construction of Penrose tiles and how to produce an application to simulate the tessellation making.
2023
Falcolini, C., Mauti, B.L., Siccardi, M., D'Angeli, A. (2023). Penrose Tiling: a Math-related Learning Interaction between HighSchool Students and a University Lab. PALESTINE JOURNAL OF MATHEMATICS, 12, 155-166.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/438787
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