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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/220898
Construïm la banda de Möbius de paper òptima
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En aquest treball, es presenta la demostració de Richard Schwartz que la banda de Möbius de paper suau i encabida ha de tenir relació d'aspecte superior a $\sqrt{3}$. També es demostra que qualsevol seqüència de bandes de Möbius de paper suaus i encabides, la relació d'aspecte de les quals convergeix a $\sqrt{3}$, ha de convergir, llevat d'isometria, a la banda de Möbius triangular. Aquests resultats proven la conjectura que B. Halpern i C. Weaver van fer el 1977.
A la segona part d'aquest treball es mostra una proposta didàctica per presentar aquesta demostració a l'alumnat de secundària, i s'analitza la implementació d'aquesta proposta a una classe de 1r de batxillerat.
In this work, we present the proof made by Richard Schwartz that a smooth embedded paper Möbius band must have an aspect ratio greater than $\sqrt{3}$. We also prove that any sequence of smooth embedded paper Möbius bands whose aspect ratio converges to $\sqrt{3}$ must converge, up to isometry, to the triangular Möbius band. These results prove the conjecture made by B. Halpern and C. Weaver in 1977. In the second part of this work, we present a didactic sequence of activities to introduce this proof to secondary school students, and we analyze the implementation of this proposal in an 11th-grade class.
In this work, we present the proof made by Richard Schwartz that a smooth embedded paper Möbius band must have an aspect ratio greater than $\sqrt{3}$. We also prove that any sequence of smooth embedded paper Möbius bands whose aspect ratio converges to $\sqrt{3}$ must converge, up to isometry, to the triangular Möbius band. These results prove the conjecture made by B. Halpern and C. Weaver in 1977. In the second part of this work, we present a didactic sequence of activities to introduce this proof to secondary school students, and we analyze the implementation of this proposal in an 11th-grade class.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Sergi Muria Maldonado
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VILA TRIADÓ, Cristina. Construïm la banda de Möbius de paper òptima. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/220898