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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2403.09277 |
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| _version_ | 1866912390405160960 |
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| author | Assis, Michael |
| author_facet | Assis, Michael |
| contents | It is well known that the set of origami constructible numbers is larger than the classical straight-edge and compass constructible numbers. However, the Huzita-Justin-Hatori origami constructible numbers remain algebraic so that the transcendental number $π$ can only be approximated using a finite number of straight line folds. Using these methods we give a convergent sequence for folding $π$ as well as other methods to approximate $π$. Folding along curved creases, however, allows for the construction of transcendental numbers. We here give a method to construct $π$ exactly by folding along a parabola, and we discuss generalizations for folding other transcendental numbers such as $Γ(1/4)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Folding $π$ Assis, Michael Number Theory It is well known that the set of origami constructible numbers is larger than the classical straight-edge and compass constructible numbers. However, the Huzita-Justin-Hatori origami constructible numbers remain algebraic so that the transcendental number $π$ can only be approximated using a finite number of straight line folds. Using these methods we give a convergent sequence for folding $π$ as well as other methods to approximate $π$. Folding along curved creases, however, allows for the construction of transcendental numbers. We here give a method to construct $π$ exactly by folding along a parabola, and we discuss generalizations for folding other transcendental numbers such as $Γ(1/4)$. |
| title | Folding $π$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2403.09277 |