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http://hdl.handle.net/11320/17785Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Nakasho, Kazuhisa | - |
| dc.contributor.author | Shidama, Yasunari | - |
| dc.date.accessioned | 2025-01-09T11:57:40Z | - |
| dc.date.available | 2025-01-09T11:57:40Z | - |
| dc.date.issued | 2024 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 32, Issue 1, Pages 187–194 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/17785 | - |
| dc.description.abstract | In this article we present the Mizar proof of the isoperimetric theorem (one of the theorems listed among Wiedijk’s Top 100 mathematical theorems), inspired by Peter D. Lax’s paper “A Short Path to the Shortest Path”. Using relatively simple formal apparatus of continuous and differentiable functions, we show that among all curves of fixed length connecting two points on the x-axis, a semicircle is the curve which maximizes the area between the curve and the x-axis. | pl |
| dc.language.iso | en | pl |
| dc.publisher | DeGruyter Open | pl |
| dc.rights | Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/3.0/ | pl |
| dc.subject | isoperimetric theorem | pl |
| dc.subject | calculus of variations | pl |
| dc.subject | parametric curve | pl |
| dc.title | Classical Isoperimetric Theorem | pl |
| dc.type | Article | pl |
| dc.rights.holder | © 2024 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 3.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2024-0015 | - |
| dc.description.Affiliation | Kazuhisa Nakasho - Yamaguchi University, Yamaguchi, Japan | pl |
| dc.description.Affiliation | Yasunari Shidama - Karuizawa Hotch 244-, Nagano, Japan | pl |
| dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17. | pl |
| dc.description.references | Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6. | pl |
| dc.description.references | Viktor Bl˚asjö. The isoperimetric problem. The American Mathematical Monthly, 112(6): 526–566, 2005. | pl |
| dc.description.references | Noboru Endou. Differentiation on interval. Formalized Mathematics, 31(1):9–21, 2023. doi:10.2478/forma-2023-0002. | pl |
| dc.description.references | Noboru Endou and Yasunari Shidama. Multidimensional measure space and integration. Formalized Mathematics, 31(1):181–192, 2023. doi:10.2478/forma-2023-0017. | pl |
| dc.description.references | Noboru Endou and Yasunari Shidama. Integral of continuous functions of two variables. Formalized Mathematics, 31(1):309–324, 2023. doi:10.2478/forma-2023-0025. | pl |
| dc.description.references | Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281–284, 2001. | pl |
| dc.description.references | Noboru Endou, Yasunari Shidama, and Masahiko Yamazaki. Integrability and the integral of partial functions from R into R. Formalized Mathematics, 14(4):207–212, 2006. doi:10.2478/v10037-006-0023-y. | pl |
| dc.description.references | John Harrison. The HOL Light system reference. 2023. http://www.cl.cam.ac.uk/~jrh13/hol-light/reference.pdf. | pl |
| dc.description.references | John Harrison. The isoperimetric inequality. 2023. Available online at https://github.com/jrh13/hol-light/blob/master/100/isoperimetric.ml. | pl |
| dc.description.references | Andreas Hehl. The isoperimetric inequality. Proseminar Curves and Surfaces, Universitaet Tuebingen, Tuebingen, 2013. | pl |
| dc.description.references | Peter David Lax. A short path to the shortest path. The American Mathematical Monthly, 102(2):158–159, 1995. | pl |
| dc.description.references | Robert Osserman. The isoperimetric inequality. Bulletin of American Mathematical Monthly, 6(84):1182–1238, 1978. | pl |
| dc.description.references | Alan Siegel. An isoperimetric theorem in plane geometry. Discrete and Computational Geometry, 29(2):239–255, 2003. doi:10.1007/s00454-002-2809-1. | pl |
| dc.description.references | Marten Straatsma. Towards formalising the isoperimetric theorem. BSc thesis, Radboud University Nijmegen, 2022. | pl |
| dc.description.references | Freek Wiedijk. Formalizing 100 theorems. Available online at http://www.cs.ru.nl/~freek/100/. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 32 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 187 | pl |
| dc.description.lastpage | 194 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0003-1110-4342 | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2024, Volume 32, Issue 1 | |
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|---|---|---|---|---|
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