A Numerical Approach for Analysing the Moving Sofa Problem
This paper presents a method for obtaining the shape and area of a sofa. The proposed approach is based on a discrete solution to the equation, which states the necessary conditions for the existence of envelopes. Based on provided examples, it was proved that the method can be used for deriving the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/7/1409 |
| _version_ | 1797415405022609408 |
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| author | Michał Batsch |
| author_facet | Michał Batsch |
| author_sort | Michał Batsch |
| collection | DOAJ |
| description | This paper presents a method for obtaining the shape and area of a sofa. The proposed approach is based on a discrete solution to the equation, which states the necessary conditions for the existence of envelopes. Based on provided examples, it was proved that the method can be used for deriving the solutions of the posed problem. The method offers an area calculation accuracy of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-09T05:47:08Z |
| format | Article |
| id | doaj.art-6e60af39d1b44529b25e4efc81d28499 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T05:47:08Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-6e60af39d1b44529b25e4efc81d284992023-12-03T12:19:53ZengMDPI AGSymmetry2073-89942022-07-01147140910.3390/sym14071409A Numerical Approach for Analysing the Moving Sofa ProblemMichał Batsch0Faculty of Mechanical Engineering and Aeronautics, Rzeszow University of Technology, Al. Powstańców Warszawy 8, 35-959 Rzeszow, PolandThis paper presents a method for obtaining the shape and area of a sofa. The proposed approach is based on a discrete solution to the equation, which states the necessary conditions for the existence of envelopes. Based on provided examples, it was proved that the method can be used for deriving the solutions of the posed problem. The method offers an area calculation accuracy of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2073-8994/14/7/1409moving sofa problemdiscrete envelope of curves |
| spellingShingle | Michał Batsch A Numerical Approach for Analysing the Moving Sofa Problem Symmetry moving sofa problem discrete envelope of curves |
| title | A Numerical Approach for Analysing the Moving Sofa Problem |
| title_full | A Numerical Approach for Analysing the Moving Sofa Problem |
| title_fullStr | A Numerical Approach for Analysing the Moving Sofa Problem |
| title_full_unstemmed | A Numerical Approach for Analysing the Moving Sofa Problem |
| title_short | A Numerical Approach for Analysing the Moving Sofa Problem |
| title_sort | numerical approach for analysing the moving sofa problem |
| topic | moving sofa problem discrete envelope of curves |
| url | https://www.mdpi.com/2073-8994/14/7/1409 |
| work_keys_str_mv | AT michałbatsch anumericalapproachforanalysingthemovingsofaproblem AT michałbatsch numericalapproachforanalysingthemovingsofaproblem |