Geometric Dissection
At the beginning of this project, the dissection of some polygons were studied and analysed. One of them is the solution of Haberdasher’s problem which is a four-pieces dissection from an equilateral triangle to a square given by Henry Dudeney. His original construction idea is applied to construct...
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| Format: | Final Year Project / Dissertation / Thesis |
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2020
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| Online Access: | http://eprints.utar.edu.my/4198/1/1700375_LEONG_YEE_HANG_GEOMETRIC_DISSECTION.pdf http://eprints.utar.edu.my/4198/ |
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| _version_ | 1833428560613736448 |
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| author | Leong, Yee Hang |
| author_facet | Leong, Yee Hang |
| author_sort | Leong, Yee Hang |
| building | UTAR Library |
| collection | Institutional Repository |
| content_provider | Universiti Tunku Abdul Rahman |
| content_source | UTAR Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | At the beginning of this project, the dissection of some polygons were studied and analysed. One of them is the solution of Haberdasher’s problem which is a four-pieces dissection from an equilateral triangle to a square given by Henry Dudeney. His original construction idea is applied to construct the dissection from a square to an equilateral triangle. After that, equidecomposability of polygons and polyhedra are discussed. Wallace-Bolyai-Gerwien Theorem states that any polygons with same area are equidecomposable. Two proofs for this theorem are given. A stronger result tells that equidecomposable polygons have a common hinged dissection. Hilbert’s Third Problem asks whether two polyhedra of equal volume are equidecomposable. Max Dehn gave an negative answer to this problem. A recent alternative solution based on Bricard’s condition is studied. |
| format | Final Year Project / Dissertation / Thesis |
| id | my-utar-eprints.4198 |
| institution | Universiti Tunku Abdul Rahman |
| publishDate | 2020 |
| record_format | eprints |
| spelling | my-utar-eprints.41982021-08-09T11:54:42Z Geometric Dissection Leong, Yee Hang QA Mathematics QA75 Electronic computers. Computer science At the beginning of this project, the dissection of some polygons were studied and analysed. One of them is the solution of Haberdasher’s problem which is a four-pieces dissection from an equilateral triangle to a square given by Henry Dudeney. His original construction idea is applied to construct the dissection from a square to an equilateral triangle. After that, equidecomposability of polygons and polyhedra are discussed. Wallace-Bolyai-Gerwien Theorem states that any polygons with same area are equidecomposable. Two proofs for this theorem are given. A stronger result tells that equidecomposable polygons have a common hinged dissection. Hilbert’s Third Problem asks whether two polyhedra of equal volume are equidecomposable. Max Dehn gave an negative answer to this problem. A recent alternative solution based on Bricard’s condition is studied. 2020 Final Year Project / Dissertation / Thesis NonPeerReviewed application/pdf http://eprints.utar.edu.my/4198/1/1700375_LEONG_YEE_HANG_GEOMETRIC_DISSECTION.pdf Leong, Yee Hang (2020) Geometric Dissection. Final Year Project, UTAR. http://eprints.utar.edu.my/4198/ |
| spellingShingle | QA Mathematics QA75 Electronic computers. Computer science Leong, Yee Hang Geometric Dissection |
| title | Geometric Dissection |
| title_full | Geometric Dissection |
| title_fullStr | Geometric Dissection |
| title_full_unstemmed | Geometric Dissection |
| title_short | Geometric Dissection |
| title_sort | geometric dissection |
| topic | QA Mathematics QA75 Electronic computers. Computer science |
| url | http://eprints.utar.edu.my/4198/1/1700375_LEONG_YEE_HANG_GEOMETRIC_DISSECTION.pdf http://eprints.utar.edu.my/4198/ |
| url_provider | http://eprints.utar.edu.my |