Leong, Yee Hang (2020) Geometric Dissection. Final Year Project, UTAR.
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Abstract
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.
| Item Type: | Final Year Project / Dissertation / Thesis (Final Year Project) |
|---|---|
| Subjects: | Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science |
| Divisions: | Lee Kong Chian Faculty of Engineering and Science > Bachelor of Science (Honours) Applied Mathematics with Computing |
| Depositing User: | Sg Long Library |
| Date Deposited: | 09 Aug 2021 19:54 |
| Last Modified: | 09 Aug 2021 19:54 |
| URI: | http://eprints.utar.edu.my/id/eprint/4198 |
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