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Geometric Dissection

Leong, Yee Hang (2020) Geometric Dissection. Final Year Project, UTAR.

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    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 (Hons) 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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