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ndltd-OhioLink-oai-etd.ohiolink.edu-kent1334273766
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ndltd-OhioLink-oai-etd.ohiolink.edu-kent13342737662021-08-03T05:38:02Z Convex Bodies with SO(2) Congruent Projections Mackey, Benjamin James Suppose two convex bodies K and L in three dimensional Euclidean space have the property that every orthogonal projection of K is SO(2) congruent to the corresponding orthogonal projection of L. The goal of this research is to prove that such bodies must themselves be congruent. After introducing several tools of convex geometry and tomography, we present a theorem which states that if the orthogonal projections of L can be translated into the corresponding projection of K, then K can be obtained by a translation of L. The rest of the thesis is spent attacking the issue of rotationally congruent projections. We present the proof found in Vladamir Golubyatnikov's book "Uniqueness Questions in Reconstruction of Multidimensional Objects from Tomography-Type Data" that, assuming no projection has a nontrivial SO(2) symmetry, the bodies K and L are either parallel or L can be obtained by reflecting K about some point. A deep lemma of Golubyatnikov's for which no symmetry assumption is necessary is also proven, as well as an analogous result about bodies which have SO(2) congruent sections rather than projections. Using the notion of polar duality, a new special case of the problem with no symmetry assumptions is considered, and it is proven the bodies K and L must coincide or be symmetric about the origin in this setting. 2012-04-13 English text Kent State University / OhioLINK http://rave.ohiolink.edu/etdc/view?acc_num=kent1334273766 http://rave.ohiolink.edu/etdc/view?acc_num=kent1334273766 unrestricted This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.
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NDLTD
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English
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NDLTD
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| author |
Mackey, Benjamin James
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| spellingShingle |
Mackey, Benjamin James
Convex Bodies with SO(2) Congruent Projections
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| author_facet |
Mackey, Benjamin James
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| author_sort |
Mackey, Benjamin James
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| title |
Convex Bodies with SO(2) Congruent Projections
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| title_short |
Convex Bodies with SO(2) Congruent Projections
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| title_full |
Convex Bodies with SO(2) Congruent Projections
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| title_fullStr |
Convex Bodies with SO(2) Congruent Projections
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| title_full_unstemmed |
Convex Bodies with SO(2) Congruent Projections
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| title_sort |
convex bodies with so(2) congruent projections
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| publisher |
Kent State University / OhioLINK
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| publishDate |
2012
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| url |
http://rave.ohiolink.edu/etdc/view?acc_num=kent1334273766
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AT mackeybenjaminjames convexbodieswithso2congruentprojections
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1719422770231640064
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