# A categorization of piecewise-linear surfaces

Cardinal Scholar
 dc.contributor.advisor Emert, John W. en_US dc.contributor.author Cox, Anna L. en_US dc.date.accessioned 2011-06-03T19:36:51Z dc.date.available 2011-06-03T19:36:51Z dc.date.created 1994 en_US dc.date.issued 1994 dc.identifier LD2489.Z78 1994 .C69 en_US dc.identifier.uri http://cardinalscholar.bsu.edu/handle/handle/185100 dc.description.abstract Any Piecewise-Linear (PL) surface can be formed from a regular polygon (including the interior) with an even number of edges, where the edges are identified in pairs to form a two-dimensional manifold. The resulting surfaces can be distinguished by algebraic means. An analysis of the construction algorithm can also be used to determine the resulting surface. Knowledge of the polygon used can also yield information about the surfaces formed.In this thesis, an algorithm is developed that will analyze all possible edge pairings for an arbitrary regular polygon. The combination of this data, along with known techniques from geometric topology, will categorize the constructions of these PL surfaces. A procedure using matrices is developed that will determine the Euler number and establish which algebraic words are equivalent.This topic extends to two-dimensional manifolds a classical method of analysis for three-dimensional manifolds. It therefore provides a more geometrical approach than has traditionally been used for two dimensional surfaces. dc.description.sponsorship Department of Mathematical Sciences dc.format.extent iv, 27 leaves ; 28 cm. en_US dc.source Virtual Press en_US dc.subject.lcsh Geometry, Differential. en_US dc.subject.lcsh Topology. en_US dc.title A categorization of piecewise-linear surfaces en_US dc.description.degree Thesis (M.S.) dc.identifier.cardcat-url http://liblink.bsu.edu/catkey/902464 en_US
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• Master's Theses [5330]
Master's theses submitted to the Graduate School by Ball State University master's degree candidates in partial fulfillment of degree requirements.