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dc.contributor.advisorO'Connor, John J. (John Joseph)
dc.contributor.advisorGratwick, Adrian
dc.contributor.authorMintz, Daniel V.
dc.coverage.spatial304 p.en_US
dc.description.abstractAlmost two thousand years ago, Claudius Ptolemy created a guide to drawing maps of the world, identifying the names and coordinates of over 8,000 settlements and geographical features. Using the coordinates of those cities and landmarks which have been identified with modern locations, a series of best-fit transformations has been applied to several of Ptolemy’s regional maps, those of Britain, Spain, and Italy. The transformations relate Ptolemy’s coordinates to their modern equivalents by rotation and skewed scaling. These reflect the types of error that appear in Ptolemy’s data, namely those of distance and orientation. The mathematical techniques involved in this process are all modern. However, these techniques have been altered in order to deal with the historical difficulties of Ptolemy’s maps. To think of Ptolemy’s data as similar to that collected from a modern random sampling of a population and to apply unbiased statistical methods to it would be erroneous. Ptolemy’s data is biased, and the nature of that bias is going to be informed by the history of the data. Using such methods as cluster analysis, Procrustes analysis, and multidimensional scaling, we aimed to assess numerically the accuracy of Ptolemy’s maps. We also investigated the nature of the errors in the data and whether or not these could be linked to historical developments in the areas mapped.en_US
dc.publisherUniversity of St Andrews
dc.relationThe Geography by Ptolemyen_US
dc.subjectHistory of mathematicsen_US
dc.subjectHistorical mapsen_US
dc.subject.lcshPtolemy, 2nd cent. Geographia
dc.subject.lcshGeography, Ancient--Mapsen_US
dc.subject.lcshError analysis (Mathematics)en_US
dc.subject.lcshCluster analysisen_US
dc.subject.lcshMultidimensional scalingen_US
dc.titleMathematics for history's sake : a new approach to Ptolemy's Geographyen_US
dc.type.qualificationnamePhD Doctor of Philosophyen_US
dc.publisher.institutionThe University of St Andrewsen_US
dc.publisher.departmentSchools of Mathematics and Classicsen_US

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