Duvenhage, Rocco2020-12-292020-12-292020/05/062019van Staden, WJ 2019, Metric aspects of noncommutative geometry, MSc Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/77893>A2020http://hdl.handle.net/2263/77893Dissertation (MSc)--University of Pretoria, 2019.We study noncommutative geometry from a metric point of view by constructing examples of spectral triples and explicitly calculating Connes's spectral distance between certain associated pure states. After considering instructive nite-dimensional spectral triples, the noncommutative geometry of the in nite-dimensional Moyal plane is studied. The corresponding spectral triple is based on the Moyal deformation of the algebra of Schwartz functions on the Euclidean plane.en© 2020 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria.UCTDDissertation12024016