Problems in Euclidean Space

ThistextforadvancedundergraduatesandgraduatestudentsexaminesproblemsconcerningconvexsetsinrealEuclideanspacesoftwoorthreedimensions.Itillustratesthedifferentwaysinwhichconvexitycanenterintotheformulationasthesolutiontodifferentproblemsinthesespaces.ProblemsinEuclideanSpacefeaturesfourchaptersthatdevelopanincreasinglydominantinfluenceofconvexity.Inthefirstchapter,convexityplaysaminorrole;thesecondchapterconsidersproblemsoriginallystatedinawidercontextthatcanbereducedtoproblemsconcerningconvexsets.Inthethirdchapter,theproblemsaredefinedstrictlyforconvexsetsandnotformoregeneralsets,andthefinalchapterdiscussespropertiesofsubclassesoftheclassofconvexsets.