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目次

Curves in the PlaneStudying Curves in the Plane with MathematicaFamous Plane CurvesAlternate Methods for Plotting Plane CurvesNew Curves from OldDetermining a Plane Curve from Its CurvatureGlobal Properties of Plane CurvesCurves in SpaceTubes and KnotsConstruction of Space CurvesCalculus on Euclidean SpaceSurfaces in Euclidean SpaceExamples of SurfacesNonorientable SurfacesMetrics on SurfacesSurfaces in 3-Dimensional SpaceSurfaces in 3-Dimensional Space via MathematicaAsymptotic Curves on SurfacesRuled SurfacesSurfaces of RevolutionSurfaces of Constant Gaussian CurvatureIntrinsic Surface GeometryDifferentiable ManifoldsRiemannian ManifoldsAbstract SurfacesGeodesics on SurfacesThe Gauss-Bonnet TheoremPrincipal Curves and Umbilic PointsTriply Orthogonal Systems of SurfacesMinimal SurfacesMinimal Surfaces and Complex VariablesMinimal Surfaces via the Weierstrass RepresentationMinimal Surfaces via Bjorling's FormulaConstruction of SurfacesCanal Surfaces and Cyclides of DupinInversions of Curves and SurfacesAppendices General Programs Curves Surfaces Plotting ProgramsBibliographyIndexName IndexMiniprogram and Mathematica Command Index