Ebook: General Theory of Irregular Curves

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Content:
Front Matter....Pages i-x
Introduction....Pages 1-4
General Notion of a Curve....Pages 5-28
Length of a Curve....Pages 29-42
Tangent and the Class of One-Sidedly Smooth Curves....Pages 43-74
Some Facts of Integral Geometry....Pages 75-117
Turn or Integral Curvature of a Curve....Pages 118-174
Theory of a Turn for Curves on an n-Dimensional Sphere....Pages 175-207
Osculating Planes and Class of Curves with an Osculating Plane in the Strong Sense....Pages 208-216
Torsion of a Curve in a Three-Dimensional Euclidean Space....Pages 217-267
Frenet Formulas and Theorems on Natural Parametrization....Pages 268-280
Some Additional Remarks....Pages 281-284
Back Matter....Pages 285-288

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Content:
Front Matter....Pages i-x
Introduction....Pages 1-4
General Notion of a Curve....Pages 5-28
Length of a Curve....Pages 29-42
Tangent and the Class of One-Sidedly Smooth Curves....Pages 43-74
Some Facts of Integral Geometry....Pages 75-117
Turn or Integral Curvature of a Curve....Pages 118-174
Theory of a Turn for Curves on an n-Dimensional Sphere....Pages 175-207
Osculating Planes and Class of Curves with an Osculating Plane in the Strong Sense....Pages 208-216
Torsion of a Curve in a Three-Dimensional Euclidean Space....Pages 217-267
Frenet Formulas and Theorems on Natural Parametrization....Pages 268-280
Some Additional Remarks....Pages 281-284
Back Matter....Pages 285-288
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