Chapter 3 • Curves in Space: Local Properties



3.1: Definitions, Examples, and Differentiation


Example 3.1.2: Lines



Example 3.1.3: Planar Curves



Example 3.1.4: Twisted Cubic


Example 3.1.7: Curves on Hyperboloid of One Sheet



Further Examples





3.2: Curvature, Torsion, and the Frenet Frame


Page 68: Definition of Unit Tangent Vector


Page 69: Definition of Principal Normal Vector



Definition 3.2.2: Frenet Frame and Definition of Binormal Vector



Definition 3.2.3: Space Curvature and Plane Curvature



Definition 3.2.4: Torsion Function


figure37     figure38

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3.3: Osculating Plane and Osculating Sphere


Definition 3.3.1: Osculating Plane



Proposition 3.3.3: Osculating Sphere


figure50     figure51

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3.4: Natural Equations


Theorem 3.4.1: Fundamental Theorem of Space Curves





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