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

Examples 3.1.5, 3.1.6, 3.1.8

Problem 3.1.20

3.2: Curvature, Torsion, and the Frenet Frame

Page 80: Definition of Unit Tangent Vector

Page 80: 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


The code for Examples 3.2.5 and 3.2.6 is built into the previous two demos.

Problem 3.2.7: Torus Knot

Problem 3.2.12: Evolute of a Helix

3.3: Osculating Plane and Osculating Sphere

Definition 3.3.1: Osculating Plane

Proposition 3.3.3: Osculating Sphere

figure50     figure51


Problem 3.3.10: Osculating Helix

3.4: Natural Equations

Theorem 3.4.1: Fundamental Theorem of Space Curves

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