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 3.1.5: Cylindrical Helix


Example 3.1.6: Conical Helix



Example 3.1.7: Curves on Hyperboloid of One Sheet



Example 3.1.8: Space Cardioid





3.2: Curvature, Torsion, and the Frenet Frame


Page 68: Definition of Unit Tangent Vector


Page 69: Definition of Principal Normal Vector


figure20a     figure20b     figure21

[Help]

Definition 3.2.2: Frenet Frame and Definition of Binormal Vector


figure31     figure32

[Help]

Definition 3.2.3: Space Curvature and Plane Curvature


figure33     figure34

[Help]

Definition 3.2.4: Torsion Function


figure37     figure38     figure39

[Help]

Example 3.2.5: Helices


Curvature of the circular helix

figure22     figure23     figure24

[Help]

Torsion of the circular helix

figure40     figure3-41     figure42

[Help]

Example 3.2.6: Space Cardioid


Frenet frame of the space cardioid

figure35     figure36

[Help]

Torsion of the space cardioid

figure43     figure44     figure45

[Help]




3.3: Osculating Plane and Osculating Sphere


Definition 3.3.1: Osculating Plane


figure29     figure30   

[Help]

Proposition 3.3.3: Osculating Sphere


figure50     figure51     figure52

[Help]




3.4: Natural Equations


Theorem 3.4.1: Fundamental Theorem of Space Curves


figure53     figure54     figure55     figure56

[Help]



Return to home page
Continue to Chapter 4