Chapter 2 • Plane Curves: Global Properties



2.1: Basic Properties


Definition 2.1.1: Closed Curve



Definition 2.1.1: Simple Curve


Circle, Ellipse, and Cardioid for k ≥ 1 or k ≤ –1





2.2: Rotation Index


Proposition 2.2.1: Rotation Index of a Curve


figure2-3     figure2-4

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Definition 2.2.3: Degree of a Mapping


figure2-5     figure2-6

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2.3: Isoperimetric Inequality


Theorem 2.3.1: Isoperimetric Inequality






2.4: Curvature, Convexity, and the Four-Vertex Theorem


Definition 2.4.2: Convex


Circle, Ellipse, and Cardioid for k ≥ 2 or k ≤ –2


Page 54 and Figure 2.6: Height Function


figure2-9     figure2-10

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Theorem 2.4.5: Four-Vertex Theorem


figure2-11     figure2-12

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