The document describes various geometric properties related to curves, including osculating planes and circles, and their associated tangent, normal, and binormal lines. Different geometric elements like curves and circles are assigned colors and animation for visualization purposes across 5 examples on different pages.

1. Osculating plane-animated
Tangent line-red
Principal Normal line-black
Binormal line -green
2/22/2013 1

2. Osculating circle-animated-red
2/22/2013 2

3. Osculating circle-animated
Tangent line-red
Normal line-black
2/22/2013 3

4. Osculating circle-gray-animated
2/22/2013 Locus of center of osculating circle-red 4

5. Space curve lying on the surface of sphere -colourful
Osculating circle of colourful curve–animated-black
Osculating sphere of colourful curv is the sphere itself
2/22/2013 5