1. Joseph Liouville 1809 – 1882 Joseph Liouville 1809 – 1882 Liouville is best known for his work on the existence of a transcendental number in 1844 when he constructed an infinite class of such numbers.

3. If we want to approximate the length of a curve, over a short distance we could measure a straight line. By the pythagorean theorem: We need to get dx out from under the radical. Lengths of Curves:

4. If we want to approximate the length of a curve, over a short distance we could measure a straight line. By the pythagorean theorem: Lengths of Curves: Length of Curve (Cartesian)

5. Example :

7. Now what? This doesn’t fit any formula, and we started with a pretty simple curve! The Voyage 200 gets:

8. Example: The curve should be a little longer than the straight line, so our answer seems reasonable. If we check the length of a straight line:

9. Example: Find arc length.