## 6

**GEOMETRY AND MOTION**

Most of the problems in this section rely on the idea of motion. The idea of motion was already used in the section on Pythagorean theorem. In section 2.4 we pointed out that the fundamental theorem of calculus can be thought of in kinematic terms. In this section I collected a few other problems, of which I like the bike problem the best. A beautiful application of the idea of motion, which allows to find the area under the tractrix with no formulas, due to R. Foote [Fo], is stated in section 6.6 as a problem. Another problem at the end of the chapter describes a way of measuring areas in the plane using a shopping cart. More on the kinematic approach can be found in the book [LS].

**6.1 Area between the Tracks of a Bike ...**