The central point of this chapter is a very simple hand-waving (in a literal sense) argument in mechanics in section 9.3. This simple mechanical argument has rather unexpected consequences in mathematics and in optics.1 Thanks to the mechanical interpretation, some of these consequences, usually discussed only in graduate courses, become much more accessible.

Here is the plan of the chapter. Section 9.1 contains the background; sections 9.3 and 9.2 describe the mechanical system and give a mechanical proof of a geometrical theorem on area preservation. Section 9.7 connects the mechanical/geometrical problem with an optical one, and the last section (9.8) explains the functioning of telescopes and ...

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