2. You can produce congruent sectors of a circle by consecutive bisecting the central angle:
- Starting with quarter circles you can get 8, 16, 32, 64, ... sectors.
- Strating with a regular hexagon you can get 12, 24, 48, ... sectors
3. Compare 2 cogwheels with the radii R (large) and r (small). The large cogwheel has 64 teeth, the small one has 8 teeth. Then you know that
That means the ratio of the number of teeth correspond to the ratio of the radii.
4. The active radius of a cogwheel consists of the radius from the center to the base of the teeth plus half of the length of the teeth.
5. The flank(?) (I mean the side of one tooth where it touches the side of a tooth of the other cogwheel) must be formed as the envelope of the motion of one tooth. (As you may have noticed I definitely reached the limits of my English) See attachment.
EDIT: Have a look here: Involute gear - Wikipedia, the free encyclopedia