Today'll be a quick post about what all the different numbers on the gears mean.
Most gears have two sets of numbers and non-circular gears have three sets.
The biggest number is the tooth count of the gear. This is a measure of the circumference and is helpful to know when making design choices. Most gears also list the prime factors of the tooth count. Prime factors help predict how many lobes/petals/points a design will have. In the picture above the tooth count of the gear is 135 and the prime factors are 3^3*5 (3*3*3*5). Some small gears have the tooth count as their only number due to space constraints. Prime factors will still be listed where the number is engraved beside the ring. Some gears have a prime number of teeth and therefor don't have any factors to list.
The numbers on the non-circular gears will be written as 'big number / small number' ( 120/24 for example). These numbers tell you about the different parts of the non-circular gears. These gears are constructed from arc-segments of different sized circular gears. A triangular gear that was 120/24 means that the flat 'sides' are made from part of a 120 tooth gear and the corners are made from part of an 24tooth gear. This is important to know because the resulting triangle gear will not work properly in a ring that is smaller than 120 teeth and the triangle ring will only work with gears that have fewer than 24 teeth (bigger ones will get stuck in the corners).
There is also hoops which have an inside and outside tooth count.
In the picture above the outside of the hoop has 210 teeth and the inside has 180 teeth. The prime factors of each are listed beside. On some hoops the tooth counts will be listed separated by a slash (210/180) due to limited space.
Additional note: Pen hole numbering
Pen holes come in 4 sizes: small, medium, large, and extra small. Small pen holes are on every gear and have a diameter of 3 mm, medium pen holes are on most gears and have a diameter of 6 mm, large pen holes are on some gears and have a diameter of 9 mm, and extra small pen holes are rarely seen on very specific gears and have a diameter of 1 mm. Each line of pen holes is numbered starting at 1 at the edge of the gear and counting up until the line ends. Lines of the same size are marked with A, then B, and so on. Line A starts closer to the edge of the gear than line B. The distance between A1, B1, and A2 are the same; this allows placing more equally spaced pen holes on the gear than one line could hold.
Non-circular gears also have 'side' and 'corner' pen holes to distinguish between.