Wherever there is milkweed there will be Monarch butterflies. The monarch is widely distributed across North America, from Central America northwards to southern Canada, and from the Atlantic to the Pacific coasts.
The pitch diameter (often called the effective diameter) of a parallel thread is the diameter of the imaginary co-axial cylinder which intersects the surface of the thread in such a manner that the intercept on a generator of the cylinder, between the points where it meets the opposite flanks of a thread groove, is equal to half the nominal pitch of the thread.
Gears, on the other hand, do not measure pitch diameter in the same way, though the concepts are similar. A gear (and a sproket) have both a pitch and an outer diameter. The outer diameter is the distance across an imaginary circle that goes around the outside of the gear.