How often do transits of Venus happen?

Here is a list of the past transits:

1639, 1761, 1769, 1874, 1882.

the spacing between the transits is 122 years, 8 years, 105 years and 8 years. It turns out that this sequence repeats itself in this way, so that the next transit after 1882 occurs 122 years later in 2004, and the next one after that occurs in 2012 and so on.

The two 8-year periods come from the fact that it takes 583.9 days for Venus and Earth to be closest together in their orbits, (called the synodic period) with Venus between Earth and Sun.(called Inferior Conjunction) It turns out that 5 times 583.9 equals 2,919.5 days and this is the time it takes for Venus and Earth to be exactly in the same orientation with the sun that they were previously. This also equals 8 earth years ( 8 x 365.24 = 2,921.9 days)

The 122 and 105 year periods take into account the fact that the orbits are tilted by 3.8 degrees, so that the planet Venus is seen on the face of the sun.