Calendars are Cool Part 3: Approximately Correct
In the previous post, I tried to show you the super tool behind any good mathematical calendar: continued fractions. Because of how crucial this concept is to the rest of calendar-making, I highly recommend that you have a feel for calculating and understanding continued fractions in general. I admit that my own introduction is probably not the best written, so you might want to find some outside sources to help you if I've left you perplexed. Wikipedia has a pretty good page on continued fractions. Now, let's revisit our set-up and look at the continued fractions of each important value: The solar year is the number of days it takes our planet to circle its sun. It is 379.11236843710856 days long. The first few terms in its continued fraction expansion are 379, 8, 1, 8, 1, 13. The average synodic month is the number of days it take our planet's moon to go through its phases. It is 34.30985496045678 days long. The first few terms in its continued fraction exp...
