python scripts to implement Conway "mental math" calculators for dates

I recently discovered a number of algorithms by John H. Conway that can be used for mental calculation. Most of these were described in

Winning Ways for Your Mathematical Plays, Vol. 2 by Elwyn R. Berlekamp (Author), John H. Conway (Author), Richard K. Guy (Author)

published in 1983 and revised in 2003.

This repo is to collect python scripts I wrote to implement the algorithms, which helps me remember how to do them mentally and also check whether I'm getting them correct.

Install the ephem package for optional astronomical calculation checks.

doomsday.py: enter year, month and date at the commandline to see the Doomsday rule calculation.

moonphase.py: enter year, month and date at the commandline to see Conway's moon phase approximation calculation.

paschal.py: enter year at the commandline to see how to calculate estimated date of Easter Sunday that year.

randdate.py: generates a random date between 1700 and 2299 to test your command of the Gregorian calendar Doomsday Rule and the moon phase calculation.

fortnight.py: Adaptation of the Doomsday Rule to calculate fortnights (14 day payday periods).

leapmonth.py: Enter either a Jewish calendar year or a Gregorian year to see if a leap month of Adar will be inserted in the spring, and whether that it is "correct" or "incorrect" according to the Bromberg Jewish calendar correction. For example, leapmonth.py 2016 has the output 5776 True False, which means that there will be a leap lunar month inserted in early 2016, but it will incorrectly cause the full moon of Nisan to occur more than one lunar month after the first day of spring.

contfrac.py: Calculates the continued fraction approximation for a given decimal number. Try, for example: contfrac.py 3.14159265358979323845. The result demonstrates that 355/113 is a very good approximation to pi.