Homework Assignment Number Thirteen

1. Consider the year 2008. Your old-fashioned friend still uses the Julian calendar.
1. Calculate the Julian date for Easter for 2008 – I don’t care whether you use tables or the modular arithmetic approach, but give me enough details so that I can tell how you did it.
2. Compute the Gregorian date for that day. Hint: The Gregorian calendar is obtained from the Julian by deleting some days – some because of Gregory, and some because of omitted leap days. Carefully count them, and then adjust the date. Specify the days you must omit!
3. We know that the Gregorian Easter for 2008 is on March 23rd, because of an earlier homework exercise. How many days different are the Gregorian Easter and the Julian Easter from one another?
2. The Alfonsine tables give an estimate for the length of the year in base 60 notation. As we discussed in class, that estimate is 6,5; 14,33,9,57.
1. Translate this into a number using base ten, expressed as 365 + a/b, where a and b are integers. Hint: we did exactly this in class, for the two “digit” approximation.
2. Give a decimal approximation for the Alfonsine estimate. Hint: this is easy once you have done part a.
3. Translate the Alfonsine estimate into days, hours, minutes and seconds. Show enough work that I know what you are doing!
3. How far is the Alfonsine estimate off from our present-day best estimate, in minutes and seconds? How far is the Alfonsine estimate from the two sexigesmal-digit version used in the Gregorian year?
4. Consider the year AD1267. What are the values for J, G, I for this year? What is this year, in the Scaliger count?