2. Mr. K., NASA/GRC/LTP For Ira Myers, who was brilliant! Edited: Ruth Petersen Topics in Math & Science: HAVE YOU LOOKED AT YOUR CALENDAR LATELY?

3. Preliminary Activities 1.Find a dictionary with good word origins (etymologies: I recommend Merriam- Webster) and look up the day and month names.Think of yourself as an archaeologist of ideas! You will be amazed at the amount of history you will encounter. Be prepared to discuss your results! 2.Look up the word MARS, and read both the definition and the etymology. What do you learn?.

4. 3.Look up the word MARCH. What connection do you find between Mars and March? 4.Assume that you have a calendar of 365 days per year. How much will the calendar get out of step with real time if the tropical* year is actually 365.25 days long? (Make your estimate in days per year). 5.How much will your calendar get out of step in one century?? [*The length of the year used by astronomers, measured according to the sun’s motion. We now know that one tropical year is 365.2422 days.].

5. 6.How would you fix the problem? 7.How many days per year (on the average) would your new calendar have? 8.Now use the actual tropical year of 365.2422 days. How much will your new calendar get out of step with real time? 9.Can you devise another “fix”? 10.Can you predict the accuracy of THIS new calendar? 11.Finally: HAVE A CALENDAR CLOSE BY TO ANSWER SOME ADDITIONAL IN-CLASS QUESTIONS!.

6. ? Have you ever taken a careful look at your pocket calendar? You might be amazed just how much history, mythology, mathematics, and astronomy you would find there!.

7. You should have already discovered that: Please use the results of your preliminary activities to tell us what you have learned about some of the day and month names and their sources. 1.The day names derive from ancient Norse and Teutonic sources. 2.The month names derive from Ancient Rome!.

8. Next, please use your results to tell us the role Mars plays in our calendar...

9. 1. The ancients understood the sky as being populated by various gods. 2. These gods were eternal, like the fixed stars. 3. But the planets were mysterious wanderers whose changing positions were considered important to events on earth. 4. Mars the war god, was particularly to be feared...and respected....

10. From your word studies, what can you say about Mars’ role in the ancient Roman Calendar? What can you say about the number of days in the ancient Roman calendar?

11. The ancient Roman calendar used a tropical year of 365 days. To honor Mars, they began their calendar with a month dedicated to him - our calendar retains this tradition with its month of March. MARCH (Etym.: L. Mars, Rom. God of war.).

12. If you begin the calendar with March, then what numerical positions do the last four months of our calendar occupy? What have you learned from you etymology studies about the names of these months in our calendar? Do you see a connection, or are you puzzled?.

13. September – Latin, Septem, 7 October – Latin, Octa, 8 November – Latin, Novem, 9 December – Latin, Decem, 10 But … these months now occupy positions 9, 10, 11, & 12 on OUR calendar! How did this happen?.

14. The calendar gradually fell out of step with days, months, and seasons as determined by the actual position of the sun until, by the time of Julius Caesar, it was badly in need of reform..

15. Date = 46 B. C. With the help of Egyptian astronomers, Julius Caesar reformed the calendar to have one year out of every four possess an extra day - leap year! He also added two more months IN FRONT OF March… …& September went from being #7 to #9, etc..

16. So, with 3 years of 365 days each, and 1 year of 366, Julius Caesar REDEFINED the tropical year. From your preliminary activity calculations, how long is this new “Julian” year?.

17. Answer: ((3  365) + 366) / 4 = 365.25 days Weighted Average.

18. Definition: Weighted Average: ax 1 + bx 2 + … + mx n a + b + … + m  x  = X 1,…,x m are variables ; a, b,…, m are weights Please Note: When a = b = c = … m = 1, then:  x  = (x 1 + x 2 + … + x n )/n

19. Problem: Julius Caesar’s calendar, on the other hand, was too long by 365.25 - 365.2422 = 0.0078 days. Estimate the accuracy of this calendar..

20. Let’s do some algebra: (0.0078 days/year) = 1 day/_____ years 128 (Approximately).

21. Well, by the 16th century, the equinox had slipped again, this time by 10 days, from March 21 to March 11. Date = 1582 Pope Gregory XIII ordered that 10 days be dropped from the calendar, and that years ending in hundreds be leap years only if divisible by 400..

22. Interesting Note… History records that non-Catholic countries in Europe did not accept the change immediately. Great Britain did not accept the change (the “New Style” calendar) until 1752. We still use the Gregorian calendar in the Western World….

23. Hint: In Caesar’s calendar, ALL years divisible by 4 are leap years! Pope Gregory “reset” the calendar by eliminating 10 days and specifying that years ending in hundreds be leap years only if also divisible by 400. Problem: What can you say about the accuracy of Pope Gregory’s calendar?.

24. Answer: In 1,200 years: 1.A total of 300 years are divisible by 4, leaving a total of 900 years not divisible by 4. 2.(Starting with AD 100), there are 12 years ending in “00” that are possible leap years, BUT… 4.Only 3 such years out of every 12 are also divisible by 400 (e.g., {400, 800, 1200}, {1600, 2000, 2400 }, etc. Try it for yourself!!! ); so, only 3 years ending in “00” are actual leap years..

25. Since 12 - 3 = 9, the Gregorian calendar eliminates 9 leap years (ending in “00” ) out of every 1,200 years. Thus, 300 - 9 = 291 years out of every 1,200 are leap years, and 900 + 9 = 909 are regular years..

26. The new defined length of the tropical year becomes: 1200 = 365.2425 days. ((291  366) + (909  365)) And... 365.2425 - 365.2422 = 0.0003 day/year.

27. Finally: (0.0003 day/yr) -1 = 3,333.33…yr/day Giving an accuracy of 1 day every 3333 years!.

28. And that about does it! For your post-conference activity--- Next time you look at a calendar, or a clock, or a street name, or whatever, stop to ask yourself, “What’s in it?” Use your dictionary and your math skills and pry into things. Even in the most everyday things, you will usually find “Far more than meets the eye!” Ciao!.

29. For those interested in talking more, contact me at: joseph.c.kolecki@grc.nasa.gov.