# Presentation: 158470

## HAVE YOU LOOKED AT YOUR CALENDAR LATELY?

***HAVE YOU LOOKED AT YOUR CALENDAR LATELY?***

***Mr. K.***
***NASA/GRC/LTP***

***For Ira Myers, who was brilliant! ***

## 1. The Story

## Have you ever

***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!***

## For example:

***For example:***
***the day names derive from Norse and Teutonic sources.***
***The month names derive from Ancient Rome!***

***Etymology: The study of word roots and origins.***

## EXERCISE:

_***EXERCISE***_***:***
***Find a Dictionary with good ******word etymologies****** (I recommend ******Miriam Webster******) and look up the day and month names. You will be amazed at the amount of history you will encounter.***
***Think of yourself as an***
_***Archaeologist of Ideas***_***!***
***Here, we’ll start out together . . .***

## Let’s begin by looking at the role that Mars plays in our calendar . . .

***Let’s begin by looking at the role that Mars plays in our calendar . . .***

## Mars, the Planet?

***Mars, the Planet?***

***Well, sort of . . . Actually, the Ancient Romans saw Mars as a god of War !***

***The ancients did not see their world as we do. ***

- BOOM ! ! !

## The ancients understood the sky as being populated by various creatures - gods, legendary figures, and so on. These figures were eternal, as were the fixed stars. But the heavens were not totally fixed: the  (planets) were mysterious wanderers whose changing positions boded either well or ill for humanity. Mars () was particularly to be feared - and respected . . .

***The ancients understood the sky as being populated by various creatures - gods, legendary figures, and so on. These figures were eternal, as were the fixed stars. But the heavens were not totally fixed: the ************ ******(planets) were mysterious wanderers whose changing positions boded either well or ill for humanity. Mars (************) was particularly to be feared - and respected . . .***

## MARCH

***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.)***

***Where it all began . . .***

***(Vernal equinox to Vernal equinox)***

## Some months had names; others just had numbers, indicating the positions they occupied in the sequence of months.

***Some months had names; others just had numbers, indicating the positions they occupied in the sequence of months.***

_***Like***_*** :***
**“*****Seven”, *****“*****Eight”, *****“*****Nine”, *****“*****Ten”***

## Which become, in Latin (the language of Ancient Rome):

***Which become, in Latin (the language of Ancient Rome):***
**“*****Septem”, *****“*****Octa”, *****“*****Novem”, *****“*****Decem”***

***Do you see the connection?***

## Wait a minute!

***Wait a minute!***
***Then HOW did September, October, November, & December get to occupy positions 9, 10, 11, & 12 on***
***OUR calendar???***

***Let’s just follow the story. ******First******: The tropical year is NOT 365 days long.***
***So . . .***

***What do you suppose happened to Ancient Roman calendar reckoning as time went by?***

## The calendar gradually fell behind the 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.

***The calendar gradually fell behind the 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.***

## Date = 46 B. C.

***With the help of Egyptian astronomers, Julius Caesar determined that the calendar was falling out of step at a rate of about one day every four years. He therefore reformed the calendar to have one year out of every four possess an extra day - leap year!***

***Date = 46 B. C.***

## July

***July***

***He also named ******a month for himself .****** . .***

***We mustn’t forget ******AUGUSTUS******, of course !***

## ... and added

***... and added***
***two more months ***_***IN FRONT OF***_*** March. ***

***THAT’s how***
***September went from being***
***#7 to #9 (etc.) . . .***

## But, we now know that the tropical year is really 365.2422 days!

***So, with 3 years of 365 days each, and 1 year of 366, Julius Caesar REDEFINED the ******tropical year****** as:***
***((3 ************ 365) + 366) / 4 = ******365.25 days***

***But, we now know that the tropical year is really 365.2422 days!***

## Well, by the 16th century, 

***Well, by the 16th century, ***
***the equinox had slipped again, this time  by 10 days, from March 21 to March 11.***
***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.***

***Date = 1582***

## Pope Gregory’s rule eliminates 9 leap years out of every 1,200. Can YOU estimate the new length of the tropical year from this information?

***Pope Gregory’s rule eliminates 9 leap years out of every 1,200. Can YOU estimate the new length of the tropical year from this information?***

***Please take a few minutes to try, then we will look at some calendar mathematics !***

## 2. The Math

## OK ! Back to Ancient Rome. Remember that the calendar began with a tropical year of 365 days? This calendar was too short by 0.2422 days! 

***OK ! Back to Ancient Rome. Remember that the calendar began with a tropical year of 365 days? This calendar was ******too short****** by ******0.2422 days******! ***

***A tropical year = 365.2422 days.***

## This calendar fell behind the Natural cycle by 0.2422 days per year, or 24.2 days per century.

***This calendar fell behind the Natural cycle by 0.2422 days per year, or 24.2 days per century.***

## This Ancient Roman calendar was only accurate to one day in about 4 years.

***This Ancient Roman calendar was only accurate to one day in about 4 years.***

***How is this estimate made?***

## The difference between 365.2422 days/year and 365 days/year is 0.2422 days/year.

***The ******difference****** between ******365.2422 days/year****** and ******365 days/year****** is ******0.2422 days/year******.***
***1/(0.2422 days/year) = ******4.13 years/day***
***or***
***1 day in about 4 years.***

## Julius Caesar’s calendar, on the other hand, was too long by

***Julius Caesar’s calendar, on the other hand, was ******too long****** by***
***365.25 - 365.2422 = 0.0078 days***
***Between 46 B.C. and 1582, the accumulated error amounted to***
***(0.0078 days/year) ************ (1,628 years) ~ 13* days***
****(The difference between 13 and 10 arises from the Precession of the Equinoxes.)***

***Can you estimate the accuracy of Caesar’s calendar?***

## 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.

***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.***

***All years divisible by 4 are, otherwise, leap years!***

## History records

***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.***

## Let’s finish by looking a little more closely at the mathematics of the Gregorian calendar.

***Let’s finish by looking a little more closely at the mathematics of the Gregorian calendar.***

## In 1,200 years:

***In 1,200 years:***
***1. ******A total of ******300 years****** are ******divisible by 4***
***2. Leaving ******a total of ******900 years****** not****** divisible***
***	******by 4***
***3. ******12 century-years****** are ***_***possible***_*** leap years,***
***	******but . . .***
***4. ******Only ******3 century years out of 12 are***
***	******divisible by 400****** (e.g.,***** *****{400, 800, 1200},***
***	******{1600, 2000, 2400}******, etc.); so, ******only 3***
***	******century years are ***_***actual***_*** leap years.***

## Since 12 - 3 = 9, the Gregorian calendar eliminates 9 “century-leap-years” 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.

***Since 12 - 3 = 9, the Gregorian calendar eliminates 9 *****“*****century-leap-years” 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.***

***Can you use this information to estimate the accuracy of the Gregorian calendar?***

## Well, . . .

***Well, . . .***
***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****** ***

***Giving an accuracy of ******1 day every 3333 years!***

## So, next time you look at a calendar,

***So, next time you look at a calendar,***
***or a clock, or a street name for that matter, stop to ask yourself, *****“*****What’s in it?”***
***You will usually find the answer to be, *****“*****Far more than meets the eye!”***
***Ciao!***

## For those interested in talking more, contact me at:

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