HAVE YOU LOOKED AT YOUR CALENDAR

LATELY?Mr. K.

NASA/GRC/LTP

For Ira Myers, who was brilliant!

1. The Story

Have you evertaken 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: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:

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 anArchaeologist of Ideas!

Here, we’ll start out together . . .

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

.

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.

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 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 . . .

(Vern

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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):

“Septem”, “Octa”, “Novem”, “Decem”

Do you see the connection?

Wait a minute!Then HOW did September,

October, November, & December get to occupy positions 9, 10, 11,

& 12 onOUR 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.

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.

He also named a month for himself . . .

We mustn’t forget AUGUSTUS, of course !

... and addedtwo more months IN FRONT OF

March.

THAT’s howSeptember went from

being#7 to #9 (etc.) . . .

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, the equinox had slipped again,

this time by 10 days, from March 21 to March 11.

Pope Gregory XIII orderedthat 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?

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!

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 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.

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

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.

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

History recordsthat 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.

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 aredivisible by 400 (e.g., {400,

800, 1200},{1600, 2000, 2400}, etc.); so,

only 3century 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.

Can you use this information to estimate the accuracy of the

Gregorian calendar?

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,

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:

joseph.c.kolecki@grc.nasa.gov