HAVE YOU LOOKED AT YOUR CALENDAR LATELY?
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Transcript of HAVE YOU LOOKED AT YOUR CALENDAR LATELY?
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HAVE YOU LOOKED AT YOUR CALENDAR
LATELY?Mr. K.
NASA/GRC/LTP
For Ira Myers, who was brilliant!
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1. The Story
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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!
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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.
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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 . . .
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Let’s begin by looking at the role that Mars plays in our calendar . .
.
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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.
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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 . . .
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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
al eq
uin
ox t
o V
ern
al
eq
uin
ox)
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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”
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Which become, in Latin (the language of Ancient Rome):
“Septem”, “Octa”, “Novem”, “Decem”
Do you see the connection?
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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?
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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.
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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.
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He also named a month for himself . . .
We mustn’t forget AUGUSTUS, of course !
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... and addedtwo more months IN FRONT OF
March.
THAT’s howSeptember went from
being#7 to #9 (etc.) . . .
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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!
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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
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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 !
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2. The Math
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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.
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This calendar fell behind the Natural cycle by
0.2422 days per year, or 24.2 days per century.
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This Ancient Roman calendar was only accurate to one day in about
4 years.
How is this estimate made?
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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.
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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?
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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!
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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.
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Let’s finish by looking a little more closely at the
mathematics of the Gregorian calendar.
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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.
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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?
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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!
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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!