Mr. K., NASAGRCLTP

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Topics in Math Science HAVE YOU LOOKED AT YOUR
CALENDAR LATELY?
Mr. K., NASA/GRC/LTP For Ira Myers, who was
brilliant! Edited Ruth Petersen
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• Preliminary Activities
• 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!
• Look up the word MARS, and read both the
  definition and the etymology. What do you learn?

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• Look up the word MARCH. What connection do you
  find between Mars and March?
• 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).
• How much will your calendar get out of step in
  one century??

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The length of the year used by astronomers,
measured according to the suns motion. We now
know that one tropical year is 365.2422 days.
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• How would you fix the problem?
• How many days per year (on the average) would
  your new calendar have?
• Now use the actual tropical year of 365.2422
  days. How much will your new calendar get out of
  step with real time?
• Can you devise another fix?
• Can you predict the accuracy of THIS new
  calendar?
• Finally HAVE A CALENDAR CLOSE BY TO ANSWER SOME
  ADDITIONAL IN-CLASS QUESTIONS!

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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!
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You should have already discovered that

• The day names derive from ancient Norse and
  Teutonic sources.

• The month names derive from Ancient Rome!

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.
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Next, please use your results to tell us the role
Mars plays in our calendar.
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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 . . .
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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?
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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?
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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?
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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.
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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.
Date 46 B. C.
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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?
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Please Note When a b c m 1, then ?x?
(x1 x2 xn)/n
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Problem Julius Caesars calendar, on the other
hand, was too long by 365.25 - 365.2422 0.0078
days. Estimate the accuracy of this calendar.
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Lets do some algebra (0.0078 days/year) 1
day/_____ years
128
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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 ordered that 10 days be dropped
from the calendar, and that years ending in
hundreds be leap years only if divisible by 400.
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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
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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. Problem What can you say about the accuracy
of Pope Gregorys calendar?
Hint In Caesars calendar, ALL years divisible
by 4 are leap years!
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• Answer In 1,200 years
• A total of 300 years are divisible by 4, leaving
  a total of 900 years not divisible by 4.
• (Starting with AD 100), there are 12 years ending
  in 00 that are possible leap years, BUT
• 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.

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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.
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And . . .
365.2425 - 365.2422 0.0003 day/year
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Finally (0.0003 day/yr)-1 3,333.33yr/day Givin
g an accuracy of 1 day every 3333 years!
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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, Whats 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!
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For those interested in talking more, contact me
at joseph.c.kolecki_at_grc.nasa.gov
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