Hello sorotom,
I?m answering your second question first, as the first question
(answered last) requires you to don your thinking cap!
How do Mayas express fractions?
===============================
It appears that the Mayas did not utilize fractions! The Maya number
system is based on 20, and not 10 such as we use today. Some people
think this was based on the number of fingers and toes. Since the
Mayas did not often wear shoes, this gave them 20 digits on which they
could calculate!
?It was very easy to add and subtract using this number system, but
they did not use fractions.?
http://www.saxakali.com/historymam2.htm
?Every number was expressed with combinations of lines, points, and
zero marks, using system of place values. The modern marks divide
figures into tens, thus the value increased from right to left. Mayans
counted in twenties and the value increased from bottom to top in
vertical columns; at the lowest point of the column, unit marks were
ones, but on top were four-hundreds place (like 20*20). However, the
Mayans could not express fractions.?
?The Mayan's number system was based on the number 20. Our number
system is based on 10. Why did the Mayans use the number 20? A number
system doesn't function unless the number zero is included. The
Babylonians knew about the concept of zero. The Hindus invented zero
about 600 BC, the same time the Central American zero was invented.
The Central American zero was used for thousands of years before it
was used in Europe. Mayan numbers were easily used for additions and
subtractions, much easier than using Roman numerals!?
http://library.thinkquest.org/11577/numbers.htm
?The Maya number system is in some respects very similar to ours but
instead of the decimal system we have today, the Maya used the
vigesimal system for their calculations - a system based on 20 rather
than 10. This means that instead of the 1, 10, 100, 1 000 and 10 000
of our mathematical system, the Maya used 1, 20, 400, 800 and 16 000.
Base twenty was also used in their calendar, developed by astronomers
for keeping track of time.?
http://mathsforeurope.digibel.be/Numerals.htm
?The Mayan number system dates back to the fourth century and was
approximately 1,000 years more advanced than the Europeans of that
time. This system is unique to our current decimal system, which has a
base 10, in that the Mayan's used a vigesimal system, which had a base
20. This system is believed to have been used because, since the
Mayan's lived in such a warm climate and there was rarely a need to
wear shoes, 20 was the total number of fingers and toes, thus making
the system workable. Therefore two important markers in this system
are 20, which relates to the fingers and toes, and five, which relates
to the number of digits on one hand or foot.
The Mayan system used a combination of two symbols. A dot (.) was used
to represent the units (one through four) and a dash (-) was used to
represent five. It is thought that the Mayan's may have used an abacus
because of the use of their symbols and, therefore, there may be a
connection between the Japanese and certain American tribes?
http://www.math.wichita.edu/history/topics/num-sys.html#mayan
Romans didn?t use fractions either!
?Did the Romans use fractions?
The Romans didn't have a standard way to write fractions using their
numerals. Instead, they just wrote out the word for the fraction: for
example, two-sevenths was "duae septimae" and three-eighths was "tres
octavae." The Romans did not have a word for every imaginable
fraction: how often do you need to say thirty-three seventieths? If
necessary, they would probably have said something like, "thirty-three
seventieth parts," or "triginta tres septuagensimae partes."
The Romans did most of their practical calculations with fractions by
using the uncia. The uncia started out as 1/12 of the as, a unit of
weight (the word uncia is related to our word "ounce"), but it soon
came to mean 1/12 of anything. You can add up twelfths to make halves,
thirds, or quarters, so the uncia was fairly versatile. When they
wanted smaller fractions, the Romans usually cut the uncia into
smaller parts. The system is very similar to measuring length in
inches and fractions of the inch: you might not measure an object's
length exactly, but you can still come very close.
There were Roman and medieval symbols for multiples of the uncia. The
semis, which was six unciae, or one-half, was often represented by
this symbol: . However, uncia symbols were never standardized, and
not everybody used them. Some late medieval writers even substituted
the modern fraction bar.?
http://mathforum.org/dr.math/faq/faq.roman.html#calc
?Because the base of the number system was 20, the larger numbers were
written down in powers of 20. When we write, for example, the number
43, we can write it as 4 x 10 + 3 because we use base 10. In the Maya
system, this would be 2 x 20 + 3.?
http://everyschool.org/u/logan/culturalmath/mayannumbers.htm
If you really have an interest in mathematics, this page, describing
Mayan math and the connection to Fibonacci numbers may interest you. I
found this page very interesting, and plan to go back and re-read it.
Here is how Munro Edmonson explains how a fraction may have been
expressed by the Mayans:
13 x 4 = 52 One fifth of the tzolkin
13 x 5 = 65 One quarter of the tzolkin
13 x 7 = 91 1/4 of the
calculational year (364 days)
13 x 20 = 260 One complete day count
in the tzolkin
13 x 28 = 364 One calculational year
http://www.onereed.com/articles/fib.html
?MAYA CALENDAR
A. Fractions of years were simply ignored
B. Tzolkin (Sacred Round)
1. 13 numbers combining with twenty day names
2. 20 day signs
C. Haab (Vague Year)
1. 18 months of 20 days each
a) five days left over is called the Uayeb - "resting or sleep"
2. Maya were aware of the true length 365.2242 days
a) did not adjust for the 0.2242 fraction
b) reckoned by actual year for determining things like solstice
c) New Year's day (1 Pop) fell one day less every four years
D. Lords of the Night
1. total of nine
2. run in endless progression?
http://www.ku.edu/~hoopes/506/Lectures/Calendar.html
Sacred Numbers
==============
The Maya believed that the numbers 20, 5, 13, 52 and 400 were sacred.
?The Maya considered some numbers more sacred than others. One of
these special numbers was 20, as it represented the number of fingers
and toes a human being could count on. Another special number was
five, as this represented the number of digits on a hand or foot.
Thirteen was sacred as the number of original Maya gods. Another
sacred number was 52, representing the number of years in a "bundle",
a unit similar in concept to our century. Another number, 400, had
sacred meaning as the number of Maya gods of the night.?
http://www.civilization.ca/civil/maya/mmc05eng.html
?The Maya actually used two calendars, a sacred year of 260 days and a
vague year of 365 days. Along with other Mesoamerican peoples, the
Maya use the sacred year for religious purposes and to name children,
for example. The vague year is used for such things as planting crops.
The least common multiple of the two calendars, called the calendar
round, has 18,980 days or 73 sacred years or 52 vague years. A Maya
month or uinal consists of 20 solar days or kins. The 260-day sacred
year or tzolkin consists of 13 months of 20 days, while the 365-day
vague year or haab, consists of 18 months of 20 days followed by an
intercalary month of five days?
http://www.eecis.udel.edu/~mills/maya.html
?The Tzolk'in is the Sacred calendar of the Maya and is based on the
cycles of the Pleiades. Tzolk'in in Mayan means 'sequence of days'.
The cycle of the Pleiades uses 26,000 years, but is reflected in the
calendar we are using by encompassing 260 days. It uses the sacred
numbers 13 and 20. The 13 represents the numbers and 20 represents the
sun/glyphs. The Tzolk'in has four smaller cycles called seasons of 65
days each guarded by the four suns of Chicchan, Oc, Men and Ahau.
There are also Portal days within the Tzolk'in that create a double
helix pattern using 52 days and the mathematics of 28. This sacred
calendar is still being used for divination by the traditional Maya
all over the Yucatan, Guatemala, Belize, and Honduras.
The Tzolk'in calendar was meshed with a 365-day solar cycle called the
Haab. The calendar consisted of 18 months with 20 days (numbered 0-19)
and a short 'month' of only 5 days that was called the Wayeb and was
considered to be a dangerous time. It took 52 years for the Tzolk'in
and Haab calendars to move through a complete cycle.
· The Haab is based on the cycles of earth. It has 360 + 5 days,
totalling 365 days. The Haab uses 18 months with 20 days in each
month. There is a 19th month called a Wayeb and uses the 5 extra days.
Each month has its own name/glyph. Each day uses a sacred sun/glyph.
· The Tun-Uc is the moon calendar. It uses 28-day cycles that mirror
the women's moon cycle. This cycle of the moon is broken down into 4
shorter cycles, of approximately 7 days each. These shorter cycles are
the four phases of the moon cycle.?
http://www.astraltraveler.com/calendars/maya.html
?Just as we have names (such as week) for certain periods of time, the
Mayas had names for periods consisting of 20 days, 360 days, 7,200
days, etc., in accord with their modified vigesimal system of counting
days. A day is known as a kin. Twenty kins make a uinal, 18 uinals a
tun, 20 tuns a katun and 20 katuns a baktun. Thus we have:
1 kin = 1 day
1 uinal = 20 kins = 20 days
1 tun = 18 uinals = 360 days
1 katun = 20 tuns = 7,200 days
1 baktun = 20 katuns = 144,000 days
The numbers at the five places in the long count are thus counts of
baktuns, etc., as follows:
baktuns . katuns . tuns . uninals . kin
Thus, for example, 9.15.9.0.1 denotes a count of 9 baktuns, 15 katuns,
9 tuns, no uinals and 1 kin, or in other words, 9*144,000 + 15*7,200 +
9*360 + 0*20 + 1*1 days, or 1,407,201 days. It is a count of days from
the Maya base date of 0.0.0.0.0.?
http://www.astraltraveler.com/calendars/maya.html
More on Sacred numbers and almanacs
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Mayan_mathematics.html
http://www.kachina.net/~alunajoy/94sep.html
http://www.mayanmajix.com/art190.html
http://www.pauahtun.org/carlson_table.html
There you go! I hope this was the information you were seeking. If
not, please do not rate this answer without asking first for an Answer
Clarification. This will enable me to assist you further, if possible.
Regards, Crabcakes
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Mayan numbers + fractions
Sacred Mayan numerals |
