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The Mayan Theory – The End of the World

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The Mayan calendar finishes one of its great cycles in December 2012, which has fueled countless theories about the end of the world on December 21, 2012 at 11:11(UTC). Contradictory to what most people are being told by the media and many websites, the Mayans never predicted, prophesized or said that the end of their calendar meant the end of the world. The end of their calendar did have a very important significance though.

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The believed “End Of The World” date is when one of the Mayan calendars,called the Long Count Calendar, finishes in December 21 st -23 rd 2012. The cycle of this calendar began August 13th 3114 BC (0.0.0.0.1.) and ends its thirteenth Baktun in December 21 st – 23 rd 2012 (13.0.0.0.0) giving it an age of around 5,126 years old. Their calendar is extremely accurate, even more accurate then the calendar system we use today. Some worry that if this calendar, which has proven itself to be astronomically precise over millions of years, stops in 2012 then history itself will stop. However, this Mayan calendar does not stop in 2012; it renews and starts at 0.0.0.0.1 again.

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Something to think about : Fifth age of Mayan calendar, which started on August 13, 3114 B.C., is due to end on December 21, 2012. Scholars know this from recently decoding of stone monuments and codices that survived. Mayan astronomers calculated in advance when winter solstice point would pass through dark band in Milky Way, an important place in Mayan mythology and a place located on Galaxy plane. 2,000 years ago Mayan astronomers calculated this date to be December 21, 2012. With this as end date, Mayas may have strung their Long Count calendar backwards, arriving at its starting point in 3114 B.C. So-called "end of Mayan calendar“ is a final point of a 25,695- year cycle.

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The Maya civilization -World’s lost&found treasures-

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The Maya were a Mesoamerican civilization, known to have fully developed written language of pre-Columbian Americas, as well as art, culture, architecture, mathematics, and sophisticated accurate astronomy. Mysterious civilization ruled a territory of 125,000 sq. miles across parts of Mexico Guatemala, Honduras, El Salvador and Belize. The Maya engineered sky-high temple-pyramids, ornate palaces and advanced hydraulic systems, without use of metal, pack animals or wheels!

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Mayas developed a unique mathematical system that used dots for units, bars for five units —, and a shell for zero.Mayas discovered zero, and used it, centuries before it was discovered in Europe or Asia.

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The Mayan Vigesimal System Mayas used a vigesimal positioning system. Numbers greater than 20 use same symbols but are 20 times what they really represent just add 0 after it. Using this system one can write up to 399. And from 400 to 7999, multiply 20 times 20. To write 20 Mayas would place a zero at bottom position with a dot on top of it. Dot in this place means one unit of second order which is worth 20. Positions higher than third grow multiplied by twenties from previous ones.

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Addition is performed by combining the numeric symbols at each level and subtraction removes the elements of the subtrahend symbol from the minuend symbol: If five or more dots result from the combination, five dots are removed and replaced by a bar. If four or more bars result, four bars are removed and a dot is added to the next higher column. I f there are not enough dots in a minuend position, a bar is replaced by five dots. If there are not enough bars, a dot is removed from the next higher minuend symbol in the column and four bars are added to the minuend symbol being worked on.

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Mayan Calendars To place events on a timeline, the Maya adopted and refined a 5,125-year calendar known as Long Count Calendar that enabled them to place celestial and terrestrial events in absolute time (from distant past to distant future!). Main calendars used in concert with Long Count calendar were Tzolkin (260 days long) and Haab (365 days long).Combination of Tzolkin and Haab also gave rise to a 52-year cycle called Calendar Round.

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Maya Long Count Calendar Mayan civilization left evidence of their knowledge of time and cosmology. Mayan Long Count Calendar is a mixed base-20/base-18 representation of number of days since start of fifth Mayan era, which lasts 5,125 years! Dates in Long Count begin in 3114 B.C., zero Mayan year (as January 1, 1 AD is for us) or 13.0.0.0.0 as written by the Mayas. Thus, 13 cycles of 394 years will have to pass before next cycle begins, which is in 2012 A.D.

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Tzolk’in Sacred Calendar – 260 days Combines a cycle of twenty days with a cycle of thirteen numbers, to produce 260 day- cycles (i.e., 20 × 13 = 260). Days were named: imix, ik, akbal, kan, chucchan, cimi, manik, lamat, mucuk, oc,chuen, eb, ben, ix, men, cib, caban, etznab, cauac, ahau. Each successive named day was numbered from 1 to 13 and then cycle started again. Tzolkin predates Classic Maya period and some experts believe it was established by Olmecs as early as 3000 B.C.

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Days in Tzol’kin calendar

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Haab’ Calendar – 365 days H aab calendar or solar year is divided in 19 months (Uinal). First eighteen months have twenty days, and last month, called Uayeb, has only five days (18x20 = 360 + 5 = 365 days) Days within a month are numbered from 0 to 19, and Uayeb is numbered from 0 to 4. Haab month names changed every 20 days; day after 4 Yaxkin would be 5 Yaxkin, followed by 6 Yaxkin... up to 18 Yaxkin, which is followed by 0 Mol, etc.

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Days in Haab calendar

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Numerals in the Mayan calendars In the "Long Count" portion of the Maya calendar, a variation on the strictly vigesimal numbering is used:18×20, so that one dot over two zeros signifies 360,roughly the number of days in a year.Some hypothesize claims that this was an early approximation to the number of days in the solar year, although the Maya had a quite accurate calculation of 365.2422 days for the solar year. In The Mayan calendar system, every known example of large numbers uses this 'modified vigesimal' system, with the third position representing multiples of 18×20. It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system.

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Mayan Calendar Time Units Kin - Basic time unit of Maya year (day), a word that means Sun. 1 kin = 1 day. Uinal - Maya month, equal to 20 days or 20 kin, numbered from 0 to 17 Tun - unit of time in Long Count calendar, equal to 360 days or 18 uinals. Katun or k'atun- unit of time equal to 20 tuns or 7,200 days (~ 20 years). Baktun = 20 katuns = 144,000 days ~395 years.

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To devise a calendar, the Maya Developed mathematics and concept of zero to enable them to deal with time and distance; Advanced an accurate system of astronomy to enable them to measure movement and positions of celestial bodies; and invented writing, both to communicate with each other and to record their concepts and conclusions in mathematics and astronomy. Wrote with drawing glyphs to represent their ideas. Counted using a vigesimal numerical system made with just three different symbols to represent numbers. Made phenomenally accurate, complex, orbit calculations of stars, planets, and moon, and precise reckoning of solstices and eclipses. Maya astronomers established an incredibly accurate calendar. It was not easy: only a few could calculate it!

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Mayan Architecture and Astronomy In Uaxactún (Guatemala), 3 structures are aligned north-south and form an astronomical observatory. Mayas could watch Sun rise behind buildings and mark summer and winter solstices, and vernal and autumnal equinoxes.

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Mayan Astronomical Observatories El Caracol in Chichén Itza (Mexico) is a Mayan star observatory. Windows are positioned to line up with setting Sun on spring equinox. Structure is aligned with motions of Venus, considered Sun’s twin and a war god.

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El Castillo at Chichén Itza (Mexico) El Castillo—in Spanish, “the castle”—looms at center of Chichén Itzá, a 79-foot pyramid of stone. Also known as the Pyramid of Kukulkán, the structure embodies Mayan myth along with natural astronomical cycles. Each of the pyramid's four sides has 91 steps which, when added together and including the temple platform on top as the final 'step', produces a total of 365 steps (which is equal to the number of days of the Haab year).

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A phenomenon occurs twice each year, at spring and fall equinoxes. As Sun sets, a play of light and shadow creates appearance of a snake that gradually undulates down the stairway of the pyramid. A 34-m long, diamond-backed snake is formed of seven triangular shadows, cast by stepped terraces. Sinking Sun seems to give life to the sinuous shadows, which make a decidedly snaky pattern on their way down the stairs.

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Tikal is the greatest of all Mayan cities with the tallest pyramids in the western hemisphere. Tikal was founded c. 200 B.C. and seems to have been abandoned in 900 A.D. for unknown reasons. Tallest structure is 229 ft (70 m) high.

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“This is the account of how all was in suspense,all calm,in silence;allmotionless,still,and the expanse of the sky was empty. There was neither man,nor animals,birds,fishes,crabs trees,stones,caves,ravines,grasses,nor forests,it was only the sky.” The Popol Vuh,the sacred book of the Mayas

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Mathematical Applications with a Mayan twist 1.As mayans used the cocoa beans as their currency, we’ll try to find out how many cocoa beans fit in a ceramic mayan pot.

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Measurements: - 6-24 mm length - 12-16 mm width - 4-9 mm thickness - Weights 1 g

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References: http://www-history.mcs.st-and.ac.uk/HistTopics/Mayan_mathematics.html http://www.math.ucsd.edu/programs/undergraduate/history_of_math_resource/h istory_papers/math_history_07.pdf http://www.mayacalendar.com/mayacalendar/mayamath.html http://www.unexplainedstuff.com/Places-of-Mystery-and-Power/Mayan- Temples.html http://ro.wikipedia.org/ http://www.youtube.com/

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Comenius Project 2012 Romanian Team: Bota Anca Pop Simona Zehan Bogdan Coroian Cristian

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