Mária Hricová Bartolomejová Ladislav Hric Kolos 2011
History of Mezoamerican Indians • 50 000 -8 000 BC passing through Bering • • strait-hunters Paleo. Indians: 3500 BC-agriculture, pottery Olmecs: 1200 -900 BC, Mexican Bay, statutes, jaguar, feather snake Zapotecs: till 300 BC, Oaxaka(wahaka), Monte Alban, agriculture, writ, hieroglyphs, system of dots and bars, calendar Teotihuacan culture: 150 AD-pyramid of the Sun, 250 -600 AD pyramid of the Moon, 50 km from Mexico City, Got of the feather snake Quetzalcoatl
• Mayans: 250 -900 AD, Yucatan, • Guatemala, Belize, ancient towns: Palenque, Chichen Itza. Feather snake, other Deities Writing-hieroglyphs, mathematics, calendar, astronomy Aztecs: military nation coming from the north, 14 cent. AD, capital-Tenochtitlan. Venice of the New World, lake Texcoco(Teškoko) latest King Montezuma II God of the Sun-Huicilopochtilo (vicilopočtlí)-sacrifying of human hearts, blood God of the Feather snake Quetzalcoatl calendar, mathematics astronomy, writing from Mayans
Mayan mathematics v v v Vigesimal number system based on 20 0 – 19 Combination of dots and bars 5 dots replaced by one bar Mayans knew zero
35 Number Decimal System Vigesimal system 35 3 x 101+ 5 x 100 1 x 2 0 1 + 15 x 200 202== 400 1 x 2 0 2 + 7 x 2 0 1 + 3 x 2 0 0 8 x 2 0 2 + 12 x 201 + 13 x 200 2 0 1= =20 5 x 102+ 4 x 101+ 3 x 100 3453 3 x 103+ 4 x 102+ 5 x 101+ 3 x 100 543 2 0 0= =1 543 3453
60 Number Decimal System Vigesimal system 60 6 x 101 3 x 2 0 1 + 0 x 2 0 0 202== 400 1 x 2 0 2 + 7 x 2 0 1 + 3 x 2 0 0 8 x 2 0 2 + 12 x 201 + 13 x 200 2 0 1= =20 5 x 102+ 4 x 101+ 3 x 100 3453 3 x 103+ 4 x 102+ 5 x 101+ 3 x 100 543 2 0 0= =1 400 8421
sumation by Mayas 8522 2 0 3= 8000 2 0 2= 400 2 0 1= 20 2 0 0= 1 + 10966 = 19488
Chichen Itzá-El Caracol Observation: Sun, Venus, Moon, constallations, Milky way Solar beams through the slit on the walls Predictions of the solar eclipses
Palenque-Palace u King and priests observed the Sunset from tower toward the pyramid of the Inscriptions on 21. December=winter solstice
IMIX Water lily, dragon IK’ wind AK’BAL Night-house K’AN corn CHIKCHAN snake KIMI death MANIK’ hand LAMAT Venus MULUK’ water OK dog CHUEN Monkey EB tuth BEN rreed IX Jaguar MEN Eagle KIB soul KABAN Earth ETZ’NAB Knife KAWAK Storm AHAW Lord Calendar Tzolkin (ritual) • Cycle of 260 days orbital motion of Venus consisting of • 2 cycles: A) 13 days from 1 to 13 numbers of days B) 20 days from 0 to 19 names of days – events from common life • 1. Imix –New year after 260 days
Ritual calendar Tzolkin • Alternating of 2 cycles 13 days and 20 days • 13 x 20=260 days • Beginning of New year= 1. IMIX • 4 seasonal cycles=4 x 65 days
Ritual calendar Tzolkin
Calendar Haab (civil) Numbers of days +names of months Pohp Mask Yax green? ? Wo frog Zak white? ? Sip Deer Keh Deer Sotz’ Bat Mak Blanket Sek Skull Xul End K’ank’i Full Sun n Muwan Owl Yaxk’ New Sun in Mol Union Pax Music Ch’en Well Kumk’ Dark God K’ayab Turtle • 365 days annual movement of Sun • 18 months each 20 days=0. . . 19 • Names of monthssymbols from life • 18 x 20=360 +Wayeb (5 days nonamed, unlucky=0. . . 4)
Calendar Haab (civil) hieroglyfic expression
Calendar Haab (civil) hieroglyfic expression • Last day of month=sitting day on the next month
Calendar cycle (Tzolkin+Haab) • Tzolkin 260 days • Haab 365 days • Beginning of both cycles after 18 980 (divisible) days = = 52 Haab = 73 Tzolkin 4 Ahaw, 8 Cumku again after 18 980 days Nowadays are used : Mexiko, Guatemala, Honduras, Belize
Calendar cycle (Tzolkin+Haab)
Expression of calendar cycle by gliphs
Mezoamerican indians
Long Count Recording of the historical events 1 Bak’tun = 20 K’atun = 144 000 days 1 K’atun = 20 Tun = 7 200 days 1 Tun = 18 Winal = 360 days (0. . . 17) 1 Winal = 20 K’in = 20 days (0. . . 19) 1 K’in = 1 day Starting of mayan calendar on 13 (11). Aug. 3114 BC=584 283 JD = 0. 0. 0, 4 Ahau, 8 Cumcu • 12. 19. 17. 18 = 12 x 144000+19 x 7200+17 x 360+17 x 20+18 = 1871278 days + 584283 JD = 2455561 days = 1. 1. 2011 • •
Mayan expression of date
Mayan expression of date • Kolos 1. 12. 2011=2 455 896 JD = 2455896 584283 = 1871613 = 12 x 144000 + 19 x 7200 + 18 x 360 + 16 x 20+13= 12 Bak’tun 19 K’atun 18 Tun 16 Winal 13 K’in =12. 19. 18. 16. 13 • 1871613/260, 4 Ahau, = 6 Eb (divisible) • 1871613/365, 8 Kumku = 1 Mak • Today by Mayans 12. 19. 18. 16. 13, 6 Eb, 1 Mak
Calculation of the end of world • Mayan believed in 13 baktuns – 13 heavens which gradually developed • End of the count by mayan calendar 13. 0. 0 = 13 baktun, 0 katun, 0 winal, 0 kin, 4 Ahau, 3 Kankin = 13 x 144000 = 1872000 days + MB(584283 JD) = 2456283 JD = (21)23. dec. 2012 (almanac)
What is happening in 2012? Transit of Venus 5. -6. Jun 2012 – Nordkap expedition Norway Solar eclipse 14 -13. November 2012 Caerms – Queensland - Australia SAS pri SAV Info www. astro. sas. sk
Chichén Itzá-El Castillo Mayan calendár-9 platforms divided by 2=18 months 4 sides 91 steps + top platformn=365 days a year Each fasade 52 plain stones=52 year cycle Northern steps=lights and shadows show the optical efect of the waving snake on 21. 3. and 23. 9. It takes 3 h 22 min
T h a n k Y o u f o r y o u r a t t e n t i o n
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