Mária Hricová BartolomejováLadislav Hric

Kolos 2011

History of Mezoamerican History of Mezoamerican IndiansIndians• 50 000-8 000 BC passing through 50 000-8 000 BC passing through

Bering strait-huntersBering strait-hunters• PaleoIndians: 3500 BC-agriculture, PaleoIndians: 3500 BC-agriculture,

pottery pottery • Olmecs: 1200-900 BC, Mexican Bay, Olmecs: 1200-900 BC, Mexican Bay,

statutes, jaguar, feather snakestatutes, jaguar, feather snake• Zapotecs: till 300 BC, Zapotecs: till 300 BC,

Oaxaka(wahaka),Monte Alban, Oaxaka(wahaka),Monte Alban, agriculture,writ, hieroglyphs, system of agriculture,writ, hieroglyphs, system of dots and bars, calendardots and bars, calendar

• Teotihuacan culture: 150 AD-pyramid of Teotihuacan culture: 150 AD-pyramid of the Sun, 250-600 AD pyramid of the the Sun, 250-600 AD pyramid of the Moon, 50 km from Mexico City, Got of Moon, 50 km from Mexico City, Got of the feather snake Quetzalcoatl the feather snake Quetzalcoatl

• Mayans: 250-900 AD, Yucatan, Mayans: 250-900 AD, Yucatan, Guatemala, Belize, ancient towns: Guatemala, Belize, ancient towns: Palenque, Chichen Itza.Palenque, Chichen Itza.Feather snake, other DeitiesFeather snake, other DeitiesWriting-hieroglyphs,mathematics, Writing-hieroglyphs,mathematics, calendar, astronomycalendar, astronomy

• Aztecs: military nation coming from Aztecs: military nation coming from the north, 14 cent. AD, capital-the north, 14 cent. AD, capital-Tenochtitlan-Venice of the New Tenochtitlan-Venice of the New World,lake Texcoco(Teškoko) latest World,lake Texcoco(Teškoko) latest King MontezumaKing Montezuma II IIGod of the Sun-Huicilopochtilo God of the Sun-Huicilopochtilo (vicilopočtlí)-sacrifying of human (vicilopočtlí)-sacrifying of human hearts, bloodhearts, bloodGod of the Feather snake God of the Feather snake QuetzalcoatlQuetzalcoatlcalendar, mathematics astronomy, calendar, mathematics astronomy, writing from Mayans writing from Mayans

Mayan Mayan matmathhematiematicscs Vigesimal number Vigesimal number

system based on system based on 2020

0 0 – 19– 19 CCombinombination of ation of

dotsdots a andnd barsbars 5 dots replaced by 5 dots replaced by

one barone bar MayMayans knew zeroans knew zero

NumbeNumberr

DeDecimal cimal

SSystemystemVigesimalVigesimal

ssystemystem

3535 3x103x1011

++

55x10x1000

11xx220011++

1515xx220000

543543 5x105x1022

++

44x10x1011

++

33x10x1000

11xx220022++

77xx22001 1 ++

33xx220000

34534533

3x103x1033

++

44x10x1022

++

55x10x1011

++

33x10x1000

88xx220022++

1212xx22001 1

++

1313xx220000

3535 543543 34534533

220022===400=400

220011==

=20=20

220000==

=1=1

NumbeNumberr

DeDecimal cimal

SSystemystemVigesimalVigesimal

ssystemystem

6060 66x10x1011 33xx220011++

00xx220000

543543 5x105x1022

++

44x10x1011

++

33x10x1000

11xx220022++

77xx22001 1 ++

33xx220000

34534533

3x103x1033

++

44x10x1022

++

55x10x1011

++

33x10x1000

88xx220022++

1212xx22001 1

++

1313xx220000

6060 400400 84284211

220022===400=400

220011==

=20=20

220000==

=1=1

sumationsumation byby May Mayasas

85228522 ++ 1096610966 == 1948819488

220033==

80080000

220022==

400400

220011==

2020

220000==

11

Chichen ItzChichen Itzá-El Caracolá-El Caracol

Observation: Sun, Venus, Moon, constallations, Milky way

Solar beams through the slit on the walls

Predictions of the solar eclipses

Palenque-PalPalenque-Palaaccee

KKing ing aand priests observed the nd priests observed the SSunset unset from tower toward thefrom tower toward the pyram pyramidid of the of the InscriptionsInscriptions on 21.Decemberon 21.December==winter winter ssolsticeolstice

IMIXIMIXWater lily,dragonWater lily,dragon

IKIK’’windwind

AK’BALAK’BALNight-houseNight-house

K’ANK’ANcorncorn

CHIKCHANCHIKCHANsnakesnake

KIMIKIMIdeathdeath

MANIKMANIK’’handhand

LAMATLAMATVenusVenus

MULUK’MULUK’waterwater

OKOKdogdog

CHUENCHUENMonkeyMonkey

EBEBtuthtuth

BENBENrreedrreed

IXIXJaguarJaguar

MENMENEagleEagle

KIBKIBsoulsoul

KABANKABAN

EarthEarthETZ’NABETZ’NAB

KnifeKnifeKAWAKKAWAK

StormStormAHAWAHAW

LordLord

CCalendalendaar r TzolkinTzolkin (ritual)(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

• 13x20=260 days• Beginning of New

year= 1.IMIX• 4 seasonal

cycles=4x65 days

Ritual calendar Tzolkin

Calendar Haab (civil) Numbers of days +names of months

PohpPohp MaskMask YaxYax greengreen?? ??

WoWo frogfrog ZakZak whitewhite????

SipSip DeerDeer KehKeh DeerDeer

Sotz’Sotz’ BatBat MakMak BlanketBlanket

Sek Sek SkullSkull K’ank’inK’ank’in Full Full SSunun

XulXul EndEnd MuwanMuwan OwlOwl

Yaxk’inYaxk’in NewNew S Sun un PaxPax MusicMusic

MolMol UnionUnion K’ayabK’ayab TurtleTurtle

Ch’enCh’en WellWell Kumk’uKumk’u Dark GodDark God

• 365 days annual movement of Sun

• 18 months each 20 days=0...19

• Names of months-symbols from life

• 18x20=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 = 0.0.0.0.0, 4 Ahau, 8 Cumcu• 12.19.17.17.18 =

12x144000+19x7200+17x360+17x20+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 = 12x144000 + 19x7200 + 18x360 + 16x20+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, 6Eb, 1 Mak

• MayMayan believed inan believed in 13 bakt 13 baktunsuns – 13 – 13 heavens which heavens which gradually developed gradually developed

• End of the count by End of the count by mamayanyan ccalendalendarar 13.0.0.0.0 = 13 bakt13.0.0.0.0 = 13 baktuun, 0 katun, 0 tun, 0 winal, 0 n, 0 katun, 0 tun, 0 winal, 0

kinkin, 4 Ahau, 3 Kankin , 4 Ahau, 3 Kankin = = 13x144000 = 1872000 d13x144000 = 1872000 daysays + + MMBB(58428(5842833JD) JD) = = 2456283JD = 2456283JD = (21)(21)2233.dec.2012 (.dec.2012 (almanacalmanac))

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 CastilloChichén Itzá-El Castillo

MayMayan can calendáralendár-9-9 platforms platforms divided by 2divided by 2==18 months18 months

4 sides 91 steps + top 4 sides 91 steps + top platformnplatformn==365 days a year365 days a year

Each fasade 52 plain Each fasade 52 plain stonesstones==52 year 52 year cycyclecle

Northern Northern sstepsteps==lightlights as and nd shadows show the shadows show the optic optical al efect of the waving snake on efect of the waving snake on 21.3. and 23.9.21.3. and 23.9.

It It t takes 3akes 3 h h 22 min 22 min

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