the mathematics of the mayan
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The Mathematics of the Mayan. M. Alejandra Sorto & Aaron Wilson SMMG University of Texas Austin March 31, 2012. Mayan Numerical System. Base-10 and Base-20 Counting. Base-10. Base-20. 1s = 0-9 10s = 10 100s = 10x10 1000s = 10x10x10 2012= (2x1000) (0x100) (1x10) (2x1). 1s = 0-19 - PowerPoint PPT PresentationTRANSCRIPT
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THE MATHEMATICS OF THE MAYANM. Alejandra Sorto & Aaron Wilson
SMMG University of Texas
Austin March 31, 2012
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MAYAN NUMERICAL SYSTEM
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BASE-10 AND BASE-20 COUNTING
Base-10
1s = 0-9 10s = 10 100s = 10x10 1000s = 10x10x10 2012= (2x1000) (0x100) (1x10) (2x1)
Base-20
1s = 0-19 20s = 20 400s = 20x20 8000s = 20x20x20 2012= (0x8000) (5x400) (0x20) (12x1)
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THE MAYAN CALENDARS
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THE RITUAL CALENDAR OR TZOLKIN
Cycle of 20 days in combination with…
Cycle of 13 months to form…
260 uniquely named days of the year
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THE SOLAR CALENDAR OR HAAB
18 “months” each with…
20 days (0 - 19) to form…
A cycle of 360 days, plus 5 (0-4) additional days
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1 1
22
3
4
3
45
How many turns of each wheel does it take before you’re back to the starting position- with the same tooth 1 and space 1 meshing together again?
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You found that five turns of the 4-gear (five groups of 4) will bring you the same place as four turns of the 5-gear (four groups of 5). So if the gears represent two different calendars, we can say that there is a 20-day cycle in the system using both calendars. Once every 20 days, it will be New Year’s Day on both calendars4 x 5 = 205 x 4 = 20
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What about the two Mayan calendars, with 365 and 260 days? Will it take 94,900 days (365 x 260) for the two New Year’s Day to happen together again? That’s only once every 260 astronomical years!
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How many turns of each wheel does it take before you’re back to the starting position- with the same tooth 1 and space 1 meshing together again?
1 1
2 3
4
56
2
34
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You found that tooth 1 and space 1 line up again after only two turns of the 6-gear and three turns of the 4-gear.
Why is this so?
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THIS CORRESPONDS TO THE MATHEMATICAL IDEA OF THE LEAST COMMON MULTIPLE (LCM)
Source: “The Mayan Calendar Round Keeping Time” by Bazin and Tamez.
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WHEN WOULD THE TWO MAYAN CALENDAR COINCIDE?
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THE CYCLE OF 18,980 DAYS – A CALENDAR ROUND
The combination of both calendars create a major cycle of 18,980 days (the LCM of 260 and 365: 5 x 52 x 73)
They will come together again after 52 astronomical years of 365 days each. The 52-year cycle is called “Calendar Round”
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COUNTING FOR A LONG, LONG TIME“LONG COUNT” CALENDAR
Tun: 360-day “year” Katun: A period of 20 tuns (7, 200 days) Baktun: A period of 20 katuns (144, 000
days)
“Great Cycle” of the Long Count: A period of 13 baktuns = 5, 200 years long (in 360-day years).
The Great Cycle will be completed on December 21, 2012