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Classic Maya Mathematics�(250 – 900 CE)

by

Myron A. Medina

PhD Candidate, Curriculum Studies

Faculty of Education

University of British Columbia, Canada

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Outline

  • Prologue: The Maya
  • Maya Writing
  • Maya Number System
  • Maya Calendars
  • Epilogue

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The Mayas are known for their:

  • keen observations
  • art & architecture
  • mathematical genius
  • astronomy
  • writing system

(the only complete writing system in Pre-Colombian Mesoamerica)

  • complex and sophisticated calendars

​

*The Maya introduced chocolate to the Old World.

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Maya Architecture

Xunantunich, Belize

Tikal, Guatemala

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Maya Engineering

El Castillo at Chichen Itza, south-east Mexico

MAYA DIETY Kukulkan ‘feathered serpent’

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First day of Spring, First day of Fall

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How did the Maya do it?

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Maya Writing

Data comes from the following sources:

Primary text

  1. Stone text (hieroglyphs carved in limestone)
  2. Inscriptions on Jade, bone, shell, and personal objects
  3. Maya Books (900 CE – Spanish Conquest)

​

Secondary text (drawings and writings on vase, ceramics, potteries)

​

​

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Stone Text: Stela

Copan, Honduras

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Stone Text: Temple Inscriptions

Caracol, Belize

Copan, Honduras

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Jade, shell, bone inscriptions

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The Nature of Maya Writing ‘pebble writing’

(a)

(b)

(c)

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Maya Books (codices)

Paris Codex (p. 23, 24)

Madrid Codex (p. 10)

Courtesy of FAMSI.org

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Dresden Codex (p. 62)

Groiler Codex (p. 23, 24)

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“We found a large number of books in these characters and, as they contained nothing in which were not to be seen as superstition and lies of the devil, we burned them all, which they regretted to an amazing degree, and which caused them much affliction”

– Diego De Landa (Translated from Martyr, 1989, p. 256).

​

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Maya Vase

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Classic Maya Number System

The classic Maya had a complete number system.

In writing, scribes employed three systems of number notations.

  • The bar and dot,
  • The head variant, and
  • The full-figure glyphs

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The bar and dot notation

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Activity: Writing Maya numbers

8000

400

20

Units

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Maya Zero Notations

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The head variant (Coe & Van Stone, 2005, p. 39)

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The full-figure glyphs (Coe & Van Stone, 2005, p. 46, 47)

144,000 days

​

​

7,200 days

​

​

360 days

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​

20 days

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1 day

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Maya Calendars

The Maya used three calendars (three systems) to record dates.

​

For the Maya, every day of the week had a personality, every day of the month had a personality.

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Tzolk’in (sacred round year)

13 numbers cycling against 20 God-glyphs

​

No. + God-glyph

​

Cycle Starts at: 1 Imix

Cycles through yielding 260 unique days

Cycle Ends at: 13 Ahau

Resets (like a clock at midnight) after 260 days

​

e.g. 4 Ahaw

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Activity: Resetting the clock

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Haab (civic or solar calendar)

No. – month-glyph

Haab (19 month names)

Order

Pop

Yax (green)

0 Pop (seating of Pop)

11 Pop

Wo

Zac

1 Pop

12 Pop

Zip (tick)

Ceh (deer)

2 Pop

13 Pop

Zotz' (bat)

Mac

3 Pop

14 Pop

Tzek

K'ank'in

4 Pop

15 Pop

Xul (animal)

Muwan

5 Pop

16 Pop

Yaxk’in (green day)

Pax

6 Pop

17 Pop

Mol (gathering)

K’ayab’

7 Pop

18 Pop

Ch’en (mosquito)

K’umk’u (round)

8 Pop

19 Pop

 

Wayeb’

9 Pop

0 Uo (seating of Wo)

 

 

10 Pop

1 Uo

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Tzolk’in + Habb = Calendar Round

(No. + God-glyph) (No. + month-glyph)

​

​

Cycle Starts at: 1 Imix 0 Pop

Cycles through yielding 18,980 unique permutations

Cycle Ends at: 13 Ahau 4 Weyeb

​

Resets (like a clock at midnight) after 52 Haab years of 365 days or 73 Tzolk’in years of 260 days.

​

e.g. 4 Ahau 8 Kumk’u

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The Long Count

  • The Classic Maya kept track of days, forward or backwards from a starting point, using a Long Count system.

​

The recorded unit days as follows:

  • Kin = 1 day
  • 20 Kins = 1 Winal
  • 18 Winals = 1 Tun (18 x 20 days) *modified base-20 system
  • 20 Tuns = 1 Katun
  • 20 Katuns = 1 Baktun

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How the Long Count works

Baktun. Katun. Tun. Winal. Kin (0.0.0.0.0)

0.0.0.0.0 is 0 day 0 kin

0.0.0.0.1 is 1 day 1 kin

0.0.0.0.19 is 19 days 19 kins

0.0.0.1.0 is 20 days 1 winal

0.0.0.2.0 is 2 x 20 days 2 winals

0.0.0.17.19 is 17 x 20 days + 19 days 17 winals + 19 days

0.0.1.0.0 is 1 tun 18 winals (18 x 20 days = 360 days)*

0.0.19.0.0 is 19 tuns 19 x 360 days

0.1.0.0.0 is 1 katun 20 tuns (20 x 360 days)

1.0.0.0.0 is 1 baktun 20 katuns (20 x 20 x 360 days)

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Example: Long Count date

Activity: Write the following in the long count system

  1. 21 days
  2. 360 days
  3. 365 days

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Activity: Reading Long Count Dates �(Coe & Van Stone, 2005, p. 49, 58)

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Maya Creation date

12.19.19.17.19

Correlates to 3114 BCE

13.0.0.0.0

Maya Calendar Software http://www.xoc.net

Mesoamerican Studies: www.famsi.org