Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
Week 06 Lecture 03
The Western Hemisphere’s Greatest Astronomers and
Mathematicians
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
The learning objectives for week 06 lecture 03 are:
– to learn a little about Maya astronomy and mathematics
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
Terms you should know for week 06, the topic of the Maya are:
– Tikal–is one of the most important Maya cities and archaeological
sites, now in Guatemala. It had up to 50,000 inhabitants in 600
AD.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World: Dr. Richard W. Franke
The Maya
Week 06 Sources:
Braun, Barbara. 1993. Pre-Columbian Art and the Post-Columbian World: Ancient Sources of
American Art. New York: Harry N. Abrams, Inc. Publishers.
Hagen, Victor W. von. 1960. World of the Maya. New York: Mentor Books.
Henderson, John S. 1981. The World of the Ancient Maya. Ithaca: Cornell University Press.
Joseph, George Gheverghese. 1991. The Crest of the Peacock: Non-European Roots of
Mathematics. London: I. B. Tauris and Co. Ltd.
Ruddell, Nancy. 1995. Mystery of the Maya. Hull, Quebec: Canadian Museum of Civilization.
Stuart, George E. and Gene S. Stuart. 1977. The Mysterious Maya. Washington, D.C.: National
Geographic Society.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
1. The Maya built a state level civilization in the area of
modern day Southern Mexico and Northern Central
America.
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
2. Their culture spread
from the highlands
of Southwestern
Mexico to the
lowlands of Yucatan.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
3. The Classic period Maya – 300 AD to 900 AD –
developed a population density as great as modern day
Europe.
4. They built large cities, with Tikal comprising
40,000 to 50,000 inhabitants in the 7th and 8th
centuries.
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
5. Archaeologists have identified the remains of at least
83 Maya cities.
6. Three of the most important centers were:
– Tikal
– Palenqué
– Chichén Itzá
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
• Tikal
– In northeastern Guatemala near the border with Belize. By 600
AD, Tikal had about 50,000 residents spread across 10 kilometers
(6 miles).
• Palenqué
– In southern Mexico west of the Yucatan. Palenqué is the site of the
famous tomb of King Pacal, who died in 683 AD. The carved
limestone sarcophagus lid is one of the most impressive examples of
Maya sculpture and portrays much of their religious system.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Tikal
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Tikal has some of Central
America’s most
dramatic pyramids
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The site will
probably yield
archaeological
treasures for
decades if not
centuries to come.
Slowly we will learn
more about the
mysterious Maya.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
• Chichén Itzá
– Near the northern end of the Yucatan Penninsula. Chichén
Itzá is the site of a famous Maya temple dedicated to the
Feathered Serpent God. Each year, at the two solar
equinoxes, the sun hits the side of the stairs illuminating
the image of a snake (on the risers of the stairs) descending
from the sacred mountain into the earth.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
7. Maya culture is as old as that of Europe – the Maya
began settled communities by 1,800 BC and had
centralized urban areas by 1,200 BC, the time of the
Trojan Wars in Greece.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Early Preclassic
1,800 BC to 900 BC
Middle Preclassic
900 BC to 300 BC
(Olmec)
(1,200 BC to 100 BC)
Late Preclassic
300 BC to 250 AD
Classic
250 AD to 900 AD
Toltec Era
900 AD to 1541 AD
Spanish Era
1541 AD to 1813 AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
8. Built massive pyramids
– Developed a complex writing system
– Developed an efficient and elaborate mathematical system
– Made precise astronomical observations
– Created a highly accurate 3-part calendar
– Made masterful stone sculptures
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke: 2012 Update
The Maya
Art historian
Barbara Braun
discovered that
Maya architecture
had a strong
influence on the
major American
architect Frank
Lloyd Wright…
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke: 2012 Update
The Maya
One of Wright’s
Hollywood houses from
1920 shows the
influence of Maya
temple design…while…
Source: Braun 1993:153
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke: 2012 Update
The Maya
The Maya
corbelled vault –
substitute for the
arch…(which
they did not
develop)…
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke: 2012 Update
The Maya
…appears as a design
feature in a San
Francisco medical
offices building at 450
Sutter Street,
constructed in 1930.
Source: Braun 1993:169.
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke: 2012 Update
The Maya
The outside of the
building also has Maya
features – sometimes
called “Neo-Mayan Art
Deco.”
Sources:
Braun 1993:41.
http://en.wikipedia.org/wiki/450_Sutter_Street
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke: 2012 Update
One of Wright’s most famous
buildings is the Solomon R.
Guggenheim Museum (19561959) in Manhattan. Wright
designed the building from his
studies on the Maya
observatory at Chichén Itzá….
Sources for the photos:
http://www.beembee.com/2011/solomon-rguggenheim-museum
https://encryptedtbn0.google.com/images?q=tbn:ANd9GcSkzbCMqlt2k
RSTKq7SG2ZSfcErNBFV0iriBtEiPsC_Rr_fj0mTMQ
http://www.greatbuildings.com/gbc/images/ci
d_cr1029_b.150.jpg
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke: 2012 Update
Sources for the photos:
http://www.cancunofertas.com.mx/english/images/galerias/c
hichen-itza_05.jpg
http://0.tqn.com/d/gomexico/1/0/I/1/-/-/chichen.jpg
https://encryptedtbn1.google.com/images?q=tbn:ANd9GcQMZ4LUHloxTR
3tDUvOnqmXHoqo420YFHW4JOnNHqofPpD3prN71g
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke: 2012 Update
The Maya
In addition to Wright, other famous artists who drew on the Maya and
other Mexican, Central American and Peruvian artistic and architectural
traditions are
• Paul Gauguin (used ancient Peruvian Chimu styles as well as his more
famous Polynesian influences)
• Henry Moore (Aztec influence)
• Diego Rivera – perhaps Mexico’s most famous painter: used all kinds of
Central American influences
• Joaquin Torres-Garcia – Mayan and Andean art and architecture
Source: Braun 1993. Braun’s book is available in Sprague Library. Dozens of spectacular photos.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
9. Like their Inca neighbors far to the south, the Maya
created their civilization in an unusual and difficult
environment without the benefit of a large river system.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
10. Instead, they organized
villages around “cenotes,” or
water holes in the limestone
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
11. Then they built reservoirs,
called “chultuns.”
– This one connects nearly a
mile to the famous temple of
Kukulkan – discussed later
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
12. Like the Naza, the Maya also constructed canals
– Some of these canals range up to a mile in length, 100 feet
in width and are 10 feet deep.
13. The Maya civilization mysteriously collapsed around
900 AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
14. The reason for the sudden abandonment of their
great cities has never been fully identified.
15. Some scholars consider soil erosion while others
argue that a volcano-induced prolonged drought killed
off thousands.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya Collapse and Modern Environmental Problems
15a. If you are interested in the possible implications of
the Maya collapse for modern societies, open the file in
the Week06 folder on Blackboard called:
Lessons from the Ancestors.doc
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
16. The Spaniards thus conquered the Maya long after
their major ability to resist a foreign invasion had
dissipated.
17. With the Spanish conquest came destruction of much
of the Maya written record…
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
18. The Lost Maya Books
“We found a large number of books in these [Maya] characters
and, as they contained nothing in which there were not to be
seen 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, 16th Century Bishop of Yucatan.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
19. Of thousands of Maya books of genealogies,
biographies, collections of songs, science texts,
histories, prophecies, ritual, and astrology, only 4
remain today.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
20. The Maya, however, also carved much of their
science and literature into the soft limestone of the
area.
21. Much of this carving occurs on “stelae,” or posts used
at the entrances to temples, neighborhoods, and other
sites.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
22. Mathematical
computations were
also carved into some
of the stele.
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
23. Although we know little of Maya medicine and other
sciences, through the stele archaeologists and others
have been able to reconstruct much of their
mathematics and astronomy.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
24. Venus
Maya calculated its revolution at 584 days.
Modern astronomy estimates it at 583.92.
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
25. The Moon
Maya gave the lunar month as 29.5302 days.
Modern astronomy says 29.53059.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
26. Lunar Eclipses
The Maya knew that the lunar eclipse occurs every
173.31 days.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
27. The Sun
Maya calculated a solar year at 365.242.
Modern astronomy gives it as 365.242198.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
28. The Equinoxes
The Maya designed the temple at Chichén Itzá to
illuminate a giant serpent on the risers of the stairs at
the solar equinoxes.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Kukulkan
Temple in
Chichén
Itzá
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
29. The Stars
Maya knew of the North Star (xamann ek), Ursa Minor,
the Pleiades (tzab), the Gemini (ak ek), Scorpio (zinaan
ek), and other heavenly bodies.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
30. Some sources:
Hagen, Victor W. Von. 1960. World of the Maya. New York: Mentor Books.
Joseph, George Gheverghese: 1991. The Crest of the Peacock: Non-European Roots of
Mathematics. London: I. B. Tauris and Co. Ltd.
Henderson, John S. 1997. The World of the Ancient Maya. Ithaca: Cornell University
Press. Second Edition.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
31. Maya Mathematics:
See the next two slides for examples
1/11/2012
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Montclair State University
Department of Anthropology:
Anth 140: Non Western
Contributions to the Western
World: Dr. Richard W. Franke
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western
World
Dr. Richard W. Franke
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
31. One of the most spectacular finds has been the
sarcophagus of the Mayan King Pacal, who lived from
603 to 683 AD. His tomb was rediscovered intact in
1952. The next slide shows the building in which the
burial was found.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Pacal’s Tomb
1/11/2012
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Montclair State University Department of
Anthropology
Anth 140: Non Western Contributions
to the Western World
Dr. Richard W. Franke
32. The lid would
originally have been
colorfully painted.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
33. Pacal’s sarcophagus
(his coffin --- especially
the lid) – from the outer
border scholars can read
dates and other
information about Pacal.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
34. Based on a technical
drawing of the sarcophagus
lid scholars have been able to
learn much about Pacal and
about Maya hieroglyphs –
their writing system.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
35. Pacal’s Sarcophagus
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
36. Maya architecture achieved great heights, however
the Maya did not quite invent the true arch.
37. Like the Inca who favored the trapezoidal shape, the
Maya invented the “corbeled vault,” a near-arch
structure.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
38. The corbeled vault holds
up more weight than a flat
ceiling but not as much as
the true arch.
1/11/2012
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
38. The vault allowed the
Maya to build large
structures with entrances but
nothing on the scale of the
European Gothic cathedrals
that were based on the true
arch.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
The true arch was probably invented in
ancient Sumar (Babylon) and became a
major feature of Roman architecture.
From there it was passed through the
European Middle Ages and the great
cathedrals to the modern world.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
The Maya
End of Slides for Week 06 Lecture 03 on
Maya Astronomy and Mathematics
1/11/2012
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