Native American Geometry
Endorsements   References
foundations
education designs
anthropology
Endorsements   References

NATIVE AMERICAN GEOMETRY is a physical, proportional geometry that originates from the simple circle. A growing body of architectural and iconographic evidence from Native America suggests it was a relatively common tradition that has been practiced for at least two thousand years. This is the same type of geometry that was discovered and developed by the ancestors of many peoples in many places, from China to the Mediterranean Basin to the British Isles. Currently, it resides among the logo designers of Madison Avenue. Generally, it maintains a similar methodological structure to the Middle Eastern tradition of classical geometry that is limited to operations carried out by the compass and straightedge, or two sticks and a rope.

In the anthropological world, there are generally two ways traditions come into being in any particular culture: diffusion or borrowing from another culture; and, independent invention or discovery.

Did the geometry have a single source and diffuse around the world over a period of several millennia? Or is there something about it, like stone working techniques, that made it independently accessible to the human mind in diverse cultures and civilizations?

Personally, I believe the geometry was discovered independently by widely disparate cultures. Why? Because this type of proportional geometry originates with the circle, one of the most popular and multi-cultural symbols in the human world. It is a shape that served as a foundation for countless domestic and ceremonial structures. Given the intimate relationship between the circle's radius and the hexagon, it is an argument I can live with, for now. This opinion does not exclude instances of cultural diffusion within specific geographic regions.

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E-mail: Chris Hardaker


Interdisciplinary Recognition of Native American Geometry
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Visual Math Institute

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Getty Foundationís Artsednet

Family Education Network
Featured Links page
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  by FamilyPC magazine, 1998)

BONUS.COM
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Alaska Native Knowledge Network
Alaska Native Science and Math Education

Native American Resources
Native American Art, Teacher Resources, Sites

Steffen's Math Resources

Interdisciplinary Educational Curriculum

Dinť College

Navajo Central Website
(Chinle Schools)

Tribal Librarians
Useful Links
Elaine Cubbins, MA-IRLS

4Directions Project
Shelly Valdez

Index for Native American Resources
At the University of Massachusetts

Intíl Study Group in Ethnomathematics

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The Global Distance Learning Channel

Yahoo! Society and Culture...Native American

Special thanks to Vino

References for Teachers
General References for Intermediate and Middle Grades
Geometric Design
Seymour D. Palo Alto : Dale Seymour Publications 1988

A Mathematical Mystery Tour: Higher Thinking Math Tasks
Wahl, Mark, Tucson: Zephyr Press 1988

General References for High School
Geometry in Architecture
Blackwell, William (A.I.A.) Berkeley, CA: Key Curriculum Press 1984

Geometrical Concepts in Islamic Art
El-Said, Issam, and Ayse Parman. Palo Alto, Calif.: Dale Seymour Publications, 1987.

Sacred Geometry: Philosophy and Practice
Lawlor, Robert. London: Thames and Hudson, 1992

Universal Patterns
Newmann, R., & M. Boles Bradford, MA: Pythagorean Press 1992a

The Surface Plane
Newmann, R., & M. Boles Bradford, MA: Pythagorean Press 1992b

On Growth and Form.
Thompson, D'Arcy. Cambridge: University Press, 1969.

Combined References
Baigent, M. and S. Leigh
1994 The Temple and the Lodge London: Thames and Hudson

John Barrows,
1995 Artful Universe, Clarendon Press, Oxford

Blackwell, William (A.I.A.)
1984 Geometry in Architecture Berkeley, CA: Key Curriculum Press

Beard, Robert S.
1973 Patterns in Space. Palo Alto:Creative Publications.

Brunes, Tons
1967 The Secrets of Ancient Geometry and its Use (2 volumes) Copenhagen: Rhodos Int'l Science Publishers

Closs, Michael (ed)
1986 Native American Mathematics Austin, TX: University of Texas Press

Critchlow, Keith.
1970 Order in Space. New York: The Viking Press.

Dozci, Gyorgy
1981 The Power of Limits. Boulder: Shambala Press.

El-Said, Issam, and Ayse Parman
1987 Geometrical Concepts in Islamic Art. Palo Alto, CA.: Dale Seymour Publications.

Feininger, Andreas
1956 The Anatomy of Nature. New York: Dover.

Fowler, Andrew P., and John Stein
1995 The Anasazi Great House in Space, Time, and Paradigm. In Anasazi Regional Organization and the Chaco System, edited by David E. Doyel Maxwell Museum of Anthropology, Anthro. Papers No. 5

Ghyka, Matila
1977 The Geometry of Art and Life. New York: Dover.

Grillo, Paul Jacques
1960 Form,Function and Design. New York, Dover.

Hambidge, Jay
1924 The Parthenon and Other Greek Temples, Their Dynamic Symmetry. New Haven: Yale University Press.

Hardaker, Chris
1992 The Tabletop Alignment: An Early Classic Hohokam Winter Solstice Alignment at Casa Grande Ruins. Ms. in possession of the author.

Hodson, Geoffrey
1976 At The Sign of the Square and Compass Madras, India: International Co-Freemasonry

Hudson, D.T.
1972 The Chaco Foot. Kiva 38 [1]: 27-40)

Huntley, H.E.
1970 The Divine Proportion. New York: Dover.

Hutchens, Rex
1988 A Bridge to Light Washington, D.C.: The Supreme Council

Judd, Neil M.
1959 Pueblo Del Arroyo, New Mexico Smithsonian Miscellaneous Collections138(1) Washington, D.C.
1964 The Architecture of Pueblo Bonito. Smithsonian Miscellaneous Collections 147(1) Washington, D.C.

Kappraff, Jay
1991 Connections: the geometric bridge between art and science. New York: McGraw -Hill

Lawlor, Robert
1995 Sacred Geometry, London: Thames & Hudson

Lekson, Stephen H.
1984 Great Pueblo Architecture of Chaco Canyon, New Mexico. Chaco Canyon Studies. Publications in Anthropology 18B. National Park Service, Alb., NM.

McKenna, Peter J., and Marcia L. Truell
1986 Small Site Architecture of Chaco Canyon, New Mexico. Chaco Canyon Studies, Publications in Achaeology 18D. National Park Service, Santa Fe.

Merlin Donald
1991 Origins of the Modern Mind, Harvard Univ. Press

Nabakov, Peter, and Robert Easton
1989 Native American Architecture New York: Oxford University Press

Newmann, R., & M. Boles
1992a Universal Patterns Bradford, MA: Pythagorean Press
1992b The Surface Plane Bradford, MA: Pythagorean Press

Pinxten, Rik
1987 Towards a Navajo Indian geometry. Ghent, Belgium : Kultuur, Kennis en Intergratie

Pinxten, Rik, Ingrid van Dooren, Frank Harvey
1983 The Anthropology of Space Philadelphia: University of Pennsylvania Press

Rohn, A. H.
1971 Mug House, Mesa Verde Natuional Park Colorado Archaeological Research Series #7d. National Park Service, Washington, D.C.

Runion, Garth E.
1990 The Golden Section. Palo Alto: Dale Seymour Publications.

Seymour Dale
1988 Geometric Design. Palo Alto, CA: Dale Seymour Publications

Singleton
1906 The History of Freemasonry New York: The Masonic Publishing Co.

Smith, D.E.
1951 History of Mathematics, (Volume 1); New York: Dover Publications

Stein, John, and Stephen H. Lekson
1992 Anasazi Ritual Landscapes. In, Anasazi Regional Organization and the Chaco System, edited by David E. Doyel, Maxwell Museum of Anthropology, Anthropological Papers No. 5.

Thompson, D'Arcy
1969 On Growth and Form. Cambridge: University Press.

Vinette, Francine
1986 In Search of Mesoamerican Geometry. In Native American Mathematics. pp. 387-407. Edited by Michael Closs, Austin, Texas: Universtity of Texas Press

Vivian, Gordon and Paul Reiter
1960 Great Kivas of Chaco Canyon. School of American Research, Santa Fe

Wahl, Mark
1988 A Mathematical Mystery Tour: Higher Thinking Math Tasks Tucson: Zephyr Press.

Weigand, P.C.
1995 Architectural principles illustrated in archaeology: A case from Western Mesoamerica. In, Arqueologia del norte y del occidente de Mexico, ed. Barbro Dahlgren. pp. 159-171. Universidad Nacional Autonoma de Mexico.

1996 The architecture of the Teuchitlan Tradition of the Occidente of Mesoamerica. Ancient Mesoamerica, 7: 91-101

Williams, Christopher
1981 Origins of Form. New York: Visual Communications Books.

Zaslow, Bert
1981 Pattern dissemination in the prehistoric southwest and Mesoamerica: a comparison of Hohokam decorative patterns with patterns from the Upper Gila area and from the Valley ofOaxaca. Anthropological research paper; no. 25. Tempe, Ariz. : Arizona State University

Zaslow, Bert, and A.E. Dittert
1977. Guide to analyzing prehistoric ceramic decorations by symmetry and pattern mathematics. Anthropological research paper ; no. 2. Tempe: Arizona State University

Copyright Chris Hardaker 1994-2000