Native Village
Youth and Education news
October 2010 Volume 2

Mathematics Used by American Indians
 North of Mexico
http://www.math.tamu.edu/~dallen/history/american/american.html
Condensed by Native Village

For the American Indians north of Mexico, number played an important role in their religious beliefs. They also used  many geometric figures in designs and in construction.

Sacred Numbers

The use
of  , , , in religious ceremonies was widespread. is the most used number. This may be due to the directions.   Examples:

was the mystical number of some of the Pacific Coast Indians. and were sacred to the Iroquois.

was used by the Zuņi, Cherokee, Creeks, and most of the Plains tribes.

was adopted by the Hopi Pawnee, and the Zuņi. It was also widely used in Central America.

 Pueblo Snake Men prepared
8 days for the Snake Dance ceremony.  There were kinds of snakes found in a days' hunt in the directions.

An Apache prayed to his gods at least
1 out of days. If possible, they prayed times a day every day. 

 In Apache remedies, medicine men used 1 and (such as roots of 1 herb, roots of varieties, ... )

If a Potawatomi chief thought an accused murderer was innocent, a pipe bearer would bring flint and steel to light the chief's pipe. If the pipe was lit within
flint strokes, the man went free. Otherwise, he was executed. 
An influential man might get away with
murders, but nothing could save him for murders.


 When smoking, the Iroquois took
puffs from a pipe. Only trials were allowed in physical contests. days or multiple days of  , must pass between the announcement and the beginning of a celebration.

 

Counting

Almost all Indian tribes counted on their fingers. When counting, sometimes the fingers were bent in,, other times the fingers were extended.

Usually, both hands, beginning with the left, were used to count 10. To get the next 10, some tribes used the toes; others used the fingers again. The Zuņi counted the second 10 on their knuckles.

Tally marks (vertical strokes) were used to denote 1. Grouping was not generally evident. The Dakotas used only the vertical stroke. The Creeks also used this but a cross was used for 10.

Evidence of subtraction has been found.  In the Bellacoola language of British Columbia:
 

16 = 1 man - 4
18 = 1 man - 2 
26 = 1 man + 2 hands  - 4
36 = 2 men - 4

Traces of multiplication are found Zuņi number words.
 

10 = all the fingers
20 =  2 times all the fingers
100 = the fingers all the fingers
1000 = the fingers all the fingers times all the fingers


 

Mounds and Other Earthworks

Most Indian mounds are found in the eastern U.S.

 

 Many were built as early as 1000 BCE. The practice seems to have ending in about 1300 CE.

Most were conical.

 

The typical pyramidal mound was a truncated quadrilateral pyramid.
The largest, in Illinois, is 100 feet high and has a 700 foot base.


A Georgia mound built by the Etowah Indians is the tallest structure in the area -- about 61 feet. The top covers about an acre of land. 
 

One Ohio mound group as bases of circles, squares, and octagons. All are nearly accurate. One with a base of over 900 feet has nearly perfect right angles -- within one degree.

 

Ohio's Adena Serpent Mound was built in the 2nd century BC. it measures 1,336 ft long by 3-6 feet high. Spirals and semicircles are part of a quite regular wavy line.
 

 Monk's mound is a quadrilateral pyramid and almost accurate square with sides pointing in the 4 directions.  It is part of Illinois' Cahokia mounds. Cahokia is the largest pyramid construction north of Mexico. At its peak, between  30,000-50,000 people lived there.
 

Monk's mound once measured 954 ft from North to South, and 775 ft from East to West



Ornamentation.

Sioux Design

 

The Sioux separated designs into numerous patterns

Woven blankets and other objects of Indian art throughout North America have assorted geometrical patterns and themes.

 

Navajo pottery has opposed sets of isosceles triangles, line bordering dots, hooked spirals, double spirals, vertical and horizontal lines, and stepped figures.

 The Apaches used trapezoids.
 

 

The Mojave used the hexagon.

Eskimos have used circles and combinations of lines.


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