| American Indian design |
For the American Indians north of Mexico, we may say that although their bonds of superstition and lack of an adequate number symbolism limited their mathematical progress, number still played an important role in their religious beliefs. In addition, they used many geometric figures in ornamentation and construction.
American Indian design
Specific reference to the use of three, four five, seven, and thirteen in religious ceremonies is extant, with four being the more prevalent. The may be due to the four points of the compass. Here are examples.
Five was the mystical number of some of the Pacific Coast Indians. Three and five were sacred to the Iroquois.
Seven was used by the Zuñi, Cherokee, Creeks, and most of the Plains tribes.
Thirteen was adopted by the Hopi Pawnee, and the Zuñi. It was also widely used in Central America.
In the Pueblo Snake Dance the Snake Men prepared eight days for the ceremony; the snakes used were of four kinds obtained from a four days' hunt in the four directions.
An Apache prayed to his gods at least once every four days, and if possible every day, for four times a day. Apache medicine men used this number in their remedies, e.g. four roots of one herb, roots of four varieties, ...
Suppose a member of the Potawatomi tribe was accused of murder, but that the tribal chief thought he was not guilty, a pipe bearer would bring flint and steel and attempt to light the chief's pipe. If he was successful within four strokes of the steel the man went free, otherwise the man was executed. An influential man might get away with three murders, but for four murders, nothing could save him.
The Iroquois when smoking would take three puffs from a pipe. Only three trials were allowed in physical contests. Five days or multiple thereof must elapse between the announcement of and the beginning of a celebration.
Counting on fingers was nearly universal among Indian tribes. Sometimes the fingers were bent in during counting, other times the fingers were extended from a fist during counting.
Usually, both hands, beginning with the left hand were used to count ten. To get the next ten, some tribes used the toes; others used the fingers again. The Zuñi counted the second ten on their knuckles.
Tally marks (vertical strokes) were used to denote one. Grouping was not generally evident. The Dakotas used only the vertical stroke. The Creeks also used this but a cross was used for ten.
Evidence of subtraction has been found. For example in the Bellacoola language
of British Columbia we have:
| 16 |   |
one man less four |
| 18 | = | one man less two |
| 26 | = | one man and two hands less four |
| 36 | = | two men less four |
Traces of multiplication can be found in the number words of the Zuñi. We
have
| 10 |  |
all the fingers |
| 20 | = | two times all the fingers |
| 100 | = | the fingers all the fingers |
| 1000 | = | the fingers all the fingers times all the fingers |
Most Indian mounds have been found in the eastern United States. Most were conical. The typical pyramidal mound was a truncated quadrilateral pyramid. The largest is located in Illinois. It is one hundred feet high and has a seven hundred foot base. Mounds have also been discovered and some excavated in Minnisota, Wisconsin, Ohio, Iowa, Georgia, and Mississippi. Many of the mounds were constructed well before Europeans arrived in the new world, some as early as 1000 BCE. The practice seems to have ending in about 1300 CE.
One group of mounds found in Ohio have bases in the shapes of circles,
squares, and octagons --- all being quite accurate to true figures. The angles
of one measuring more than 900 feet on its base made angles differing from
right angles by less than one degree. Could this have been achieved by line of
sight? It is an interesting exercise to explain how a people, living in the
wilderness, with no tradition of geometry and little tradition of contruction
could have made not just one but four nearly right angles on so gigantic a
scale. Below is the Adena Serpent mound near Locust Grove, Ohio. Constructed
in the second century BCE, it measures 1336 ft (405 meters) long by about 3-6
feet high. Note the use of spirals and semicircles as a part of a quite
regular wavy line.
One
mound in Georgia constructed by the Etowah Indians is the tallest structure in
the area (about 61 feet), and furnishes an impressive view of the Etowah River
Valley. The top covers about an acre of land. Another quadrilateral pyramid
was a near accurate square with sides pointing in the compass directions.
Below is a picture of the terraced-pyramidal Monk's mound rising 100 feet
above the surrounding lansdscape, which is a part of the Cahokia mounds in
Illinois, just across the Mississippi river from St. Louis. Cahokia is the
largest pyramds construction north of Mexico. At its peak it was home to
30,000-50,000 people. Depending on the elevation used it measures 954 ft in
the north-south direction and 775 ft in the east-west direction.
Two
purposes of these mounds emerge. They were a location of temples and dwellings
for the upper crust of the tribes. These sites were clearly more defensible in
the event of rather common attacks from neighboring tribes. The other purpose
was for burial, and some mounds were exclusively for this purpose. Though
these mounds have supplied archeologists with a steady supply of artifacts
about the the customs and daily life of the tribes, there has been little by
way of mathematical abilities uncovered.
Anyone who has visited New Mexico has seen the beautiful blankets still woven
by the local Indians. These blankets and other objects of Indian art
throughout North America have an assortment of geometrical patterns and
themes. Navajo pottery, for example, exhibits opposed sets of isosceles
triangles, line bordering dots, hooked spirals, double spirals, vertical and
horizontal lines, and stepped figures.
The Sioux separated designs into numerous designs which include:
The Apaches used trapezoids. The Mojave used the hexagon. Eskimos have used
circles and combinations of
lines.