The Possible Origins of Geometrical Shapes for Native Americans

    I  realize I’m asking a question to which an absolute answer can never be given.  However, I still would like to investigate and come to some understanding of how the Native American people discovered simple geometric shapes.  In looking at the art, buildings and everyday lives of these people the influence of geometrical shapes can greatly be seen.  In this paper I will discuss some possible and maybe even likely ways geometrical ideas and the Native American people created shapes. Through this I hope to see how, in this imperfect world, the Native American people saw order and the possibility of pure exact shapes.

    Humans are certainly an interesting creature; we are very inquisitive, curios, and visual.  Shapes and designs show these special traits which humans’ posses.   Even in much earlier civilizations humans created magnificent structures, pictures and shapes.  These creations were both representative of the people’s surroundings but at the same time distinctly human.  These shapes exposed the perfectionist ideals of people.  It seems that in nature few things, if any, are perfectly round, straight or square.  Yet, people create or at least try to create these perfect shapes in making designs or structures.  The Native American people were no different in these ideals.  This is apparent in many things for instance the elaborate rugs of the Navajo people show extreme detail to geometry along with pottery and architecture of the other western Native Americans and structures of countless other Native American cultures.

    The idea of the origin of the square and other geometrical shapes for the Native American people has troubled me.   The answer I received in class of simply “the arrow head” only made me question more.  In these thoughts I have broken down as many possible ways, that I can think up, for the Native American people to have discovered some forms of Geometry.  However, I am fully aware that I could totally off base with some or all my ideas.

    The first idea that I felt was needed for geometrical shape is the idea of a straight line.  I realize that this could have been developed in about an infinite amount of ways.  Some likely ways could be the fact that the shortest distance between to points is a straight line.  For instance in showing a journey a straight path could be marked on the ground.  A blade of grass or reed can be pulled at opposite ends to create a straight line.  Making baskets was an important part of many Native American societies and in creating these baskets a line could have definitely emerged.  Another way the idea of a straight line could have been created is by connecting the dots in the sky.  We know that Native American people saw images in the stars and certainly straight lines were in these images as can be seen from the Navajo Astronomy hand out.  An applicable use for a straight line is an arrow.  A straight arrow flies with much greater accuracy than a crooked or curved arrow.  In my eyes this could have been a big contributor in the belief that straightness is desirable.  Also in the first video we watched in class about the fort builders in Chaco canyon buildings walls where in a fairly straight line both vertically and horizontally.  This also showed that the Native Americans saw the value in creating things on a straight line and understood the advantages of geometric thinking.  Finally in creating a wall carving like those seen in A Field guide to Rock art symbols of the Greater Southwest can certainly be understood that it is much easier to create bodies and other shapes in straight lines.

    Next, the idea of symmetry definitely existed in the Native American people.  First off, humans are a fairly symmetrical creature along with many other animals.  Things like deer antlers, trout markings, and bird feathers also would seem to promote the idea of symmetry.  The value of symmetry could also go back to the spears and arrows that Native Americans used.  It could of certainly been seen by the experienced hunters that a uniform symmetrical arrow head and shaft flies much more accurately than does a lop sided arrow.  I feel that the Idea of precision and exactness could also have been brought out with the need for symmetry.

    The next portion I will discuss is the circle.  I can remember the assignment we did constructing a square from circles Dr. Giamati said, “well we know they had the circle”.  Well the question of how they found the circle also concerned me.  The first thing that came to mind was that a circle is really just a line segment that is connected at opposite ends and has a constant distance from opposite points.  Simply creating a circle could have been an easy thing for the Native American people by simply bending for instance a pliable stick or reed and joining the ends.  I tried this and found it easy to create a good circle without knowledge of a radius.  Dream catchers a common Native American craft were often constructed this way using a pliable stick.  The idea of the circle definitely could of came directly from the sun or moon which both dominate as round objects in the sky.  It also could have been influenced by the Native American belief that life is circular.  The circle also exists in a huge array of places that could be an influence anything from trees, animal markings, stones, flowers and even animals themselves (turtles and sand dollars).

    Triangles are the next shape I will tackle.  A teepee to me was the first thing that came to mind.    One reason that the Egyptian Pyramids were built as Pyramids was do to the fact a triangle is an easy shape to create.  The same was true for the teepee and a teepee draw is a triangle.  However, not all Native American people used teepees for shelter so other influences would of needed to exist.  The arrowhead has a triangle shape which is an ideal shape for its purpose and is still used today.  The triangle also could have given rise to many of the other geometrical shapes like the square.

    The idea of squareness or having ninety degree or nearly ninety degree angles for an object or structure.  This is to me the toughest part of the question for me.  Nature may have some things that are straight, round, and symmetrical but I had a hard time to think of anything that is square.  This is what so fascinated me in the Navajo rugs.  The detail in the elaborate designs and how a square image ever came to be. With four sticks the Native American people could have fairly easily created a rectangle making them equal lengths a square could have been created.  One working use of the square was a stretcher for fur.  This makes sense because a rectangle is an easy thing to create if you want to stretch say a big bison or deer pelt.  The Native American people must have seen the value of the rectangle in building.  Straight somewhat square walls conserve both time and supplies along with space.  This was especially true in the fort builders of the west.   A wall that is built perpendicular to the ground will stand much stronger and longer than one built off of that angle.  Totem poles are another example a Native American creation that was built square to the ground so it could stand. The Native American people must have understood the value of creating things perpendicular and rectangular because today many of their structures still stand.

    A final point that can be made is that a rectangle or other simple geometric shape can easily create a simple or elaborate tessellation.  This can especially be seen in countless rugs of the Navajo people.  The Native Americans must have valued and understood these shapes finding that with these simple shapes beautiful designs could be created.  The thing that most fascinates me about the designs in the Navajo rugs and from art is the way that geometric shapes could be used to create so much beauty and that this beauty comes from the human mind.
 
 

Navajo Astronomy guide,  Chinie CurriculumCenter, 1993, Chinie, Arizona

Rug Guide website,  http://navajorugs.spma.org/rugs.html

Rock art Symbols Of the greater Southwest,  Alex Patterson,  Johnson Books
    Boulder, Colorado

Two Grey hills Navajo rugs. , http://www.subee.com/nd/rugs.htm

American Indians and the natural world. http://www.clpgh.org/cmnh/exhibits/north-south-east-west/index.html