Two origami philosophies create a math-art.

**Mathematical Philosophy** - Modern mathematical origami is portrayed as a puzzle or geometric sequence. Basic understanding of the sequence allows the shape to be mass-produced and replicated. The idea begins with bases. Almost every origami starts with a common base composed of triangles and rectangles that are then rearranged to make the final product. New models in modern origami depend heavily on a few established bases. They use a Bird base, which is the halfway shape of Orizuru, in creating not only birds but also animals or flowers.

Bird Base Diamond Base Windmill base

Also, in modern origami the meaning of the base has become altered. Now a creator designs a new base to construct origami. As a result, new advanced theories have been developed by Meguro Toshiyuki, Kawahata Fumiaki, Robert Lang, and others. In this theory, a base is regarded as a set of independent areas and distinguished by the length and arrangement of the areas.

Formula's have been invented for making origami.

**Kawasaki's Theorm**:

Angles surrounding a single vertex in flat origami crease pattern are...

a_{1}, a_{2}, a_{3}, ..., a_{2n}, then: a_{1}+a_{3}+a_{5}+….a_{2n-1}=180 and a_{2}+a_{4}+a_{6}+…a_{2n}=180. In other words the sum of angles around a point is 180 degrees.

**Humiaki Huzita Theorm:**

Viewing origami as simply folds on a paper using raw edges and points...

1) Given two lines L_{1} and L_{2}, to fold a line placing L_{1} onto L_{2}.

2) Given two points P_{1} and P_{2}, to fold a line placing P_{1} onto P_{2}.

3) Given two points P_{1} and P_{2}, to fold a line passing through both P_{1} and P_{2}.

4) Given one point P and one line L, to fold a line passing through P and perpendicular to L.

5) Given two point P_{1} and P_{2} and one line L, to fold a line placing P_{1} onto L and passing through P_{2}.

6) Given two point P_{1} and P_{2} and two lines L_{1} and L_{2}, to fold a line placing P_{1} onto L_{1} and placing P_{2} onto L_{2}.

__According to mathematicians, origami construction does not require more than these six folds to create all possible shapes.__

__Artistic Philosophy-__ Portrayed as unique, expressive, and creative. The notion that individual artists have intellectual property in each folding sequence is a common idea. No mass-production of artistic origami is possible, making the shape different each time. Allows unique expression through use of shape, paper, and color.

*Shapes-- *Crane=Children's peace

*Color-- * Blue=Calm

*Paper-- *Washi is used to wet fold shapes to make a more rounded model.

Kami weighs slightly less than normal paper and is used for a variety of shapes. It usually comes prepackaged already printed with colors and patterns.

In modern time the use of printed bills is often used to shape origami due to its availability and convenience.

Copyrights have created a new art appreciation movement in origami. Traditionally, origami shapes were passed down from family to family and the creator remained anonymous. With copyrights we now associate creators names with each design. This allows individual association with each shape in contrast to a wide spread model with a unknown creator. As poeople reproduce the model in their own private lives they learn to appreciate the creator and the design.

__Origami as an Math-Art__

In simple terms mathematical origami focuses on formulas to construct a repeated process. Artistic origami is based on the individual expression of the creator. These contrasting viewpoints on origami could explain the appeal to large numbers of people in the western world. Whether you are a mathmatican/scientist or an artist, significance can be found in it. Origami is currently considered both an art from and math. Therefore, the act of Japanese paper folding encompasses both math with artistic expressiveness making it what some call a math-art. Only in origami can artists and mathematicians practice art and math simultaneously .

Combining the two philosophies creates a math-art that allows for a broader interest of origami in the western world.

__Sites Used__

http://origami.ousaan.com/library/historye.html

http://www.paperfolding.com/math/

http://www.langorigami.com/art/artmain/artmain.php4

## Comments (0)

You don't have permission to comment on this page.