Showing posts with label Origami. Show all posts
Showing posts with label Origami. Show all posts

Monday, October 30, 2017

The Mathematics of ORIGAMI

English: This illustrates Maekawa's Theorem in...
This illustrates Maekawa's Theorem in the mathematics
of paper folding. I
(Photo credit: 
Wikipedia)
If you have ever held a piece of origami in your hand you have in all probability been at least tempted to open it just to see how the folding was done. The geometry involved in the piece is something you could easily see in the creases displayed on the opened paper.

Scientists and artists have studied these geometric aspects as well as origamists and mathematicians. Mathematicians throughout time have developed ways to use geometry to define origami; they have designed highly sophisticated models using fundamental theorems. They have studied and found amazing similarities between tessellations and origami (tessellations is the name for a figure comprised of a shape that is repeated over and over again with no gaps or overlap when fitted to a flat surface).  Teachers around the world have used origami to teach different concepts in chemistry, physics, and architecture as well as math.

Origami construction is defined as the folding of paper using the raw edges, points of the paper and any creases or points subsequently created by those folds.  The folded paper is seen as both an art piece and a geometric form.  The folds produce varying sizes of triangles, rectangles, and other shapes.  A single fold can bisect an angle twice or as in the case of a reverse fold, make 4 triangles at once.

When the first steps to making a figure are applied to other figures, resulting in a number of figures having common shapes, the common shapes are called bases.  There are several established bases such as the bird, the kite, the windmill and the water-bomb to name a few.   Modern origami relies heavily on these existing bases alone and in combination when designing new figures.  As an example, the kite base is used to make quite a few of the different zoo animals.



Studying the creases of existing models has led to the creation of many new models.  These creases show definite patterns of triangles, rectangles, and other shapes.  The geometric study of the crease lines over the last twenty-five years has paved the way for the discovery of new bases.  Not all designs are combinations or parts of other bases; some like the box pleat is completely original.  

Some origamists saw the base as a set of areas each independent of the other differing only in their length and arrangement.  With this in mind, they went on to develop computer programs that are capable of doing all the math necessary to generate crease patterns for any base from a given length and area arrangement.   With the aid of computer programs using intricate mathematical theorems, origami has become as much a puzzle as a piece of art.

Mathematical origamists are now designing more and more complex, realistic models still sticking to the simple rule of one sheet of paper with no cuts.  These programs are also used to solve problems involving getting large pieces of paper folded to fit a specific sized flat surface.




Thursday, May 11, 2017

The Mathematics of ORIGAMI

English: This illustrates Maekawa's Theorem in...
This illustrates Maekawa's Theorem in
the mathematics of paper folding.
(Photo credit: 
Wikipedia)
If you have ever held a piece of origami in your hand you have in all probability been at least tempted to open it just to see how the folding was done. The geometry involved in the piece is something you could easily see in the creases displayed on the opened paper.

Scientists and artists have studied these geometric aspects as well as origamists and mathematicians. Mathematicians throughout time have developed ways to use geometry to define origami; they have designed highly sophisticated models using fundamental theorems. They have studied and found amazing similarities between tessellations and origami (tessellations is the name for a figure comprised of a shape that is repeated over and over again with no gaps or overlap when fitted to a flat surface).  Teachers around the world have used origami to teach different concepts in chemistry, physics and architecture as well as math.

Origami construction is defined as the folding of paper using the raw edges, points of the paper and any creases or points subsequently created by those folds.  The folded paper is seen as both an art piece and a geometric form.  The folds produce varying sizes of triangles, rectangles and other shapes.  A single fold can bisect and angle twice or as in the case of a reverse fold, make 4 triangles at once.

When the first steps to making a figure are applied to other figures, resulting in a number of figures having common shapes, the common shapes are called bases.  There are several established bases such as the bird, the kite, the windmill and the water-bomb to name a few.   Modern origami relies heavily on these existing bases alone and in combination when designing new figures.  As an example the kite base is used to make quite a few of the different zoo animals.

Studying the creases of existing models has led to the creation of many new models.  These creases show definite patterns of triangles, rectangles and other shapes.  The geometric study of the crease lines over the last twenty-five years has paved the way for the discovery of new bases.  Not all designs are combinations or parts of other bases; some like the box pleat are completely original.



Some origamists saw the base as a set of areas each independent of the other differing only in their length and arrangement.  With this in mind they went on to develop computer programs that are capable of doing all the math necessary to generate crease patterns for any base from a given length and area arrangement.   With the aid of computer programs using intricate mathematical theorems origami has become as much a puzzle as a piece of art.

Mathematical origamists are now designing more and more complex, realistic models still sticking to the simple rule of one sheet of paper with no cuts.  These programs are also used to solve problems involving getting large pieces of paper folded to fit a specific sized flat surface.




Wednesday, March 1, 2017

Therapeutic Advantages of ORIGAMI

Origami has been proven to possess therapeutic advantages. The activity is been used to help individuals with psychological aspects such as feelings of acceptance. People who are having emotional and mental problems sense a feeling of acceptance while being taught the art of origami. Realizing someone is willing to take the time to teach and show them how to do this activity promotes positive emotions.

Modular origami stellated icosahedron made fro...
Modular origami stellated icosahedron made from custom papers (Photo credit: Wikipedia)

When origami is demonstrated in a group setting, it helps the troubled individual experience a sense of belonging. It enables them to interact with others and connect with people who they can relate to. It's also a bonus when origami is being taught by a psychologist because any time a person feels the need to share their feelings, there's a professional there to intervene. 

The art of origami is effective in promoting positive behavior. In a group setting it helps an individual learn how to act appropriately in a social environment. This would be good for children who are having trouble communicating or getting along with other children. This activity requires patience and so it teaches people how to be patient. Again this would be beneficial for children. Origami involves problem solving and this is a skill that is needed daily by individuals of all ages. Getting people interested in activities such as origami encourages people to develop a hobby where they can be creative and be involved in a group activity. 

The therapeutic advantages of origami are amazing. To be able to take a simple concept such as paper folding and watch it make a difference in people's lives is awesome. Origami is a learning experience that incorporates communication skills and problem solving skills. It's also a great activity to promote goal setting. Finishing an origami project takes time but the results are beautiful and fulfilling. Seeing the outcome of the project in a picture and working toward it provides an individual with a goal. It's important to have goals in life and it's great that an activity such as origami can help a person learn about it. Origami provides an opportunity to relax and have fun. The enjoyment that goes along with this activity is definitely good therapy. 

Not everyone is quick to open up and share their feelings with another individual, even a psychologist or other medical professional. It's essential that the person administering help and advice present a non-threatening image. Origami can be used as a means of breaking the ice, a warming up technique. It can help the patient and psychologist find mutual ground. Origami can be used to bridge the gap between patient and doctor.



This will certainly make it easier for the patient to be comfortable and more inclined to share their feelings and work on their problems. It is imperative that a doctor and patient develop a good relationship. Not everyone is willing to discuss emotional issues and/or psychological problems. If origami helps to build a bridge that leads to healing, it can definitely be considered a therapeutic advantage.



Wednesday, February 1, 2017

Who Uses ORIGAMI in Society Today?

The art of origami dates back to the 1600's. First practiced by the Chinese and Japanese, the art of paper folding was and continues to be popular in many cultures. When it was originally started, origami instructions were passed on verbally. Over the years the details and steps required for origami projects have been written down and/or relayed through diagrams. Folding paper may not seem to be very challenging but as the projects advance, origami can in fact be quire complicated and complex. 

Origami star
Origami star (Photo credit: Wikipedia)

Who uses origami in society today? No doubt there are many people who still do origami simply as a pass-time or hobby. For children and adults alike this activity can provide hours of enjoyment. Origami is great on rainy days and snow days. Once starting a project, it's difficult to stop until the desired result is achieved. It may take several attempts but eventually the results will be top-notch.

Origami has grown in popularity as a teaching tool. Educators and teachers are using origami in the classroom. This activity has proven to be effective in teaching children to be patient and attentive. Both of these skills are necessary in a group as well as in every day living. Origami also teaches children about problems solving and other aspects of mathematics that are relative to life. It also encourages children to set goals and work toward achieving them. 

Psychologists and physicians use origami as a therapeutic tool. It has proven to be successful in the treatment of mental health patients. It helps the patients to become more relaxed in their environment and with their doctor. Besides filling many lonely hours in the hospital, origami teaches patients to get along with and help one another. The art of paper folding can actually bring people out of their shell and encourage them to participate in conversation and group activities. 

Parents use origami at home to help their children develop different skills. This activity can help children develop their reading and writing skills. For young children it can help them learn how to use both hands together. Origami teaches concentration, patience and problem solving, all imperative to the growth and development of children. Besides the educational and behavioral advantages of origami, parents can use this activity to occupy a child who's bored or lonely. It's an inexpensive activity that a parent and child or children can do together. This means time spent together and an opportunity to build a good parent/child relationship. 



When people first began practicing the art of origami, they probably had no idea of the amazing benefits this activity would produce. Likely initially used as a decoration or simply a way to kill a few hours, origami has been transformed into an activity that has many magnificent uses. There are books written about the art of origami and its benefits for various situations. The Internet has loads of information about the origami. If you'd like to learn more about this great activity, log onto the worldwide web and start learning.



Friday, December 30, 2016

Basic ORIGAMI Folds Terms & Techniques

As with any other craft origami has its own terms and techniques.  Here are some basic horizontal and vertical folds.  It is very important to keep all your folds crisp and clean. 

The Book - fold a piece of paper (rectangular or square) down the middle vertically making certain the opposite edges line up one on top of the other.  For many origami figures you will need to add another book figure - open the paper and make another fold across the middle horizontally again, making sure the edges lie one on top of the other.   If you don't open the book before making the second fold you end up with the handkerchief fold which gives you a small square with four layers of paper one on top of the other.  

English: How to fold a paper fortune teller 12...
How to fold a paper fortune teller 12 steps (Photo credit: Wikipedia)
The Cupboard - using a square piece of paper make the book fold then open the paper and take each outside edge and fold it to the center line.  By bringing each edge over to the next line you will end up making even more equal vertical strips.

The Fan - with either a square or rectangular piece of paper fold a Cupboard.  Open the Cupboard; three valley folds (downward angles) divide the Cupboard into four equal sized strips.  Turn the figure over; fold the edges onto the outer lines making two mountain folds.  Turn the figure over and refold the Cupboard.  Turn the Cupboard over once again and fold the edges into the middle line resulting in two mountain folds (upward angles). Fold up the figure and you have made an eight fold fan with alternating mountain and valley folds, also called an accordion fold.

The Lattice - make a Cupboard from a square piece of paper.  Open the Cupboard and repeat the procedure folding in a horizontal direction.  Open the paper and you have the Lattice.  It is 16 equal sized squares used to make boxes, houses and simple animal bodies. 

The Shawl - Make a diagonal fold down the middle of a square piece of paper making sure your edges and corners lay on top of each other.   If you need a second diagonal fold open the sheet of paper completely before starting the second fold to get a more exact line.

The Envelope - using a square piece of paper make diagonal folds down the center in both directions.  Open the paper and bring each corner up to the middle.



The Picture Frame - First make the Envelope.  Open the envelope; turn each corner up to the outer diagonal line.  Now fold the four corners inward and you have a picture frame. 

Heaven and Hell - Fold an Envelope.  Turn the Envelope over and fold each corner up into the center again.  Turn the figure over and you will see pockets on the other side.  Open these pockets.  This figure was dubbed Heaven and Hell because it was usually made on red and blue paper.  This particular fold can be used for making simple hand puppets and animal heads



A List of ORIGAMI Books