Design and research work “Modular origami. Project modular origami Project origami theme using technology
Purpose of the project I have been doing origami in an origami circle for several years. I, like many of my friends, really like this activity. And I decided to find out why this beautiful art has gained popularity all over the world. The purpose of this project is to study the stages of development of origami, the simplest description of the technique of creating products, in addition, I want to demonstrate what beautiful things can be created with only paper and scissors at hand.
The emergence of the art of origami For a deeper understanding of any art, it is necessary to know the history of its origin. Despite traditionally attributed Japanese roots, the art of origami goes back to ancient China, where paper was discovered. Origami was originally used in religious rituals. For a long time, this type of art was available only to the Japanese aristocracy.
In the second half of the 19th century, Japan opened its doors wide to the rest of the world, and Europeans began to become acquainted with classic figures made using the origami technique: a frog, a fish, a crane. Origami means “folded paper” in Japanese. “Ori” means folding, and “kam i” means paper. Thus, origami is the ancient art of folding figures from paper, paper plastic.
The modern stage of origami development A new stage in the development of origami began after the Second World War and is associated with the name of the famous Japanese master Yoshizawa Akira. With the help of the simple symbols he invented, it was possible to represent the process of folding any product in the form of a series of drawings.
Origami technique I would like to point out that origami is an art accessible to everyone. Origami requires only a piece of paper, making it one of the most accessible arts. Any paper can be used for origami, but there is a certain standard for folding. Standard origami paper should be thin, durable, and should hold wrinkles well. The completed origami figure is called a model, the method of folding the model is called a project, and the drawn instructions for the model are called a set of diagrams.
Origamists love to fold models of animals, as well as all objects of wildlife. In addition to animal models, models of almost all physical objects have been created, including people, faces, plants, vehicles, buildings, etc. Some origami artists fold abstract or mathematical shapes, others specialize in modular origami, where large complex structures are assembled from many folded simple parts.
Using Origami When I started researching who can use origami, I was very surprised that a wide variety of groups of people use it. Artists use origami as a way to express themselves creatively. Scientists, architects and mathematicians explore origami geometry for beauty or for practical applications. Doctors and teachers use origami to help their patients recover from illness or for teaching purposes. And a huge number of people fold paper simply because it's fun.
Conclusion In conclusion, I want to emphasize that origami is, first of all, an art designed to give people joy. Some people have made paper figurines their profession. Paper birds and fish, animals and polyhedra decorate shop windows. Beautiful and expressive masks are widely sold as wall decorations.
Ministry of Education and Science of the Republic of Adygea
Municipal budgetary educational institution "Secondary School No. 15"
Design and research work
"Modular origami"
Completed by: 7th grade student
MBOU "Secondary School No. 15"
Dudko Veronica
Head: teacher
technologies
Grigorenko Irina Nikolaevna
annotation
This project will introduce you to the original Japanese folding technique
paper - modular origami. You will learn the history of this technology,
and also learn how to fold modules and connect them in different ways,
resulting in beautiful voluminous products. This development can be used in club lessons and extracurricular activities of students.
Goals:
1. Find out the importance of the art of Origami for the development of children.
2.Enrich your collection of figurines folded using the origami technique.
3.Develop creativity.
Tasks:
1.Study the history of this art.
2.Learn to work with additional literature.
3.Make a swan figurine.
4. Develop a technique for making a peacock figurine (based on a swan)
1.Relevance of the topic.
2. History of origami.
3. Materials and tools.
4. Technology for making a peacock figurine (based on a swan)
5. Environmental justification for the project.
6. Economic calculations.
7. Conclusion.
8. Sources and literature.
9. Application.
Relevance of the topic.
The relevance of origami is not only interesting entertainment. Origami classes
contribute to the development of spatial imagination, eye, attention, and also allows you to create magic, requiring diligence and patience
and fantasies. Our calendar is rich in holidays. And on holidays it’s customary
give gifts. A beautiful product made with soul and with your own hands
will bring more joy to loved ones and relatives, and will also arouse the admiration of others than a purchased trinket, which will soon be discussed
everyone will forget.
Fantasies are subject to
Paper sheets-
For home and as a gift,
And just for the game...
History of origami.
Simple in childhood paper crafts delighted us. Paper airplanes, boats, firecrackers are firmly entrenched in our childhood memories. It’s amazing how much children enjoy simple things, despite the fact that it is no longer possible to surprise the younger generation with anything. Computer games, remote control cars and airplanes no longer excite their imagination. And how happy a child is when a paper plane is launched into the sky! Because he made it himself!
"Paper folding" is an art. The history of the origin of origami is rooted in the deep past. Getting acquainted with it should begin with ancient China, where, starting from 105 AD. the first prerequisites for the emergence of origami appeared. This year, the official Cai Lun officially reported to the emperor that paper production technology had been created. For many years, the creation of the white sheet was kept in the strictest confidence. But gradually the secret began to travel to Japan along with Chinese monks. In the 7th century, the wandering monk Dan-Ho made his way to Japan and taught the monks to make paper using Chinese technology. Japan quickly established paper production, which in many ways surpassed China.
The history of origami, the art of folding any shapes from a square sheet without the help of scissors, begins in Japan. The very first pieces of paper folded into figures first appeared in monasteries. In Japanese, "God" and "paper" sound the same. Therefore, such paper figures had a symbolic meaning. They decorated temples, they participated in religious ceremonies, and they were placed on the sacrificial fire. The history of origami has preserved for us the first paper figures - “sanbo” boxes, where the Japanese put pieces of vegetables and fish for sacrifices. This was not real art. It was just a piece of paper marked with the name of God and, at that time, worth a lot of money.
The history of origami goes beyond the temples and reaches the imperial court during the Kamakura (1185-1333) and Muromachi (1333-1573) periods. The court monks were necessarily trained in the “art of folding.” Many families used origami as a coat of arms. Then mass production of paper began, its prices fell, and origami penetrated into the life of the nobility. It was then that the art of the samurai appeared. Knowledge of origami has become a sign of education and good manners. Notes folded in the shape of a butterfly, flower or crane were a symbol of friendship and love. They expressed what words sometimes cannot say. Sometimes the note was folded in such a way that only an initiate could open it. It was considered a sign of good manners when a nobleman could entertain his lady at a ball with his ability to fold paper figures. Origami was used to decorate the home, at weddings or festive processions. Many families used origami as a coat of arms.
During the Azuchi-Momoyama (1573-1603) and Edo (1603-1867) periods, origami was a common way to pass the time. New figures are being invented, and among them is the famous Japanese crane - a symbol of happiness and longevity. It was believed that if a patient folded a thousand paper cranes, then all his illnesses would go away.
In the second half of the 19th century, the history of the development of origami reached the European level. Europeans became acquainted with Japanese paper figures: rice flower, fish, frog, crane. The history of paper origami does not only belong to Japan. The Spaniards, for example, thought of making some paper figures on their own. Among them, Spanish birds - "pajaritas" - stand out. The "Spanish school" spread in the countries of South America. It highlights the name of Miguel Umanumo, who is the creator of many figurines. He even published two books on origami. In France, origami appeared on the scene. A blank sheet of paper in the hands of a magician turned into a bird with flapping wings. The history of the origin of origami in Russia has not been fully researched, but it is known that origami was one of children’s favorite activities. Due to the high cost of paper, the history of origami moved very slowly towards its goal. further development. Instead of paper, they folded fabric, such as collars, caps, and often headdresses worn by maids, monks, and sisters of mercy.
It is worth noting the names of famous people, origami lovers, from whose hands many wonderful paper figures came out. This is Leonardo da Vinci, Lewis Carroll, Houdini. It is known that Leo Tolstoy is a great expert in origami.
The real history of origami creation began after World War II thanks to the activities of Akira Yoshizawa. The history of the origin of origami is connected with the name of this internationally recognized master. During the war, he was an employee of a military factory and dreamed of doing origami professionally. After the war, enduring hunger and poverty, Akira Yoshizawa invented hundreds of amazing figurines. He proved that art can be copyrighted and invented conventional folding signs that can be represented in the form of drawings - drawings. Thus, the process of folding certain figures was recorded on paper. Game skills could be recorded and transferred to other people. In any professional edition of a book on origami you can find a description of these signs.
The history of the emergence of modular origami again dates back to Japan. This type of origami folding technique uses several sheets of paper. Each sheet is folded into a separate module, and then the modules are connected to each other by folding them into each other. This is a complex but very beautiful type of origami. The history of modular origami is partially reflected in the book "Ranma Zushiki" by Hayato Ohoko in 1734. It contains an engraving that depicts a group of traditional origami models. One of these models is the cube. It is shown in two angles, and in the explanation it is called a “magical treasure chest.” The history of modular origami is noted in Isao Honda's book "The World of Origami", which also mentions a cube model, but this model is called the "Cubic Box". Notable models of Chinese modular origami are the lotus and the pagoda.
The history of the development of origami continues to this day.
Materials and tools
To make a swan figurine I needed:
1.Glue stick.
2. Scissors.
3.Paper (12 sheets): white - 10 sheets, red - 1 sheet,
black - 1 sheet.
To make a peacock tail:
1.Glue stick.
2. Scissors.
3. Paper (10 sheets): white - 7 sheets, red - 1 sheet,
yellow - 2 sheets
let your hands
work wonders...
Technology for making a peacock figurine (based on a swan)
Manufacturing of modules:
The module is made of a rectangular sheet of paper, aspect ratio
the rectangle should be about 1:1.5, you can make the necessary
rectangles by dividing the format sheet into equal parts.
Swan can be made in different sizes, so choose rectangles
at your discretion.
1. Place the rectangle with the back side facing you, bend the rectangle in half.
2.To mark the middle of the rectangle, bend and straighten the leaf.
3. Fold the edges of the leaf towards the middle. (At this stage you can unfold
part “mountain” towards you and bend the edges towards the middle of the leaf on the other side.)
4.Turn over.
5.Fold the corners (between the folded corner and the top rectangle
It is advisable to leave a small gap).
6. Fold the edges up.
7. Fold the triangle.
8. The module that was made has 2 corners and 2 pockets.
We connect the modules in two stages:
1. We create a design for a swan figurine (description and photo we use the website http://www.liveinternet.ru/users/sem_9011/post2595455072. 2. We create a design for a peacock’s tail (my design) This swan, made from paper modules, is the most easy to make.To make it you will need 458 white paper triangles and 1 red (you can replace it with orange or yellow) for the beak.
Swan made of modules. Scheme.
Let's start making a swan from modules:
1. Make the first two rows. Place the three modules as shown in the picture.
Insert the corners of two triangular modules into the pockets of the third. You will get this design.
2. Prepare two more modules and insert them into the structure made earlier.
3. In the same style we connect two new modules. But this design is quite unstable and can very easily fall apart. In order for everything to work out as it should, you should collect three rows at once.
4. Add a third row and make the structure even stronger.
The design should look like this. One row of it is made of 30 modules.
5. Just like you did the third row, do the fourth and fifth.
6. Now you need to carefully take the entire structure with two fingers and press on its middle with your thumbs so that it turns out
7. Now bend the edges of the structure upward to get the shape shown in the picture.
This is what it looks like from the side.
And here's what it looks like from below.
8. We put on the 6th row of modules in the same way as before.
9. When Row 7 begins, get ready to give your paper swan wings. First you need to attach 12 modules of the eighth row to the structure. Next, skip two modules and attach 12 more modules. Where you missed 2 modules will be the neck, and in the other empty area you will build the tail.
10. Start building the 9th row, reducing each swan wing by one triangle.
This is what it looks like from the side
11. Continue building the wings, decreasing the row by one module until there is only one module left.
12. Making the swan's tail. Also reduce the row by one module.
13. Making the neck and head. Prepare 19 white and 1 red modules, in which you need to glue the corners to make a beak. To make a neck, you first need to arrange two modules as shown in the picture, and then insert the corners of one module into the pockets of the other.
14. The final touch - you need to place the neck on the remaining two corners between the swan's wings.
That's all!
Peacock tail. Scheme
1,2 row. We connect 21 modules together.
3rd row. We connect the modules with alternating colors (2 white, 1 yellow).
4 row. From the beginning we skip the corner and repeat row 3.
5 row. Repeat 4 rows.
6th row. From the beginning we skip the corner, connect the modules alternating
(2 white, 1 yellow, 1 white), skip 2 corners, alternate (1 yellow,
2 white, 1 yellow) so we connect to the end.
7th row. We skip the corner, connect the modules alternating (2 white,
1 yellow); (1 yellow, 2 white), so connect to the end.
8 row. We skip the corner, connect the modules alternating (2 white.
1 yellow), (1 yellow, 2 white), (1 white, 1 yellow, 1 white), so we connect
to end.
9 row. We skip the corner, connect the modules alternating (2 white,
1 yellow, 1 white), (1 white, 1 yellow) .
10 row. We connect the modules alternating (1 white, skip a corner
yellow, skip a corner, white).
Feathers.Connection of structural parts.
We put 1.7 white modules on top of each other.
2. We put 2 modules on the module of the 7th row, each on a corner. According to this scheme
we make 3 feathers.
3. Place feathers on the missing corners of the tail. (alternate red and white.
4. We put 2 yellow modules on the head module (with the addition of glue).
5. Connect the peacock’s tail with the figurine. The product is ready!
Environmental justification for the project.
Environmentally friendly material was used to manufacture the product -
paper. We also used glue that has a certified
a trademark confirming that this material does not cause harm
environment
Economic calculations.
Conclusion.
The novelty of the work lies in the fact that it created its own model of a peacock,
using modular origami technique with partial use of instructions
and schemes. Having experience in making various products, I can make changes to various designs, as well as create my own models.
The practical significance of the work is justified by the fact that the products made
using this technique can serve as decoration for the interior of a school or home,
a gift to family and friends, as well as being works for participation
in decorative and applied arts competitions.
Sources and literature.
1.Zgurskaya M.P. Series “Master Class” Origami. Kharkov.Folio.2011.
2. Prosnyakova T.N. “Funny figures. Modular origami, M.AST-PRESS-
4. http://www.vlasta-idea.ru/articles/istoriya_origami.htm
Application
My development. Peacock.
Peacock tail 
My collection:
Origami Author: Karimov Emil Almazovich, 4th grade, MBOU for DDMSHV “Primary school- kindergarten" With. Nachalovo Teacher: Krasilnikova Rashida Kurmashevna, 2012. Goal: to master the origami technique and use it in life. Objectives: - study the history of origami; - familiarization with origami techniques; - learn to create origami products; - identify the connection between origami and geometry; - find ways to use origami in everyday life. Relevance: The ability to be creative is a distinctive feature of man, thanks to which he can live in unity with nature; everything created by the creator has always been and will be unique, original and valuable. Manual artistic work is a means of developing the sphere of feelings, aesthetic taste, reason, and creative powers. This is the main relevance of this topic. A little about the history of its origin. Origami is the Japanese art of paper folding. Origami originated in the Heian era (794-1185). Origami emerged as a ceremonial art. In temples, special sanbo boxes were made from paper, into which sacrifices were placed - pieces of fish and vegetables. During the Kamakura (1185-1333) and Muromachi (1333-1573) periods, origami was symbolic (notes in the form of butterflies...) During the Azuchi-Momoyami (1573-1603) and Edo (1603-1867) periods, origami was a way of spending time. Europe became acquainted with origami in 1853. The explosion in popularity of origami occurred after World War II thanks to Akiro Yoshizawa, who made an invaluable contribution to the development of this art. Origami today. Directions and schools of origami were divided into three movements: 1. Traditional origami - adherents use a traditional square as a basis. 2. Followers of this movement fold figures from sheets of triangular, rectangular, hexagonal and octagonal shapes. 3. Modular origami - making models from a certain number of similar modules. Conclusion: Origami: - teaches various techniques for working with paper; - develops the ability to work with hands; - teaches concentration; - introduces basic geometric concepts; - develops spatial imagination, artistic taste and creativity. References: 1. N. G. Yurina. Based on the book “I know the world” 2. http://www.origami.ru 3. Vygonov V.V. Primary school: Labor training: Crafts, models, toys: A book for teachers. - M.: Publishing house “First of September” , 2002. 4. Vygonov V.V. Primary school: Labor training: Crafts, models, toys: A book for teachers. - M.: Publishing House “First of September”, 2003. 5. Serzhantova T.B. Origami. The best models.-M.: Iris-press, 2003. 6. Serzhantova T.B. Origami for the whole family.-M.: Iris-press, 2004. 7. Shcheglov O. Origami. The magical world of paper. New origami book. Rostov n/a: Publishing House “Vladis” M.: Publishing House “Ripol Classic”, 2007.
Completed by a student of class 2 "A" Muller Artem Teacher: Alekseeva E. N. 2015 GBOU secondary school "Education Center" village. Varlamovo Project
Problem: I wanted to know what origami is.
Goal: To study the topic “Origami”.
Read literature in which authors talk about origami. Collect interesting patterns for making crafts using the Origami technique. Make several works using this technique. Design a project and prepare a presentation for a speech on the topic “Origami”. Tasks:
Origami is the art of folding paper figures. The word "origami" translated from Japanese means "folded paper". At first, only the Japanese were involved in origami, but now both children and adults living in different countries. Clubs and circles of paper folding enthusiasts have formed, and a lot of literature on the art of origami is published.
Origami was born in Japan. Despite the fact that the paper itself appeared in China, it was in Japan that they figured out how to fold amazingly beautiful figures out of it. Perhaps the fact that in Japanese the words “paper” and “god” are very similar also played a role here. The word origami is made up of two hieroglyphs: ori - “paper” and kami - “folding”. In the early days, origami was used in temple rituals. For example, pieces of fish and vegetables intended as gifts to the gods were placed in sanbo paper boxes. After some time, the ability to fold paper figures became an obligatory part of the culture of the Japanese aristocracy. This skill was passed down from generation to generation.
Once upon a time on earth there lived a very poor master who devoted his entire life to origami and was amazingly kind to everyone and everything that surrounded him. He spent whole days folding various figures from sheets of paper, and then distributed them to the children. But one day he met a wandering monk on the road and gave him a figurine of a crane. The monk was touched. Then he said: “Stack your figures further. The main thing is your belief in their importance. Even if there is war around, stay true to your art, and it will thank you by making you rich and famous.” Soon, as the monk prophesied, the war began. The young men went off to fight, but there was no end in sight to this horror. Only the poor master stubbornly continued to waste paper on his figures. Angry, the people decided to burn down his workshop. But when they found themselves in it, they were amazed at the variety and splendor of the figures. Then the master gave everyone a figurine according to their liking and taste. In front of the guests, the master folded a crane out of a leaf, which immediately flapped its wings and flew away - he was a messenger of peace. People believed in themselves, were inspired, and soon victory was theirs.
Conclusion: I learned what Origami is and learned how to work according to patterns. While working on the project, I learned how to make crafts using the Origami technique. As a result of my work, I learned a lot of new and interesting things that complement school textbooks. I enjoyed working with adults.
http:// www.yourorigami.ru http://www.myshared.ru http:// www.origami-paper.ru http: //www.yandex.ru http://www.nashydetky.ru http:/ /www.oriart.ru http://www.origamka.ru
Project "Origami is mathematics!" participated in Science Week.
municipal educational institution - secondary school No. 3 in Krasny Kut, Saratov region.
Project on:
"Origami is mathematics!"
The work was completed by: students of class 6 “A” Zakora V.,
Myasnikova V. and student 11 “A” class Ulyanov A.
Head: 1st category mathematics teacher
Rodygina L.N.
Goal and objectives of the project:
Target: Explore the origins of origami and the connection of this art with mathematics.
Tasks:
1. Study the concept, types, history of the origin of origami.
2. Analyze the connection between origami and mathematics using the example of the basic elements of the origami alphabet and solving mathematical problems.
Hypothesis: Does origami help you learn math?
Relevance: Recently, children have become increasingly reluctant to study, and in particular to mathematics. To attract students' attention to mathematics, we decided in our project to show that mathematics is a creative science.
Introduction 3
Chapter 1. Concept of origami 4
1.1. Origami Story 5
1.2. Types and techniques of origami 7
Chapter 2. Origami ABC 9
2.1. Origami is mathematics! 9
2.2. Origametry. eleven
Conclusion 14
Used literature 16
Applications 17
Introduction.
Many people are surprised when they hear the word “origami”. "And what is it?" - they ask. Meanwhile, every person probably at least once in his life created the simplest product from a square sheet of paper - a boat or an airplane. And in those days, when stores did not have such a selection of straw hats and panama hats, people in the summer often made themselves a “cap” from a newspaper. Both the paper boats and the cap are made using the origami principle.
Origami is an amazing art of paper plasticity. Origami is the Japanese art of paper folding, derived from the Japanese oru (to fold) and kami (paper). Today, many people all over the world are interested in the art of origami. Paper figures are made by children and adults, artists and designers. It is even taught in schools, books are written about it and magazines are published with interesting articles and descriptions of various models. We noticed that when folding origami figures, we encountered mathematical concepts. We became interested in how the mysterious art of folding origami paper figures and mathematics, which has long interested us, are connected.
Chapter 1. The concept of origami
This art was born in Japan. The Japanese Chronicle says that its beginning dates back to the year 610. Who would have thought, looking at a simple boat, that initially a lot of meaning was put into products made from a paper square! In the east, the square was treated with great respect. In Buddhism, it was considered a reflection of the Cosmos, that great Emptiness from which all things come. The Japanese also treated paper with respect, as everything short-lived, fragile, living for a moment. They believed that in every such thing - a butterfly, a dewdrop, a thin piece of paper - there lives the breath of eternity and one must be able to catch it.
Thus, the square - a symbol of the Cosmos, from which things come to Earth and take shape, and paper - a moment in which the breath of eternity is contained, became the parents of origami. And, really, isn’t it a miracle: to make anything you want without scissors and glue, without any improvised means, from a simple sheet of paper: a person, an animal, a bird, a flower, a fairy-tale dragon...
Over time, the art of origami conquered the whole world. It has reached us too. Even the great Leo Tolstoy described in his article “What is Art” a case when he was taught “to make out of paper, folding and turning it in a certain way, cockerels, which, when you pull them by the tail, flap their wings.”
A description of a simple, child-friendly model can be found in every issue of the Japan magazine. And in the Russian magazine "Origami", to which you can freely subscribe, you will find the simplest models - for beginners, and complex ones - for experts, as well as articles about the history of "origami", and the latest news.
Now the original philosophical meaning of this toy has been forgotten. In addition to traditional square crafts, many other ways of creating paper figures have been invented. These can be models made up of a regular triangle and half a square, torn off vertically or diagonally, or even from pentagons, hexagons, or octagons. The latest “fashion” is to fold origami from a sheet of regular standard-sized writing paper.
They also make models woven from endless tape - this is where origami turns into macrame. The method of making models from many identical parts (modules) has also completely departed from the traditional “origami”. So, from several squares you can make a beautiful bracelet or even a tiara.
Nowadays, origami has ceased to be just a toy. Scientists and designers became interested in this art. Scientific symposiums on origami are held. The most complex technical structures are already being created - paper models...
But children, of course, are most interested in origami as an opportunity to create a new toy. Or you can create new, your own three-dimensional paper figures.
So, origami is the art of paper folding.
1.1. History of origami
Getting acquainted with origami should begin with ancient history. It was there, in Ancient China, in 105 AD, that the first prerequisites for the emergence of origami appeared - the art of folding any figures from a square sheet of paper without the use of scissors and glue.
As history shows, in that significant year, the official Tsai Lun made an official report to the emperor that a paper production technology had been created. For many decades, under pain of death, the Chinese kept the secret of creating a white sheet. But over time, when the monks of China began their travels to Japan, some of the secrets of this country began to travel with them. In the 7th century, the wandering Buddhist monk Dan-Ho, whom contemporaries said was rich in knowledge and knew how to make ink and paper, made his way to Japan and taught monks how to make paper using Chinese technology. Very soon, Japan was able to establish its own mass production of paper, largely ahead of China.
The first pieces of paper folded into unusual figures appear first in monasteries. It couldn't be any other way. Indeed, in Japanese, the concepts “God” and “Paper” sound the same, although they are denoted by different hieroglyphs. Paper figures had a symbolic meaning. They became participants in religious ceremonies. They decorated the walls of temples. They were placed on the sacrificial fire. One of the first paper figurines that have survived to this day are “sanbo” boxes, into which the Japanese put pieces of fish and vegetables, offering them as sacrifices. But it was not art yet. Just a piece of paper, very valuable and expensive, bearing the name of God, became an integral part of the life of the Japanese.
In the Middle Ages, when paper production made it possible to reduce its price, the art of folding penetrated into the life of the nobility. And then the art of the samurai appeared. In those days, it was considered a sign of good upbringing for a rich nobleman to be able to entertain his lady at a ball by folding paper figures. At the same time, the art of folding secret letters arose. Using their skill, the samurai folded their notes in such a way that only an initiate could unfold it. In addition, origami figurines were often used in wedding ceremonies, home decorations, or festive processions.
Over time, origami (and this term appeared only in 1880) became a mandatory activity in many Japanese families. Mothers passed on their knowledge to their daughters, showing the few figures they knew.
The revival of origami is also closely connected with the terrible tragedy that occurred on August 6, 1945, when “people” decided to test an atomic bomb on a person, signing a death warrant for the city of Hiroshima. The consequences of the monstrous experiment were terrible: out of 420 thousand residents of the city, 80 thousand died. Within 20 years, another 200 thousand people died from the effects of radiation. There were many children among the dead.
In memory of the victims of the atomic bombing, the Peace Park was founded in Hiroshima. In May 1958, a monument dedicated to the dead children was unveiled there. The monument depicts a bomb, on top and on the sides of which there are figures of children with their hands raised to the sky.
It was then that among the children doomed to death, a belief arose about a free bird, a symbol of life - the crane. The children sincerely believed that by making 1000 cranes out of paper, they would be healed and remain alive. The twelve-year-old girl, whose death was the reason for the construction of the monument, managed to make only 644 cranes. Amazing children's solidarity swept across all countries of the world. Japan began to receive millions of parcels from all continents with priceless cargo - paper cranes, collected in garlands of 1000 pieces. These garlands still adorn the monument today and are a protest against the war and a reproach to adults.
1.2. Types and techniques of origami
Modular origami
One of the popular types of origami is modular origami, in which a whole figure is assembled from many identical parts (modules). Each module is folded according to the rules of classic origami from one sheet of paper, and then the modules are connected by inserting them into each other, the friction force that appears in this case prevents the structure from falling apart. One of the most common objects in modular origami is kusudama, a three-dimensional spherical body.
Simple origami
Simple origami is a style of origami invented by British origami artist John Smith, which is limited to using only mountain and valley folds. The purpose of origami is to make it easier for inexperienced origami artists, as well as people with limited motor skills. The above limitation means the impossibility of many (but not all) complex techniques familiar to ordinary origami, which forces the development of new methods that give similar effects.
Flat folding
Scan (English creasepattern; fold pattern) is one of the types of origami diagrams, which is a drawing that shows all the folds of the finished model. Folding using a development pattern is more complicated than folding according to a traditional pattern, however, this method provides not just information on how to fold the model, but also how it was invented - the fact is that developments are used in the development of new origami models. The latter also makes obvious the fact that for some models there are no diagrams other than the sweep.
Wet folding
Wet folding is a folding technique developed by Akira Yoshizawa that uses paper moistened with water to give figures smooth lines, expressiveness, and rigidity. This method is especially relevant for such non-geometric objects as figures of animals and flowers - in this case they look much more natural and closer to the original.
Not all paper is suitable for wet folding, but only those to which water-soluble glue is added during production to hold the fibers together. As a rule, thick types of paper have this property.
Chapter 2. ABC of origami.
In the international literature on origami, a certain set of conventional signs has long been formed, necessary in order to sketch the folding diagram of even the most complex product. Conventional signs play the role of a kind of “notes”, following which you can reproduce any work. Every origamist should know these signs and be able to use them for writing. In addition to signs, there is a small set of techniques that occur quite often. Usually they are given in books without commentary. It is believed that any beginner can perform them in practice. International conventional signs, together with a set of simple techniques, make up a kind of origami “alphabet”, which any folder should be familiar with. Most of the conventional signs were introduced into practice in the middle of the 20th century by the famous Japanese master Akira Yoshizawa. In recent decades, several new ones have been added to these signs. The introduction of any additional notation should be treated very carefully, and, of course, you should not “reinvent the wheel” and try to write down folding patterns in your own way. All symbols in origami can be divided into lines, arrows and signs. ( Annex 1.)
2.1. Origami is mathematics!
Many people think that origami is a fun activity with which people create various shapes, but a lot of origami has to do with mathematics. Origami is associated with geometry, origami, as a science, can amaze us with shapes, the possibility of whose existence we may not have even guessed.
In the process of folding origami figures, we get acquainted with various geometric shapes: triangle, square, trapezoid, etc., we learn to easily navigate in space and on a sheet of paper, divide the whole into parts, find the vertical, horizontal, diagonal, and learn much more that relates to geometry and mathematics. The American teacher F. Frebel already in the middle of the 19th century noticed the geometric feature of origami and introduced it as a school subject.
The first attempts to use origami in pedagogical practice in Europe are rightly associated with the name of the German humanist Friedrich Wilhelm August Froebel (1792-1852). It was he who began to create kindergartens and then a school at the beginning of the 19th century. Froebel considered Nature the best teacher. At first he himself was a forester, he loved and appreciated nature very much, and therefore did not want children to engage in cramming at school. Frebel believed that life, movement and knowledge are the three main components of Human development. His theory of views on education and personal development includes 4 main components:
1. Free activity.
2. Creativity.
3. Participation in society.
4. Muscle activity.
For example, he proposed studying the basics of geometry not with the help of compasses, rulers and some concepts, but using the example of figures of folding paper. He actively introduced origami into the pedagogical process. Unfortunately, at that time Froebel did not have the same technique of folding figures as he does now. But the system of his kindergartens survived, already in 1892 a special Froebel College was founded in England, there were also in America, Japan, and many Asian countries.
Froebel's ideas are still very interesting today. It is not surprising, therefore, that today origami continues to play a certain role in development and education. Origami promotes the activity of both the left and right hemispheres of the brain, as it requires simultaneous control of the movements of both hands.
At the end of the 20th century a new term arose "origametry" denoting a region of geometry in which problems can be solved only by folding.
One of these tasks is dividing the original square without preliminary drawings and measurements. How to do this without using a pencil? Let's give examples of dividing a square sheet of paper into two, three, four, ... ten equal parts. ( Appendix 2. )
Nowadays, origami with mathematical precision is moving across the planet by leaps and bounds. Scientists have come up with the idea of using origami techniques in space, namely Miura-ori, a rigid folding pattern that has been used to deploy large solar array installations on space satellites.
Mathematics is one of the aspects of origami and, on the contrary, origami is one of the guiding principles of mathematics.
2.2. Origametry.
Origami is used in geometry to prove theorems and solve problems. Solving problems using origami is an unusual and interesting method, since many concepts in a school geometry course are simply and clearly explained by demonstrating origami. Origametry – the field is very young, and so far there are no corresponding programs or textbooks that would provide such material systematically. At the same time, many concepts of the geometry course at school are much simpler and more clearly explained with the help of origametry.
To build the theory, a system is used axioms . Indeed, the axioms of origametry exist! They were proposed by the Japanese mathematician HumianiHuzita, who lives in Italy. From his point of view, there are only six such axioms.
Axiom 1. There is a single bend passing through two given points.
Axiom 2. There is a single fold that combines these two points.
Axiom 3. There is a single fold that combines these two straight lines.
Axiom 4. There is a single bend passing through a given point and perpendicular to a given line.
Axiom 5. There is a single bend that passes through a given point and places another given point on a given line.
Axiom 6. There is a single bend that places each of two given points on one of two given intersecting lines.
In 2002, Japanese origamist Koshiro Hatori discovered a bend that is not described in the axioms of H. Husit.
Axiom 7. For two given lines and a point, there is a fold line. Perpendicular to the first line and placing the given point on the second line.
Proving theorems using origami.
Theorem 1. The sum of the angles of any triangle is 180 degrees.
Proof. Take a sheet of paper that has the shape of an arbitrary triangle.
1) Draw a fold through one of the vertices of the triangle, perpendicular to the opposite side (the height of the triangle).
2) Align the vertices of the triangle with the point at the base of the altitude of the triangle.
3) We find that angles 1, 2 and 3 of the triangle coincide when superimposed with the unfolded angle, therefore, the sum of the angles is equal to 180 degrees.
Theorem 2. Crosswise angles formed when two parallel lines intersect with a transversal are equal.
Proof. 1) Take a sheet of paper with two parallel sides and a secant AB. Let's compare the lying angles - angles 1 and 2.
2) Let's combine the vertices crosswise of the lying corners - points A and B.
3) Angles 1 and 2 coincide when superimposed, therefore, angle 1 is equal to angle 2. This means that the crosswise angles formed when two parallel lines intersect with a transversal are equal.
Task: A line passing through the middle of the bisector AD of triangle ABC and perpendicular to AD intersects side AC at point M. Prove that MD //AB.
Solution: Let's take a sheet of paper that has the shape of a derivative triangle. Let's draw a bisector AD by bending the sheet so that side AC aligns with side AB. Let's mark the middle of AD, combining points A and D. Let's draw OM perpendicular to AD. Let's bend the sheet along the line MD. To prove the parallelism of MD and AB, compare angles 1 and 3, to do this, bend the sheet along AD and combine points A and D. Angles 1 and 3 coincide, and they lie crosswise, therefore, MD // AB.
Conclusion.
Origami and mathematics are like two sisters who do not tolerate inaccuracy and haste. Origami itself gives flights of fantasy, and mathematics dresses this fantasy in the dress of science.
The Japanese art of origami has very widely entered our Russian life and has become an integral part for intellectual and cognitive development. According to the results of a survey in our school, both teachers and students believe that origami primarily contributes to the development of mathematical qualities (observation, attention and volition, logical and spatial thinking, accuracy and precision) of a person. This skill is necessary both in the main lessons - mathematics (geometry, stereometry), fine arts, labor, and in additional elective classes and clubs. (Appendix 4.)
While studying this topic, we were able to touch the secrets of origami and understand the meaning of mathematical principles in paper plastic. Carrying out geometric figures in the origami technique, students become acquainted with new geometric concepts, basic definitions, and visually study the patterns of behavior of a two-dimensional plane in three-dimensional space. So origami really helps to study mathematics.
Origami is a family, collective leisure activity that brings people together and improves the psychological background of the family and the team. Each origami figure has its own story, its own legend and many options for use in life.
References:
1. Afonkin S.Yu., Afonkina E.Yu. All about origami/Handbook. St. Petersburg: publishing house Crystal, M: “Onyx”, 2005
2. N. G. Yurina. Based on the book “I Explore the World”, 2004
3. O. V. VesnovskayaOrigami: ornaments, kusudama, polyhedra . -Cheb.: ed. "Russika", 2003
4. S. N. Belim Geometry problems solved by origami methods. – M.: ed. "Akim", 1998,
5. Yu.I. Dorogov, E.Yu. Dorogova “Origami step by step”, 2008
6. Takahashi Koki “Origami is mathematics!”
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