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Origami project. Project on the theme "origami"

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Project "Modular origami and mathematics"
Prepared by students of the 6th grade of MBOU "Oboyan secondary school No. 2" Project leader: mathematics teacher Maltseva N.V.

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Project participants

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Hypothesis: The art of origami is related to mathematics.

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Objective of the project:
Get to know the history of origami art Learn to work with additional literature Organize an exhibition of works Establish a connection between origami art and mathematics

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Subject and object of research Object: connection between the art of origami and mathematics. Subject: sheet of paper. Research methods Search for information from various sources (special literature, Internet resources). Practical work.

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To achieve the goal and test hypotheses, it is necessary to solve the following tasks: 1. Analyze literary sources on the topic of our study. 2. Compose an experimental model from modules. 3. Carry out measurements and necessary calculations. 4. Draw conclusions about the work done.

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History of paper
Chinese chronicles report that paper was invented in 105 AD. e. Tsai Lun. Cai Lun crushed mulberry fibers, wood ash, rags and hemp. He mixed all this with water and laid out the resulting mass on a mold (wooden frame and bamboo sieve). After drying in the sun, he smoothed this mass with the help of stones. The result is strong sheets of paper.

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History of paper
In the VI - VII centuries. AD Fei-Tien (“flying coins”) paper money was already in circulation in China. It was the first paper money in the history of mankind. In the VI century. AD China already makes real paper books.

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What is ORIGAMI?
translated from Japanese (折り紙) means "folded paper". ORI - instantly folded KAMI - divine paper
折り紙

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History of origami
Origami is an original Japanese art of creating models of various objects, animals, birds, flowers by folding a sheet of paper.

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History of origami
Origami is the ancient art of paper folding. The art of origami has its roots in ancient China, where paper was invented. Initially, origami was used in religious ceremonies. For a long time, this type of art was available only to representatives of the upper classes, where a sign of good taste was the possession of paper folding techniques.

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History of origami
The first unusual figures folded from sheets of paper appeared in monasteries. In Japanese, the word "God" and "paper" sound the same, although they are denoted by different hieroglyphs. Paper figurines have a symbolic meaning. And not only the Japanese used paper for folding - long before them, the Chinese already did it. paper folding it became known in the Japanese version - origami.

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From ordinary paper, the Japanese can work wonders. The paper figures they made decorate temples and dwellings.

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In Japan paper balls-kusudamas, cranes are talismans and bring happiness. Therefore, they are often given as gifts and hung as decorations during folk holidays.

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The Japanese master Akira Yoshizawa was the first to come up with the idea of drawing patterns for folding figures.

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There are three main streams in origami: The first stream is traditional origami, where a square is used as a basis. The second trend - the models are made up of sheets of triangular, rectangular, five-, six-, octagonal shapes. The third trend is modular origami, models are made from some, sometimes quite a large number of the same type of modules.

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modular origami
Modular origami gained popularity in 1993 Features of this technique: the use of a fairly simple triangular module; a typical way of connecting modules (modules are connected by nesting them into each other); Very a large number of modules, which makes it easier to create large models with a complex structure. Models modular origami can be both flat and three-dimensional.

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The meaning of origami for us
teaches various techniques for working with paper; introduces basic geometric concepts; stimulates the development of attention, memory, spatial imagination; develops fine motor skills hands and eye; helps to form the ability to follow oral instructions, read and draw product diagrams; develops artistic taste and Creative skills; contributes to the creation game situations, expands communication skills; improves labor skills, forms a culture of work, teaches accuracy.

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Origami and Mathematics Japanese wisdom says: "The great square has no limits." Try to fold a simple figure, And in an instant you will be carried away by an interesting thing. Figures in origami are made from geometric shapes, so this is one of the points of contact of origami with mathematics.

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Technological stage
Tell me - I will hear, Show me - I will remember, Let me do it myself - I will understand! ”... Japanese proverb

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A4 paper can be divided into an equal number of rectangles

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DIAGRAM How to fold a triangular origami module 1. Put the rectangle with the back side towards you. Bend in half. 2. Bend and straighten to outline the middle line. 3. Bend the edges towards the middle. (like an airplane). 4. Turn over.

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5. Fold up the corners. (Please note: it is better to leave a small gap between the folded corner and the upper triangle). 6. Raise the edges up 7. Fold the triangle The resulting module has two corners and two pockets. Modules are inserted into each other, collecting row by row.

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Making a swan

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Mathematical calculations
Sheet size A4 210 * 297 mm S = 62370 mm2 = 623.7 cm2
The size of one rectangle is 52.5*74.25mm S=3898.125mm2=38.98125cm2
Number of white modules 2500 pcs =150 sheets A4 S =9355500mm2=93555cm2
Number of modules pink 100 pcs =7 sheets A4 S=436590mm2=4365.9cm2
Number of red modules 1 module 52.5*74.25mm2 S=3898.12mm2=38.9812cm2
Total 158 sheets S=97959.88125cm2=9.8m2

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Mathematical calculations
Economic component: White paper - 0 rubles; colored paper - 8 sheets of 1.5 rubles each, total 12 rubles.

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Mathematical calculations
S= a ∙ b

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Mathematical calculations
The surface area of the swan is 1377.35 cm2, which is 71.127 times less than the area of the used paper.

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Mathematical calculations
Total spent 8605 modules, 513 sheets of paper, which is 31.9 m2.

Project "Origami is Mathematics!" participated in Science Week.

municipal educational institution - secondary school No. 3 of the city of Krasny Kut, Saratov region.

Project on:

"Origami is math!"

The work was completed by: students of class 6 "A" Zakora V.,

Myasnikova V. and student 11 "A" class Ulyanov A.

Head: mathematics teacher of the 1st category

Rodygina L.N.

Purpose and objectives of the project:

Target: To study the origin of origami and the relationship of this art with mathematics.

Tasks:

1. To study the concept, types, history of the origin of origami.

2. Analyze the connection between origami and mathematics using the basic elements of the origami alphabet, solving mathematical problems as an example.

Hypothesis: Does origami help you learn math?

Relevance: Recently, the guys are increasingly reluctant to study, and in particular to mathematics. In order to draw students' attention to mathematics, we decided in our project to show that mathematics is a creative science.

Introduction 3

Chapter 1. The concept of origami 4

1.1. Origami story 5

1.2. Types and techniques of origami 7

Chapter 2

2.1. Origami is math! 9

2.2. Origametry. eleven

Conclusion 14

References 16

Apps 17

Introduction.

Many people are surprised when they hear the word "origami". "And what is it?" they ask. Meanwhile, every person for sure at least once in his life created the simplest product from a square sheet of paper - this is a boat or an airplane. And in those days when the shops did not have such a choice of straw hats and panama hats, people often built themselves a "cap" from the newspaper in the summer. AND paper boats, and the cap are made according to the principle of "origami".

Origami is an amazing art of paper plastics. Origami is the Japanese art of paper folding, derived from the Japanese oru (to fold) and kami (paper). Today, many people around the world are addicted to 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 have noticed that when folding origami figures, we encounter mathematical concepts. We became interested in how the mysterious art of folding origami paper figures is connected with mathematics that has long interested us.

Chapter 1

This art was born in Japan. The "Japanese Chronicles" says that its beginning dates back to the year 610. Who would have thought, looking at a simple boat, that initially a lot of sense was invested in paper square products! In the east, the square was treated with great respect. In Buddhism, he was considered a reflection of the Cosmos, that great Void 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 - the breath of eternity lives and one must be able to catch it.

So, the square - a symbol of the Cosmos, from which things come to Earth and take shape, and paper - the moment in which the breath of eternity is contained, became the parents of origami. And, really, isn’t it a miracle: to make anything without scissors and glue, without any improvised means, from a simple paper sheet: a person, an animal, a bird, a flower, a fabulous dragon ...

Over time, the art of "origami" conquered the whole world. It has come to us. 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 their tail, flap their wings.”

A description of a simple, child-friendly model can be found in every issue of Japan magazine. And in the Russian magazine "Origami", which you can freely subscribe to, you will find the simplest models - for beginners, and complex ones - for connoisseurs, 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 to create paper figures have been invented. These can be models composed of a regular triangle and half a square, torn off vertically or diagonally, or even from five-, six-, octagons. The latest "fashion" is to fold origami from a sheet of ordinary writing paper of a standard size.

They also make models woven from an endless ribbon - here origami goes into macrame. The way to make 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 diadem.

Nowadays, origami is no longer just a toy. Scientists and designers became interested in this art. There are scientific symposiums on origami. 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 new toy. And you can create new, your own voluminous paper figures.

So, origami is the art of paper folding.

1.1. History of origami

Acquaintance 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 Cai Lun made an official report to the emperor that 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, about whom contemporaries said that he was rich in knowledge and knew how to make ink and paper, made his way to Japan and taught the monks how to make paper using Chinese technology. Very soon, Japan managed to establish its own mass production of paper, in many ways overtaking China.

The first pieces of paper folded into unusual figures appear first in monasteries. It couldn't be otherwise. Indeed, in Japanese, the concepts of "God" and "Paper" sound the same, although they are denoted by different hieroglyphs. Paper figurines had a symbolic meaning. They became participants in religious ceremonies. They decorated the walls of temples. They were placed on a sacrificial fire. One of the first paper figures has survived to this day - the "sanbo" boxes, in which the Japanese put pieces of fish and vegetables, offering them as sacrifices. But it wasn't art yet. Just a sheet 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 the production of paper made it possible to reduce its price, the art of folding penetrated the life of the nobility. And then the art of the samurai appeared. In those days, the ability of a wealthy nobleman to entertain his lady at a ball by folding paper figures was considered a sign of good upbringing. 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, origam figurines were often used in wedding ceremonies, home decorations, or festive processions.

Over time, origami (and this term appears only in 1880) becomes a mandatory occupation 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 the atomic bomb on a person, signing the death warrant for the city of Hiroshima. The consequences of the monstrous experiment were terrible: out of 420 thousand inhabitants of the city, 80 thousand died. Within 20 years, another 200 thousand people died from the effects of radiation. Among the dead were many children.

Peace Park was laid in memory of the victims of the atomic bombing in Hiroshima. In May 1958, a monument dedicated to the dead children was opened there. The monument depicts a bomb, on the 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 - a crane. The children sincerely believed that by making 1000 cranes out of paper, they would be healed and stay alive. The twelve-year-old girl whose death prompted the construction of the monument managed to make only 644 cranes. Amazing children's solidarity swept like a wave across all countries of the world. Japan began to receive millions of parcels from all continents with an invaluable cargo - paper cranes, collected in garlands of 1000 pieces. These garlands adorn the monument even 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 varieties of origami is modular origami, in which the whole figure is assembled from many identical parts (modules). Each module is folded according to the rules of classical 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 does not allow the structure to fall apart. One of the most common objects of 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 limitation given above means that many (but not all) of the complex techniques familiar to ordinary origami are impossible, which forces the development of new methods that give similar effects.

Reamer folding

Development (English creasepattern; pattern of folds) is one of the types of origami diagrams, which is a drawing that shows all the folds of the finished model. Folding according to a sweep is more complicated than folding according to the traditional scheme, however, this method provides not only information on how to fold the model, but also how it was invented - the fact is that sweeps are used in the development of new origami models. The latter also makes it obvious that for some models there are no diagrams other than a sweep.

Wet folding

Wet Folding is a folding technique developed by Akira Yoshizawa that uses paper soaked in water to give figurines 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 the one to which a water-soluble adhesive is added during production to bind the fibers. As a rule, dense grades of paper have this property.

Chapter 2

In the international literature on origami, a certain set of conventional symbols has long been formed, which are necessary in order to sketch the folding scheme 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 records. In addition to signs, there is a small set of tricks that are quite common. Usually they are given in books without comments. It is believed that any beginner knows how to perform them in practice. International conventional signs, together with a set of simple tricks, make up a kind of origami "alphabet" that any folder should be familiar with. Most of the conventional signs were put into practice in the middle of the 20th century by the famous Japanese master Akira Yoshizawa. In recent decades, several new signs have been added to these signs. The introduction of any additional designations should be treated very carefully, and, of course, it is not at all worth "reinventing the wheel" and trying to write folding schemes somehow in your own way. All symbols in origami can be divided into lines, arrows and signs. ( Annex 1.)

2.1. Origami is math!

Many people think that origami is fun, with which people create various shapes, but a lot of origami is related to mathematics. Origami is associated with geometry, origami, as a science, is able to amaze us with forms, the possibility of the existence of which, perhaps, we did not even know.

In the process of folding origami figures, we get acquainted with various geometric shapes: a triangle, a square, a trapezoid, etc., we learn to easily navigate in space and on a sheet of paper, divide the whole into parts, find a vertical, horizontal, diagonal, learn much more that related to geometry and mathematics. The American teacher F. Fröbel 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 teaching practice in Europe are rightly associated with the name of the German humanist Friedrich Wilhelm August Fröbel (1792-1852). It was he who at the beginning of the 19th century began to create kindergartens, and then a school. Fröbel 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 study by heart at school. Fröbel believed that life, movement and knowledge are the three main components of the development of Man. His theory of views on education and personality development includes 4 main components:

1. Free activity.

2. Creativity.

3. Participation in the life of society.

4. Muscle activity.

For example, he proposed to study the basics of geometry not with the help of a compass, ruler and some concepts, but using the example of folding paper figures. He actively introduced origami into the pedagogical process. Unfortunately, then Fröbel did not master the technique of folding figures as he does now. But the system of his kindergartens survived, already in 1892 a special Frebel College was founded in England, they were also in America, Japan, and in many Asian countries.

Fröbel's ideas are still very interesting today. It is not surprising, therefore, that today origami continues to play a role in the 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 the area of geometry in which problems are solved only by the folding method.

One of these tasks is dividing the original square without preliminary drawings and measurements. How to do this without resorting to 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 walks the planet with leaps and bounds. Scientists came up with the idea of using origami techniques in space, namely Miura-ori, a rigid folding scheme that was used to deploy large arrays of solar panels on space satellites.

Mathematics is one of the sides of origami and vice versa origami is one of the guides of mathematics.

2.2. Origametry.

Origami is used in geometry - to prove theorems and solve problems. Solving problems using orimetry is an unusual and interesting way, since many concepts of a school geometry course are simply and clearly explained by a demonstration of origami. origametry – the area is very young, and so far there are neither appropriate programs nor 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 orimetry.

The system is used to construct the theory axioms . Indeed, the axioms of origametry exist! They were proposed by the Japanese mathematician Humiani Khuzita, who lives in Italy. From his point of view, there are only six such axioms.

Axiom 1. There is only one fold passing through two given points.

Axiom 2. There is a single fold that combines the two given points.

Axiom 3. There is a single fold that combines the two given lines.

Axiom 4. There is a single fold through the given point and perpendicular to the given line.

Axiom 5. There is a single fold passing through a given point and placing another given point on the given line.

Axiom 6. There is a single fold that places each of the two given points on one of the two given intersecting lines.

In 2002, the Japanese origamist Koshiro Hatori discovered a fold that is not described in H. Huzit's axioms.

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 with origami.

Theorem 1. The sum of the angles of any triangle is 180 degrees.

Proof. Take a piece 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) Match the vertices of the triangle with the point at the base of the height of the triangle.

3) We get that the angles 1, 2 and 3 of the triangle coincided when superimposed with a developed angle, therefore, the sum of the angles is 180 degrees.

Theorem 2. Crosswise lying angles formed at the intersection of two parallel lines of a secant are equal.

Proof. 1) Take a sheet of paper with two parallel sides and a secant AB. Let's compare the lying corners - corners 1 and 2.

2) Let's combine the vertices of cross lying corners - points A and B.

3) Angles 1 and 2 coincided when superimposed, therefore, angle 1 is equal to angle 2. Hence, the crosswise angles formed at the intersection of two parallel lines of a secant are equal.

Task: The line passing through the midpoint 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 derived triangle. Draw the bisector AD by bending the sheet so that side AC is aligned with side AB. Let's outline the midpoint of AD by aligning 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, we compare angles 1 and 3, for this we bend the sheet along AD and match 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 inaccuracies and haste. Origami itself gives a flight of fantasy, and mathematics dresses this fantasy in the dress of science.

The Japanese art of origami has entered our Russian life very widely and has become an integral part of the intellectual and cognitive development. According to the results of the survey in our school, both teachers and students believe that origami contributes primarily to the development of mathematical qualities (observation, attention and arbitrariness, logical and spatial thinking, accuracy and accuracy) of a person. This skill is necessary both in the main lessons - mathematics (geometry, stereometry), fine arts, labor, and in additional elective classes, circles. (Appendix 4.)

In the course of studying this topic, we were able to touch the secrets of origami, understand the meaning of mathematical principles in paper plastic. Performing geometric figures using the origami technique, students get 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 family, collective leisure, bringing together, improving the psychological background of the family and the team. Each origami figure has its own story, its own legend and many applications in life.

References:

1. Afonkin S.Yu., Afonkina E.Yu. All about origami/Handbook. St. Petersburg: ed. Kristall, M: "Onyx", 2005

2. N. G. Yurina. Based on the book “I know the world”, 2004

3. O. V. Vesnovskaya Origami: ornaments, kusudama, polyhedrons . -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 math!"

http://www.origami.kulichki.ru/modules.php?name=Pages&go=page&pid=2

Dinara Nurulina
Research project on the topic: “ magic paper. Modular origami»

Yurminsky secondary school

"magic paper. modular origami"

Work completed:

1st grade student

Yurminsky secondary school

Imangulova Adeline.

Supervisor: Nurulina D. Sh.

Research project on the topic: "modular origami"

I.Introduction…. 3

II. Main part…. 4

1. What is origami?

2. modular origami.

3. Why do you need origami?

4. Tools and materials needed for classes origami.

5. Technological sequence of product manufacturing.

6. Safety precautions when working with paper and glue.

7. Conclusion.

III. References ... 9

Introduction

SL I've been looking with loving eyes for a long time

On ancient art - Origami.

Not needed here wizards and mages,

There's nothing to be particularly smart about here.

And you just need to take a leaf paper

And try to put something together.

Rationale for choice project.

Handmade things bring comfort and warmth to our home. I am convinced of this when we visit our aunt. Being at their house, I feel like in a fairy tale. DC3-4 Here are swans, bunnies, duckling, flowers. And all this from a simple color paper made in the technique modular origami.

I also wanted to bring something fresh, new, original in your room, to create coziness and comfort, where I spend a lot of time. Namely, to learn how to create such crafts.

First, I asked my aunt to tell me about the technique of making such beautiful crafts, and then studied the literature on this topic. Then I mastered the technique modular origami.

ST5 Goal project:

create a technical product modular origami.

Tasks project:

1. Learn the history of the emergence of technology « Origami» .

2. Get acquainted with the basic technique of folding the base part - modular triangle.

3. Master the technique « modular origami» .

Problem:

Is it possible to create different products using only one folding scheme?

Hypothesis:

Small module is the key to a great work of art.

Main part

SL6 What is « origami» ?

Mage that invented colored paper

Red, yellow and blue

He believed, probably, that the guys can

Make figures from different squares.

These figurines all over the world

Only Japanese children knew.

The white crane became the symbol of peace,

The symbol of happiness paper boat.

Fairy butterflies, pink hares

You can do it with your fingers.

I suggest to try with you

Learn technique « origami» .

Each person probably at least once in his life created the simplest product from a sheet paper- boat or plane. And in those days when the shops did not have such a choice of straw hats and panamas, people often built themselves in the summer "cap" from the newspaper. AND paper boats, and the cap is made according to the principle « origami» .

Origami is the art of paper plastic born in Japan. Even though she herself paper originated in China, it was in Japan that they guessed to put figures of amazing beauty out of it.

SL 7 Origami is different:

1. Traditional origami, where the square is used as the basis.

2. Models are made up of sheets of triangular, rectangular, five-, six-, octagonal shapes.

3. In modular origami, models are made from a large number of parts of the same type (modules) .

SL 8 What is modular origami?

One of the popular varieties origami is modular origami, in which the whole figure is assembled from many identical parts (modules) . Every module formed according to the rules of the classical origami from one sheet of paper, and then modules connected by inserting them into each other.

Why is it necessary origami?

By using origami you can create various crafts and compositions.

crafts origami – lovely gift, especially if they are made with soul. Origami great for home decoration.

The main working material origami is paper. Paper the most affordable and cheapest material for creativity. Paper is familiar, easily amenable to any changes. A application for folding paper of any quality, allows you to do origami for everyone regardless of age and education.

What tools and materials are needed for classes origami?

Class origami does not require special devices, equipped workplace. Therefore, everyone can fold figures everywhere, in any situation. After all, only hands and a leaf are needed paper.

Which paper for origami?

For origami is better to take such paper, which after bending does not form cracks. Paper must be clean, not mint.

What scissors are needed for origami?

It is desirable to have scissors with rounded ends and developed levers. When using scissors, do not forget about the technique security: do not swing them while working, monitor the position of the left hand, do not work with scissors with loose hinges, put the scissors on the table so that they do not hang over the edge.

What kind of glue do you need origami?

Glue must meet the following requirements: dry quickly, not too runny (to paper is not wet, do not discolor paint, do not leave stains on paper. It is best to use PVA glue.

SL 9 HOW TO FOLD A TRIANGULAR ORIGAMI MODULE?

1. We put a rectangle from paper back side towards you. We bend it in half. 2. To mark the middle line, bend and unbend the rectangle. 3. Bend the edges of the rectangle to the middle. 4. Turn over. 5. We bend the corners, leaving a small gap between the upper triangle and the folded corner. 6. Raise the edges up. 7. Fold the triangle. 8. 9. The resulting triangular origami module Has two pockets and two corners.

SL 12-13 Technological sequence of product manufacturing

After looking various options products on the Internet, I settled on the manufacture of flowers and vases.

Tulips are one of the first spring flowers, harbingers of the sun and warmth. But to admire these delicate flowers, it is not necessary to wait for spring. Tulips from origami can please you all year round.

To make a single flower, we need: 105 triangular modules- for bud formation, and green paper- for the stem and leaves of the flower.

We take color paper, cut into squares, fold and can be folded from triangular tulip modules.

We begin to add parts from a small pyramid, in the first row there are three module, two in the second and one in the third. Gradually add modules in each row, they will hold each other. When you have 15 parts in the first row (respectively, 14 and 13 in the remaining rows) it is necessary to close the circle by connecting the first module row with the last one and putting one on top module, and in the third row, adding two more. You have a ring that needs to be turned out as shown in the figure. Press the center with your finger, the edges rise. Now on these edges we will build on the 4th and 5th row modules, each containing 15 modules. Starting from the 6th row, we form petals for the tulip. In the photo for clarity, these modules are made of red paper. You insert them four at a time, making a gap of two between them. module. We will finish the assembly individually on each petal: first row - 4, second - 3, third - 2, fourth - 1.

From the green we twist the bundle of paper, cut out a wide sheet, glue to the bundle, wrapping around. We insert the resulting stem inside the tulip box, if necessary, put it on glue to hold it more securely.

Bouquet beautiful tulips from multi-colored modules ready, I can safely give it, or I can keep it with pleasure and admire the creation of my own hands every day.

ST 14 Conclusion

I am satisfied with my work. Our room has become more comfortable and beautiful. My crafts turned out to be interesting, beautiful, unusual, which allowed me to tastefully diversify the interior of my room, as well as gain new experience in making products with my own hands using technology. modular origami. I believe that my the project was a success.

My wish to everyone who is at least a little interested in my project.

To know art origami,

Add to fantasy and knowledge

Great desire to create!

Patience, diligence, accuracy,

Keep putting in the work!

And good wonderful decisions

Create in a great mood!

Thank you for your attention!

Bibliography

1. "365 models origami» . T. Serzhantova. M.: Iris-Press. Rolf." 1999

2. « Origami paper toys» . S. Sokolova. M.: "Swallowtail". 1999

3. "Wonderful crafts from paper» . B. Bogatova. M.: "Education". 91

4. "Let's make from paper» . M. Steinbeck. Tallinn "Valgus".1988

5. "Amazing paper» . I. Chernysh. M.: "AST-Press".1998

6. « Origami on holiday table» . Afonkins. M.: "Akim".1998

8. "Work with paper: crafts and games». I. Kobitina. M.: "Sphere".1999

9. "World of toys and crafts". Collection. Smolensk "Rusich".1999

10. "My first handicraft book". "Bustard".1995

11. Magazine " Origami. The art of folding paper". 1995 - 2003

12. Origami. holiday models. Sokolova S. 2005

Rogozina Olga

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Municipal educational institution

"Secondary school No. 16"

Creative project on technology

WONDERFUL LAND OF ORIGAMI

MOU "Secondary School No. 16", Grade 10

Head: Khnykina I.M.,

MOU "Secondary School No. 16"

Solnechnodolsk 2011

	Justification of the project ………………………………	page 3
	Historical reference……………………………….	page 4
	Variability………………………………………..	page 5
	Main part……………………………………….	pp.6-8
	Safety precautions……………………………….	page 9
	Economic justification……………………….	page 9
	Environmental justification…………………………	page 9
		page 10
	Conclusion……………………………………………	page 11
	Bibliography…………………..	page 12
	Applications…………………………………………...	pp.13-14
	Annex 1. Product photo………….. Appendix 2. Product selection………………….	page 13 page 14

Project justification

simple piece of paper,
But in experienced hands
He can turn around
Firebird in the clouds.

Magic activity
For hands and mind
And world perception -
Wonderful country!

I was inspired to make origami by my younger brother.

One day, he began to look for video tutorials on assembling a paper airplane in a boarding school.

It turns out that just a paper airplane is also origami. Then I saw video tutorials for making other origami figures. I was very interested in this, and I was so carried away by this occupation that I had nowhere to put the finished figures.

Now this is my hobby. And for the technology project, I decided to choose exactly this, because origami is pouring and cognitive activity. During the work, I better studied the technique of origami, used the knowledge gained in the lessons of mathematics and fine arts, and when designing creative project expanded knowledge of computer science.

In the future, I will be able to make gifts for relatives and friends with my own hands.

But still, origami, first of all, is an art designed to give people joy.
paper birds and fish, animals and polyhedrons adorn shop windows. Beautiful and expressive masks are widely sold as wall decorations.

Many entrepreneurs order paper figurines from craftsmen to use as a company symbol.

Municipalities pay for the decoration of city festivals, shows and carnivals. Paper figurines are used to create commercials and posters.

2.Historical reference

Origami (jap. "folded paper")- the ancient art of folding paper figures. The art of origami has its roots in ancient China where the paper was opened.

Initially, origami was used in religious ceremonies. For a long time, this type of art was available only to representatives of the upper classes, where the possession of paper folding technique was a sign of good taste. Only after the Second World War, origami went beyond the East and came to America and Europe, where it immediately found its fans.

Classical origami prescribes the use of one square evenly colored sheet of paper without glue and scissors. Contemporary art forms sometimes deviate from this canon.

Origami is an original Japanese art of creating models of various objects, animals, birds, flowers by folding a sheet of paper. No one knows who exactly and when invented origami and how its unwritten rules were developed. There is even an opinion that this art is older than paper. That the first origami figures originated from the art of draping fabric in the manufacture of traditional Japanese clothing. Many generations of Japanese have contributed to origami, passing on the ability to fold a flat sheet into a wonderful figure. Since ancient times, origami has played a different role in the life of the Japanese. Paper figurines accompanied ritual processions in Shinto shrines, graceful butterflies adorned the wedding table, samurai entertained ladies at medieval balls by folding simple figurines, caring relatives hung magical paper balls over the sick person's bed to exorcise evil spirits. From generation to generation, the ancient art was improved, selecting the most elegant, most expressive figures for posterity. Over time, origami went beyond the religious framework and became a court art. Only a select few could deal with it, since paper was a rare and very expensive material. The ability to fold a figure from a square sheet was considered a sign of good education, refined manners and refined taste.

3.Variability

At the beginning of the project, I had a choice - what product to make in the origami technique?

№1

Flowers. I thought the product was too simple for the project.

№2

Birds. I love birds, especially swans. The product is airy. Can be used as a gift to close friends.

№3

Christmas decorations. Products can only be used for the New Year.

Using everything possible options I settled on #2. To perform origami, I was helped by training videos from the Internet.

4.Main part

Routing

Making a paper swan

No. p / p	Operation description	Graphic image	Tools and material
	Fold the rectangle in half		Square sheet of paper and scissors
	Bend and unbend to outline the midline. Turn the mountain towards you		paper
	Fold the edges towards the middle		paper
	flip		paper
	Raise edges up		paper
	Bend the corners, bending them through a large triangle		paper
	Unbend		paper
	Again, fold the small triangles along the marked lines and lift the edges up		paper
	fold in half		paper
	The resulting module has two corners and two pockets.		paper
	Now we start connecting the modules together. We insert the corners of the first two modules into the pockets of the third, we get one basic element
	Next, we take two more modules and attach them to the resulting element on the sides. So, triangle after triangle, we close the first ring. It consists of two rows, each with 30 modules: an inner row, whose modules are on the short side, and an outer row, whose modules are on the long side.
	Now we carefully take on the workpiece and, holding on to its edges, we turn the entire ring inside out, as it were. 5 layers should now look like a stadium when viewed on top of her.
	Now we begin to make out the wings for ourpaper swan. Add the 6th row, consisting of 30 modules. Choose the side where the swan's head will be. We take a couple of corners (from two neighboring modules). This will be the place where the neck is attached. To the left and right of this pair we insert in a row of 12 modules. As a result, the 7th row consists of 24 modules and has two gaps. We begin to build up the wings, each next row will be 2 modules less.
	We fold the elements for the neck in a different way: we insert two corners of one module into the pockets of the other. We connect the modules, giving them the desired bend along the way

5. Safety

Working with scissors

Store scissors in a specific place.
Put them with closed ends away from you.
Pass the scissors to each other with handles (rings) forward.
At the end of the work, put the scissors in the place provided for storage.
Tidy up your workspace.

6. Business case

The cost of my product will consist of the cost of necessary materials which I had to purchase.

Environmental rationale

All materials used in the manufacture of origami figures are environmentally friendly, which means they will not cause allergies and can be in the children's room. Since the paper passed the quality test.

Advertising

Japanese wisdom from ancient times says:
"The great square has no limits."
Try to fold a simple figure,
And in a moment it will carry away an interesting thing.

9. Conclusion

No matter how comfortable your home is. A unique individuality can only be given to it by things made with one's own hands, with love and imagination. The process of making origami is fascinating. Such an occupation develops aesthetic taste, instills accuracy, perseverance, diligence, a creative attitude to work, forms certain skills and abilities that can be useful in practical activities.

Product rating

Positive sides.

The goal has been reached.
Materials available
Manufacturing technology is feasible
The product is safe to use
Design fit for purpose
Aesthetically beautiful.
Develops fine motor skills

Bibliography

Municipalcontest

student creative research projects

Bytechnologies

"The world through the eyes of children"

Origami

Done by a 4th grade student

MOU "Podgornenskaya secondary school"

Koveshnikova Tatiana

Supervisor

teacher primary school

Chichenkova S.I.

Podgornoye

year 2014

Translated from Japanese, "origami" means "folded paper", in the land of the rising sun, the art of origami is called the art of a whole sheet. This is one of the most important rules of origami - do not add or subtract anything extra. This is the law that all origami artists have followed for centuries. Thanks to this, this type of art has been considered the most unusual and original for thousands of years.
Origami appeared almost immediately after the appearance of paper in Japan. It was the Japanese, and not the discoverers of a new writing material - the Chinese, who guessed to use paper as a raw material for decorative ornaments and products.

The words "paper" and "God" in Japanese are consonant. Therefore, all paper products began to be given a religious meaning. In the temples, the walls were decorated with paper depicting the gods and their written commandments. With the help of sheets, sacrificial fires were lit. It was customary to bring gifts to temples in special paper boxes.
In the monasteries of paper, for the first time, unusual figures began to be folded. They symbolized various gods, animals, people, even the seasons and natural phenomena. And since tearing a sheet of paper was considered a terrible sin, the sheet was always used in its entirety. Gradually, the strictly regulated number of church figurines began to increase, the technique was polished and became a real art.

From generation to generation, the ancient art was improved, selecting the most elegant, most expressive figures for posterity.

Over time, origami went beyond the religious framework and became a court art. Only a select few could deal with it, since paper was a rare and very expensive material. The ability to fold a figure from a square sheet was considered a sign of good education, refined manners and refined taste.
Origami art gained mass character only in the twelfth or thirteenth centuries. When paper spread all over the world, when its prices dropped significantly and made this material affordable.

At some point, entire competitions and tournaments were organized in origami. Rich and noble people willingly undertook to sponsor these events. Any relation to origami in those days was considered significant and prestigious. It often came to the point that origami figures began to appear on the family coats of arms of noble and wealthy houses. They have become symbols and protectors of the home, family, hearth, well-being.

But the term "origami" itself arose and gained a foothold much later, compared with the art itself. This happened only in 1880, when this art became part of the aristocratic society, when it entered the life of all Japanese families. The secrets of folding various paper figures were passed down from generation to generation, and such a heritage of centuries gradually became no cheaper than gold or family jewels.

There is a certain set of conventional symbols necessary to sketch the folding scheme of even the most complex product.

valley fold, valley fold line.		mountain fold, mountain fold line.
Cross over the valley.		Jump over the mountain existing line.
zipper pleat (fold combination valley and mountain).		Combine noted points.
Flip the shape invisible line.		rotate figure in one plane.
Pull, drag.		Double fold-zipper (inside).
Double fold-zipper (out).		To uncover (usually a pocket).
Bend inside.		Pull out.
bend inside, drown.		Repeat action (
Equal angles.		Equal parts.
		Wrap up.
Increase Images.

After that, some masters learned to write and hide messages in figures that could be read without tearing, only by a person initiated into the secret of origami. Such messages often took the most beautiful forms of birds, butterflies, flowers, or simple abstract geometric shapes.

But most often the shape of the crane was used, which since ancient times in Japan was considered a symbol of longevity and happiness. Such a figurine was called a tsuru. From those distant times to this day, cranes have been a very important and bright sign for origamists. This bright bird, which is not difficult to execute on paper, has been an image of freedom and hope for many centuries. Perhaps it was the connection of the bird with the sky, as well as its majesty and grace, that served this

The Japanese have always carefully and lovingly folded the origami crane for 2,000 years. Back in 1797, a book was published, which was called "The Folding of a Thousand Cranes". It published a lot of options for folding cranes in various interpretations. For this, it was necessary to have only one square of paper.

After the Second World War, the crane took on another meaning, namely the symbol of peace. Many people know the story of the little girl S. Sasaki, who was born in 1943 and was left an orphan after the atomic bomb that fell in Hiroshima. The girl was very strongly irradiated and when she was in the hospital, she began to fold a paper model of a crane. Sadako Sasaki believed very much in the old story that if she made 1000 cranes, her wish would come true. When she first started doing them, she really wanted to get well, but later her desires changed. Sadako began to dream about big world throughout the planet Earth. She was able to make 644 models and died on 10/25/1955. After this story, all the children on earth began to send paper cranes to the museums of the world, which is located in Hiroshima, as a symbol of peace.

The art of origami, at the beginning of the 20th century, begins to go beyond Japan and freely marches around the world. Most people became very interested and carried away by this simple and at the same time complex art.

My job

Today, the art of origami is experiencing a rebirth. This art attracts with its originality and simplicity. After all, in order to engage in such art, nothing is needed except hands and paper.