Lined sheets. Origami. Materials and tools Paper bite dog

21.05.2021 Audio players

One of the ideals of origami requires folding the original square without preliminary drawings and measurements. With this folding, a problem arises if you need to fold a sheet of paper, for example, in three. How to do this without using a pencil? This article discusses the issue of dividing a square sheet of paper into two, three, four, ... ten equal parts.

Dividing a sheet of paper into two parts is not difficult, since it is realized simply by folding the basic form of a book. Let's move on to the more complex problem of dividing a square sheet into three parts.

This task is no longer so simple. To solve it, we need Hag's theorem. Add the corner of the square to the middle of the opposite side. In this case, the point of intersection of the other side opposite this corner and the side adjacent to it divides the side in a ratio of one to two. Thus, using only the folds, we have found a third of the side of the square.

The next task is to divide the side of a square into four equal parts. To do this, it is enough to divide them in half, and then, each of the halves again in half. This is exactly what happens when we fold the base shape of the door.

As you might guess, dividing a square into five parts by folding is a much more difficult task. Its solution is shown in the figure. Try to prove for yourself that in this way we really divide the square into exactly five parts.

In order to divide the side of the square into six parts, we just need to divide it into three parts, as shown earlier. And, then, divide each of the parts in half.

You can see that it is especially difficult to divide the square into the number of parts, which is a prime number. Let's start dividing the side into seven identical parts. To do this, first we divide the square into five equal parts, and then, we will do the action shown in the picture.

It's easy to divide a square into eight equal parts. To do this, it is enough to divide it into four equal parts, and then divide each of them in half.

There are two ways to divide it into nine equal parts. The first is to divide first into three equal parts, and then repeat the division by three for a small square. However, this method is bad in that, when applied in practice, it will be difficult to maintain sufficient accuracy, since the errors made at different stages add up.

Another way is more original and is based on the development of the Haga theorem, which was proposed by Koji and Mitsue Fushimi. Note that this method was used when dividing a square into seven and nine parts. Maybe it is applicable to dividing it into nine parts?

Children learn the art of origami from school, and in most cases they get acquainted with paper, glue and scissors back in kindergarten, where, together with the educators, they make the first primitive crafts. Cutting out figures from paper, first flat, then voluminous, the child prepares for the study of geometry in and it is very important to instill in him a love for Aristotle's science right away, so that later interest does not disappear, and everything works out. A three-dimensional square of paper is a figure with which one usually starts acquaintance with stereometry. Having learned the simple techniques of making this polygon, you will be able to construct amazing structures, which are based on an ordinary cube.

The basics of geometry

Everyone without advanced mathematical knowledge will be able to make origami out of paper. A square - at first glance, the figure is very simple, and it will not be difficult to build it. However, you need to start the process prepared, having an idea of paper assembly and not being very upset at the first failures. Before you start wondering how to make a square out of paper, you need to familiarize yourself with the basics of geometry. Do not forget that a cube is a rectangle in which all sides are equal and the corners are straight. This condition is mandatory, but errors of a couple of millimeters are permissible.

Materials for assembly

The production of a square takes place in several stages. You will need paper sheet, glue or tape, ruler, pencil and scissors. If you are afraid to draw the diagram yourself, you can print the finished scan on a printer. To make the cube bright, each side can be pasted over with colored paper, shiny tape, or painted with multi-colored paints or crayons. So that the sides of the square do not get dirty over time and retain their original appearance, it is recommended to cover it with a transparent film.

Paper square: manufacturing scheme

Children and adults will love to make geometric figures - the process is so exciting that very soon you will have a whole collection of various cubes. Before starting work, you need to stock up on the right amount of paper, which is enough for all sides, so that later you do not have to glue the missing elements to the existing frame. The sweep is performed on whatman paper or cardboard. The material should be moderately dense so that the figure does not wrinkle during assembly, but a sheet of paper that is too thick will also not work. A special condition is the presence of additional edges on the sides of some sides, with the help of which the cube will be glued. A three-dimensional square consists of eight identical sides. In order not to be mistaken with the choice of whatman paper, perform all calculations before drawing the drawing on a sheet of paper.

Assembling the cube

As soon as the reamer is ready, it must be cut with scissors. The connection can be made with any glue or To make the edges of the square even, each fold line must be bent several times before gluing. The pencil drawing can now be erased to give the cube an aesthetic appearance. Depending on the purpose for which the craft is being made, it can be decorated different ways: Cover with shiny glossy film or colored paper, paint or stick bright stickers.

Offer a fun process, and soon a collection of bricks will appear in your home different colors and sizes. Once you know how to make a square out of paper, it will be easy for you to create miniature crafts that can be turned, for example, into dice. If the house grows Small child, you can glue multiple figures with colored tape to create a unique set of doll furniture.

A little fantasy ...

If you decide to make an unusual origami out of paper, the square can be turned into.To do this, it should be made of material white... The optimal length of each face is 1.5-2 cm.Before you start making a miniature cube, you need to practice and start learning the art of origami from a figure bigger size... Once the technique is fully studied, you will be able to create masterpieces based on simple.Knowing how to make a square out of paper, you can easily move on to the next stage of training - modeling the original volumetric crafts.

Paper people

In Russia and in the West, there has long been a tendency to release children's kits for creating people and animals, which are based on a three-dimensional square of paper. The scheme is no different from unfolding a simple cube, only the proportions are changed for some parts. So, by bringing together squares of different sizes, you can construct interesting crafts... Having dealt with this simple technique with your child, you can create masterpieces with your own hands and not spend money on expensive needlework kits. It is better if the drawing will be applied to the paper immediately, and not after assembling the entire figure.

To preserve the aesthetics of the product, it is necessary to glue the edges with hard glue, not tape. it is clearly visible on paper, and the craft will not look its best. Having figured out how to make a square out of paper, you can easily make unique crafts and assemble a whole collection, because origami is a fascinating art that is available to people of all ages.

The inner chambers of the palace of Sultan Ibrahim ibn Said consist of one hundred identical square rooms arranged in a 10 × 10 square. If two rooms have a common wall, then it must have exactly one door. And if the wall is external, then it must have exactly one window. How many windows and doors are there in Ibrahim ibn Said's chambers? An airplane carpet flies only when it is rectangular. Ivan Tsarevich had a flying carpet measuring 9 × 12. Once the Serpent Gorynych crept up and cut off a small rug 1 × 8 from this carpet. Ivan Tsarevich was very upset and wanted to cut off another 1 × 4 piece to get an 8 × 12 rectangle. But Vasilisa the Wise suggested doing something differently. She cut the carpet into three pieces, from which she sewed a 10 × 10 square flying carpet with magic threads. Can you guess how Vasilisa the Wise remade the damaged carpet? A point was marked in the circle. Cut the circle a) into three; b) into two parts so that they can be composed new circle with the marked point in the center.

Solution.

a) Draw a line containing one of the sides of the square. If a point lies on the other side of this straight line than a square, then it certainly does not lie in a square. Otherwise, draw a line containing the second side of the square and carry out similar reasoning. By drawing all four lines containing the sides of the square, we find out if the point lies inside the square.

b) First we draw two lines containing the diagonals of the square. They will split the piece of paper into four pieces. From the answers to the first two questions, we find out in which of these parts the point lies. Now draw a line containing the side of the square that lies in the same part of the plane as the point. This line will split the indicated part of the plane into two more parts, one of which will be inside the square, and the other - outside. By answering the third question, we find out if the point lies inside the square. Pay attention: now we know not only whether the point lies inside the square, but also which of the four parts of the square (into which it is divided by the diagonals) it lies.

This solution does not say anything about the cases when the point is on one or more of the straight lines that we draw. Deal with these cases yourself.

What paper is best for making crafts? How to make a lot faster? What is the best module size? This section will reveal the secrets modular origami and will help you take your first creative steps.

Paper selection

Office paper. Office paper is most suitable for modular origami, since it is not too smooth and dense enough, the modules adhere well to each other and there is no slipping when connected. Office paper in different colors is dyed on both sides and does not turn white on the folds.

Blocks for notes (stickers). Square stickers are used for the Shamrock module and the Superball kusudama modules. Triangular modules are usually folded from pieces of paper rectangular... The aspect ratio of a rectangular leaf is 2: 3 (for example, 4 x 6 cm). However, square stickers can be used. cut in half. In this case, the sides will have a 2: 1 ratio. The module itself will turn out to be thicker, which is good for some crafts. Sometimes you can find rectangular stickers that do not need to be cut.

Origami paper. In Japanese, special origami paper is called kami. The sheets are already cut into a square shape, but the sheet size may vary. In such a set of paper, there are several colors of paper, one side of the sheet is usually white, and the other is colored. You can find paper with an ornament or colored paper on both sides.

Colored paper for children's creativity. Such paper should be checked for fold strength before use - it can easily tear. For modular origami, you need a large amount of paper of the same color, and in these sets, there are mainly several sheets of the same color. Sometimes it is difficult to find black or brown paper, then you will have to use just such a set.

Magazine paper. For modular origami, paper from modern glossy magazines is great. It is advisable to choose not very thin paper. Having sorted the modules by color, you get interesting pictorial effects in the assembled product.

Module paper size

Triangular modules can be folded from pieces of paper of different sizes - small and large. The size of the future product depends on this. It is convenient to use 1/16 or 1/32 pieces of a standard A4 sheet for triangular modules.
If the sides of an A4 sheet (long and short) are divided into 4 equal parts, and the sheet is cut along the outlined lines, then the rectangles will come out about 53 x 74 mm in size.
If the side of an A4 sheet is divided into 8 equal parts, and the short side into 4, and cut the sheet along the outlined lines, then the rectangles will come out about 37 x 53 mm in size.

You can also choose another size. Choose for yourself one module size for your craft and stop there. And if you make all the crafts from modules of the same size, then all the products will be compatible with each other and the Christmas tree folded for the New Year can turn into a palm tree, and then into a peacock or something else.

Tools and additional materials

Stationery knife and ruler. First you have to prepare and cut the paper into squares or rectangles before folding the modules. Cut several layers of paper at once. Scissors will be difficult to cut, so use a utility knife and cut with a straight edge. The ruler must be firm. Place a board under the paper. A dedicated paper cutter can be purchased if available.

Glue. Glue is used to attach small parts - a peephole, jewelry, etc. Try to make all products without glue, so any craft can be disassembled and create something new. But if you will use the craft as a toy for children or a gift, then of course you need to take care of its durability.
When assembling, you can use thick PVA glue or glue stick. And when working with the Trefoil module, glue is required. Flower petals are connected with glue, it is also needed when attaching leaves and making stems.

Adhesive mass. Great invention! The mass resembles a cross between white plasticine and double-sided tape. You can tear off a piece, roll it into a ball and fix any part inside or outside the craft. The part can be removed when necessary. The adhesive does not leave marks.

Paints. If you complete the entire craft from white office paper, then you can cover it with any color paint from a spray can.

Sewing thread with a needle. Kusudama "Superball" modules are interconnected with a needle and thread.

Additional details. Ready-made eyes for toys will come in handy when making crafts. The eyes can be drawn by ourselves on thick paper or ready-made images of the peephole of the desired size and type, printed on a printer. Beads, ribbons, beads, sequins, etc. are suitable for decorating crafts.

The creation of various shapes using the origami technique is available to almost everyone. At the same time, even beginners can create a lot of crafts. From paper using the origami technique, you can fold various crafts, including animal figures. At the same time, a simple square is able to turn into cranes, cats, dogs and other animals. In this master class, I will show 10 options and schemes for folding a dog using the origami paper technique - how to do it yourself with step-by-step photographs.

Especially such crafts are relevant before the New Year. The time is coming when the yellow earth dog will rule the world. And this animal is the symbol and mascot of 2018.

01. Brown dog in origami technique

To create it you need to take:

2 square brown sheets of paper (single-sided);
black marker;
glue stick.

We will make the dog's head from one brown square, and the body from the second.

Let's start with the head. To create it, fold the sheet along two diagonals. After that, we leave the blank folded in the form of a triangle.

Bend the bottom corner from the top layer of the triangle up.

To form the ears of the dog, you need to bend the side corners.

Now they need to be straightened in the form of rhombuses.

Bend the upper part of the workpiece down a little.

In order for the dog to have a nose, it is necessary to bend the lower corner a little upward.

We fold our workpiece along the middle line, we get the head of the dog in profile.

Now take another square and start creating the torso. To do this, fold the sheet diagonally.

On the underside of the resulting triangle, mark the middle with a fold.

Now we form the tail of the dog. To do this, bend the right corner.

We turn the bent corner outward, we get a white tail.

Bend the left side of the triangle to the middle, focusing on the previously made fold on the lower side.

We bend the upper part of the body blank to the left in the form of a triangle.

Gently turn the workpiece out so that the dog's breast is white.

Using glue, we fix the head to the body.

Draw the eyes of the dog with a black marker.

Our first origami paper dog is ready.

02. Dog fox terrier breed in origami technique - scheme

Creating crafts in the form of animals is interesting not only for children. Dog lovers will surely enjoy making this craft in the form of a fox terrier. This dog breed is friendly, good with children and energetic.

It has quite characteristic shapes, which allows you to embody this dog in the form of origami crafts. Step by step manufacturing fox terrier is shown in this master class.

To create a dog, take:

paper in the form of a square;
black marker.

First, bend the sheet along two diagonals.

Now we will bend the side corners (oppositely located) to the center.

One corner should become the dog's tail. To do this, bend the left corner a little to the side, it should protrude beyond the boundaries of our workpiece. And on the right side we bend a small corner inward. On this side, we will form the dog's face.

Fold the workpiece in half. This is how we make the body of the fox terrier.

The top layer needs to be bent in the form of a triangle to the left and up.

Now we bend the upper left corner into reverse side.

Turn the blank of the dog over to the other side.

Here we have to repeat all the steps, but in a mirror image. Therefore, we bend the corner to the right and up.

Now the bent corner needs to be bent in the opposite direction. So the contours of our dog have already been outlined.

To form the muzzle, it is necessary to straighten the inner fold outward at the bottom.

Bend the ears of the dog down on both sides.

It remains to draw the nose and eyes for our fox terrier.

The origami dog is ready.

03. Origami box in the shape of a dog

How to make such detailed master class see here.

04. Origami dog from a banknote

A small dog made from a bill is a symbol of prosperity and endless cash flow into the house. You can make a small dog out of a banknote using the origami technique. It may not be yellow or earthy, but it will definitely protect financial stability and happiness in the house. Usually dogs for this and live next to people to serve as a reliable guard.

You can make a dog using the origami technique according to the technique below in just a few steps. The result is a small sleeping puppy. Toddlers will love this kind of creativity.

To model a small dog, prepare:

bill;
black half-bead;
pencil.

How to make origami a dog out of money step by step:

01. Begin folding money from a horizontal position.

02. A similar scheme is designed for a square, not a rectangle. But it makes no sense to cut a bill, because they have a certain value, this is money that, if desired, can be used for its intended purpose. To immediately define a square shape, aim the two narrow sides of the rectangle towards the center vertically.

03. In this position, continue making bends. Bend the resulting booklet triangle horizontally, smooth out the resulting narrow rectangle.

04. Unfold the previous fold. But the bill should remain folded into a square. Bend two adjacent side corners by about 1 cm, highlighting small right-angled triangles.

05. Then bend the bottom corner on the other side, but deeper, about 2 cm. But do not join the bottom side with the center.

06. And fold the remaining top corner. The resulting triangle should be beveled. Begin to rotate the paper from the center, and back off a short distance from the side.

07. Bend the resulting structure horizontally in the center. All corners should remain folded using the previously described method.

08. Turn one side of the resulting workpiece to the side, highlighting a triangular fragment. Place your finger on top between the layers of folded paper and turn the side towards you, straightening the triangle.

Thus, two parts of the dog figurine will appear in front of you - the back with a tail and the front (head with ears).

09. Grab the sharp ends of your ears and spread them apart. The figurine is now fully assembled. Banknote folded several times keeps its shape well, so you don't have to use glue. The figurine of the dog seems to be lying and resting, with its head bowed to the side.

10. Now you can make a face on the triangle. For this, we prepared a simple pencil and a half-bead (it is better to have it on an adhesive base). Gently draw the closed eyes with a pencil (if desired, in the future, the thin line can be eliminated with an eraser). Glue the black spout. A cute dog - a talisman of happiness and prosperity is ready.

Making origami from a bill is an interesting type of creativity that attracts with its simplicity and the possibility of non-standard use of money. The author of this master class is Elena Nikolaeva.