Solution of the task, how to draw an envelope without taking hands. Do not breaking hands or rope drawing complex geometric drawings without taking hands

Instruction

It is assumed that the specified figure consists of points connected by straight or curved segments. Consequently, at each such point it converges a certain segment. Such figures are customary to call graphs.

If an even number of segments converges at the point, then this point itself is called an even vertex. If the number of segments is odd, then the peak is called odd. For example, the square in which both are carried out, possesses four odd vertices and one even - at the point of intersection of diagonals.

In the segment by definition two end, and therefore, it always connects two vertices. Therefore, having aroused all incoming segments for all vertices of the graph, it is possible to obtain only an even number. Therefore, whatever the count, odd peaks in it will always be an even number (including zero).

The graph in which there are no odd vertices at all, you can always draw, without taking hands from paper. At the same time, it's not like that top to begin.

If the odd vertices are only two, then such a graph is also unicursalen. The path must begin in one of the odd vertices, and will end - to another of them.

The figure in which odd vertices four or more is not unique, and without repetitions, it will not be able to draw it. For example, the same square with the diagonals conducted is not unicursalen, since it has four odd vertices. But the square with one diagonal or "envelope" is a square with a diagonal and a "lid" - you can draw one line.

To solve the task, you must imagine that each conducted line disappears from the figure - the second time it cannot be passed. Consequently, depicting the unicuristic figure, you need to ensure that the remaining part of the work does not disintegrate on non-interconnected parts. If this happens, bring the case to the end will not work.

Sources:

• How to draw without taking hands a closed envelope?

Square is an equilateral and rectangular quadrangle. It is very simple to draw it. Start the workout first on the notebook in the cage. With the help of a simple pencil and an invisible square from the points, learn how to draw a square without pulling off the paper from paper.

You will need

• - simple pencil;
• - leaf in a cage;
• - A4 sheet;
• - line.

Instruction

We take to start in the cage, it is comfortable to draw a square. Rates from the left edge and from above approximately 3 cm, put the point. From her, right, count 5, put another point.
Then, from these points down the line, we finish another 5 cells that put 2 more points. It turned out an invisible square. And with the help of a pencil neatly connect 1,2,3 and. 2.5 cm square square quad.

You can such a square on the usual, A4 format, with a side of 3 cm. Place a sheet vertically. Return 10 cm paper from the top edge. Use the line to put points in a straight line. Attach a ruler to the left edge so that the edges of the line and paper coincide, it is necessary for the correct image of the square. Squeeze from the edge about 5 cm (for the field). Put the first point. Next to the left, after 3 cm another point - the second. Then rotate the line by 90 degrees. The beginning of the line will coincide with the top edge of the paper, and from the first point down, measure 3 cm, put the third point. Move the line to the second point and from it down, at a distance of 3 cm put the fourth point. Now neatly smooth lines connect all the points without taking the pencil from the picture.

Contemporary children are difficult to carry something. They love to watch cartoons and play computer games. But smart parents are always able to interest their child. For example, they can offer him to find a way to draw an envelope without taking hands. Read about some tricks of this task below.

Workout

Before starting to torment the child with logical tasks, you need to carry out preparatory work with it. Why is it needed? So that the child is not Mukhleval, when it starts to break his head over the question of how to draw an envelope without taking hands. After all, the most interesting thing in this task is that the line should go from point to the point continuously.

What tasks can be suggested as a workout? Of course, the first it should be eight. Drawing this figure and stress removes, and the brain cleans, and the hand trains. In general, useful exercise. After that, you can move to drawing rounded forms. It may be curls or any other stools, the main thing is that in the process of drawing the child did not break the pencil and depicted with a single smooth line.

How to draw a closed envelope

Many parents themselves spent not one hour before to offer such a task to the child. You can also try. But we can immediately disappear - to perform such a task, I don't think a little, it is simply impossible. Therefore, we will tell you the way that will help you and your child go beyond the framework of ordinary logic to understand how to draw a closed envelope without taking hands.

We take a sheet of paper and bend the edge from him. Fill it back. Now our task is to draw the top edge of the closed envelope just on the bend line. To make it easier to understand, put the points at the ends of the rectangle. Number them starting from the upper left corner. Here will stand the number one and further clockwise. From the number 4 to 1, we carry out the line, now connect 1 C 2 and now draw a diagonal to 4. From 4 to 3 we drive a straight line, and then again diagonal to 1.

Now go to the most interesting. We drive the edge of our sheet and depict a zigzag that forms a cap of our envelope. It will take place from 1 to 2. It remains to connect 2 and 3 straight line - and the puzzle is solved. Filing a part of the sheet back. The riddle, how to draw an envelope without taking hands, you can offer not only children, but also to friends or colleagues.

How to draw an open envelope

Those who carefully read the previous paragraph and on the description created its drawing, have already understood how to answer the question adjusted above. After all, the decision of the riddle, how to draw an open envelope without taking off the hands, will be similar to the written in the previous paragraph. Only here you do not have to bend and flexing the parts of the sheet. All image will be made by one line by the same scheme.

But if you do not want to repeat, then we offer another way that will result in the same result. How to draw an envelope without pulling hands in the second way? To begin with, we draw a rectangle with points again and again it is numbered, as in the previous paragraph. From the number 4 to 2, we drive a diagonal, from 2 to 3 - a straight line, and from 3 to 1 - again diagonal. Next you need to draw a corner. From 1 to 2 draw a zigzag, which indicates the top of the envelope. From 2, we return to 1 straight line and end our construction alternately spending directs from 1 to 4 and from 4 to 3.

Why do such tasks need

These must be performed not only to children, but also adults. Thanks to them, the human brain is strained and starting to work. If you have to do yourself to perform in a similar task every day, after a month it will be possible to notice that in critical situations the solutions are generated faster and forces is spent less. Schoolchildren are especially useful to study the tasks for logic. Thus, they train creativity and learn to not standard approach standard issues.

We were inspired by the Japanese Animator and Illustrator Kazuhiko Okushita.

The artist creates drawings without taking a pencil from paper. Very useful lesson! Develops fantasy, thinking, hops the schedule and trains the hand.

Lera could not stop))

Children's fantasy do not sleep! This is not the whole result of its turbulent activity) But sharks struck me! Everything is drawn by the daughter, without taking hands.

And then we came up with the method of drawing without tearing hands.

For such drawing, you will need: PVA glue - a lot, threads - any thick, sheet A3, paints and brushes.

First, we pour the glue into a comfortable container, omit in the glue thread - it must be pretty soaked in Pva.

Then get it in this way.

Or so))

By the way with gluing hands very interesting to play)

And lay out the thread on the sheet of paper. We form a pattern. If your thread is interrupted, then you need to put a new one by the end of the old one. But in principle, it is possible in any order.

And Lere liked the case then handy dry glue from the hands)) The occupation is very multifaceted)))

And now add paints!

Egor was so carried away, which even painted with fingers.

I think that everyone should like this drawing! Show what happened to you!

Portraits drawn by "doodles" August 4th, 2014

Artist from Malaysia Vince Lowe (Vince Low) draws portraits of celebrities with a pen on paper, "without taking hands from a sheet" - according to some. The illustrator was able to convey the expressions of the persons and emotions of Hollywood stars, singers, scientists and kinheroev with incredible accuracy. Winx Lowe called his series of Vince Lowe - "Faces".

Under the cut will be a job that can be considered with a strong increase, then you will understand what the unusualness and essence of this creativity.

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The idea of \u200b\u200bcreating original portraits of Ceboribritis was born from him spontaneously: at the beginning he, like many, loved to make sketches of drawings in a notebook. Seeing that the result is quite impressive, Vince Low decided to create a whole series of unusual works.

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The artist tells that it is extremely important for him to transfer the soul and character of the person shown in the figure. Not doubting their capabilities, he decided to master the mastery of "stroke" painting. Of course, this direction in modern art is not new, among the recognized masters, you should remember the names of Takahashi and Pierre Emmanuel Godet, drawing "doodles", as well as an illustrator-amator Reddit, which creates pictures with a continuous line. However, Vince Low managed to take a completely special niche in monochrome portraitis.

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Often doodles are perceived as a solid pampering, meaningless lines that the page can be mastered. However, Vince Low knows how to streamline this chaos by creating artistic images from it. His realistic portraits are emotional and expressive, the artist skillfully uses the game of light and shadows, draws in detail the features of the face. Unsuitable, at first glance, the approach to creating a picture allows you to achieve excellent results of Vince Low.

Here is another to you with a great magnification. Click on the picture.

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And another one …

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I. Setting the problem situation.

Probably, everyone remembers since childhood, the following task was very popular: without taking off the pencil from paper and without holding one line twice, draw "Open Envelope":

Try to draw "Open Envelope".
As you see, some it turns out, and some have no. Why is this happening? How to draw to what happened? And why is it needed? To answer these questions, I will tell you one historical fact.

Königsberg city (after World War, he is called Kaliningrad) stands on the river Prestol. There were no 7 bridges there, which connected the coast and two islands among themselves. Residents of the city noticed that they could not take a walk in all seven bridges, having passed on each of them exactly once. So there was a puzzle: "Is it possible to go all seven Königsberg bridges exactly once and return to its original place?".

Try and you, maybe someone will work.

In 1735, this task became known to Leonard Euler. Euler found out that there is no such path, that is, proved that this task is insoluble. Of course, Euler decided not only the task of Königsberg bridges, but a whole class of similar tasks for which the solution method developed. It can be noted that the task is to hold the route on the map, without taking off the pencil from paper, bypass all seven bridges and return to the starting point. Therefore, Euler began to consider instead of a bridge map diagram from points and lines, throwing bridges, islands and shores, as not mathematical concepts. That's what he did:

A, B - Islands, M, N - coast, and seven curves - seven bridges.

Now the task is to get around the contour in the picture so that each curve is carried out exactly once.
Nowadays, such schemes from points and lines began to call graphs, the points are called the vertices of the graph, and the lines of the edges of the graph. In each vertex of the graph converges several lines. If the number of lines is even, then the peak is even if the number of vertices is odd, then the top is odd.

We prove the insoluteness of our task.
As we see, in our column all the vertices are odd. To begin with, we prove that if the count of the graph begins not from an odd point, then it will definitely end at this point

Consider for example a vertex with three lines. If we came on the same line, they came out on the other, and on the third, they returned again. Nowhere to go now (there is no more ribs). In our task, we said that all the points are odd, it means, coming out of one of them, we must finish at once in three other odd points, which cannot be.
To Euler, no one came to mind that a puzzle about bridges and other puzzles with a circuit bypass, relating to mathematics. The analysis of Euler such tasks "is the first sprout of the new region of mathematics, today known as the topology."

Topology - This section of mathematics studying such properties of figures that do not change during deformations produced without breaking and gluing.
For example, from the topology point of view, the circle, ellipse, the square and the triangle have the same properties and are the same figure, as you can deform one to another, but the ring does not apply to them, because to deform it in the circle, A gluing is needed.

II. Signs of drawing graph.

1. If there are no odd points in the column, then it can be drawn by one stroke, without taking a pencil from paper, starting from any place.
2. If there are two odd vertices in the column, then it can be drawn by one stroke, without breaking the pencil from paper, and you need to start to start in one odd point, and finish to another.
3. If in the column more than two odd points, it is impossible to draw it with one pencil route.

Let us return to our open envelope task. Calculate the number of even and odd points: 2 odd and 3 even, it means that this figure can be drawn by one stroke, and you need to start at an odd point. Try, now everyone happens?

Secure the knowledge gained. Determine which figures can be built, and which cannot be.

a) all points are even, so this figure can be built, starting from any place, for example:

b) There are two odd points in this figure, so it can be built without tearing, pencil from paper, starting from an odd point.
c) in this figure four odd points, so it cannot be built.
d) Here all points are even, so it can be built, starting from any place.

Check how you learned new knowledge.

III. Independent work on cards with individual tasks.

The task: Check whether you can make a walk through all the bridges, passing for each of them exactly once. And if you can, then draw the way.

IV. The results of the classes.