The impossible is still possible. And a vivid confirmation of this is the impossible Penrose triangle. Discovered in the last century, it is still often found in the scientific literature. And no matter how surprising it may sound, you can even make it yourself. And it's quite easy to do so. Many fans of drawing or collecting origami have been able to do this for a long time.
Meaning of the Penrose triangle
There are several names for this figure. Some call it an impossible triangle, others just a tribar. But most often you can find the definition of the Penrose triangle.
These definitions mean one of the main impossible figures. Judging by the name, it is impossible to get such a figure in reality. But in practice, it has been proven that it is still possible to do this. That's just the shape of a triangle, the figure will take, if you look at it from a certain point at the right angle. From all other sidesfigure is very real. It represents three edges of a cube. And making a similar design is easy.
Discovery history
The Penrose Triangle was discovered back in 1934 by Swedish artist Oscar Reutersvärd. The figure was presented in the form of cubes assembled together. In the future, the artist began to be called "the father of impossible figures."
Perhaps the Reutersvärd drawing would have remained little known. But in 1954, the Swedish mathematician Roger Penrose wrote a paper on impossible figures. This was the second birth of the triangle. True, the scientist presented it in a more familiar form. He did not use cubes, but beams. Three beams were connected to each other at an angle of 90 degrees. The difference was also that Reutersvärd used parallel perspective while painting. And Penrose applied a linear perspective, which made the drawing even more impossible. Such a triangle was published in 1958 in a British psychology journal.
In 1961, the artist Maurits Escher (Holland) created one of his most popular lithographs "Waterfall". It was inspired by the article about impossible figures.
In the 1980s, tribars and other impossible figures were depicted on the state postage stamps of Sweden. This went on for several years.
At the end of the last century (more precisely, in 1999), an aluminum sculpture was created in Australia, depicting the impossible Penrose triangle. It reached a height of 13 meters. Similar sculptures, only smaller in size, are also found in other countries.
Impossible in reality
As you might have guessed, the Penrose triangle is not really a triangle in the usual sense. It is three sides of a cube. But if you look from a certain angle, you get the illusion of a triangle due to the fact that 2 angles completely coincide on the plane. The nearest from the viewer and the far corners are visually combined.
If you are careful, you can guess that the tri-bar is nothing but an illusion. The actual appearance of the figure can give out a shadow from it. It shows that in fact the corners are not connected. And, of course, everything becomes clear if you pick up the figure.
Making a figure with your own hands
Penrose triangle can be assembled by yourself. For example, from paper or cardboard. And the diagrams will help in this. They just need to be printed and glued. There are two diagrams on the Internet. One of them is a little easier, the other is more difficult, but more popular. Both are shown in the pictures.
Penrose Triangle will be an interesting product that guests will definitely like. It certainly won't go unnoticed. The first step to create it is to prepare the schema. It is transferred to paper (cardboard) using a printer. And then it's even easier. It just needs to be cut around the perimeter. The diagram already has all the necessary lines. It will be more convenient to work with thicker paper. If the diagram is printed onthin paper, but you want something denser, the blank is simply applied to the selected material and cut out along the contour. To keep the pattern from moving, you can attach it with paper clips.
Next, you need to determine the lines along which the workpiece will be bent. As a rule, it is represented by a dotted line in the diagram. We bend the part. Next, we determine the places that are subject to gluing. They are coated with PVA glue. The part is connected into a single figure.
Detail can be painted. Or you can initially use colored cardboard.
Drawing an impossible figure
Penrose triangle can also be drawn. To begin with, a simple square is drawn on the sheet. Its size doesn't matter. With the base on the bottom side of the square, a triangle is drawn. Small rectangles are drawn in its corners inside. Their sides will need to be erased, leaving only those that are in common with the triangle. The result should be a triangle with truncated corners.
A straight line is drawn from the left side of the upper lower corner. The same line, but slightly shorter, is drawn from the lower left corner. A line extending from the right corner is drawn parallel to the base of the triangle. It turns out the second dimension.
According to the principle of the second, the third dimension is drawn. Only in this case, all lines are based on the corners of the figure, not the first, but the second dimension.
