The impossible is still possible. And a vivid confirmation of this is the impossible Penrose triangle. Opened in the last century, it is still often found in the scientific literature. And no matter how surprising it may sound, but it can even be made independently. And to do this is not difficult at all. Many fans of drawing or collecting origami have long been able to do this.
Penrose Triangle Value
There are several names for this figure. Some call it an impossible triangle, others simply a tribar. But most often you can meet the definition of "Penrose triangle."
Under these definitions one of the main impossible figures. Judging by the name, it is impossible to get a similar figure in reality. But in practice it has been proven that this can still be done. That's just the shape of the triangle, the figure will take if you look at it from a certain point at the right angle. On all other sides, the figure is quite real. It represents three edges of a cube. And to make a similar design is easy.
Discovery story
The Penrose Triangle was discovered back in 1934 by an artist from Sweden, Oscar Reutersward. 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 Reutersward's drawing would have remained little known. But in 1954, the Swedish mathematician Roger Penrose wrote an article about impossible figures. This became the second birth of the triangle. True, the scientist introduced him in a more familiar form. He used not cubes, but beams. Three beams connected to each other at an angle of 90 degrees. The difference was also that Reutersward used a parallel perspective while painting. And Penrose applied the perspective of a linear nature, which gave the picture even more impossibility. Such a triangle was published in 1958 in a British journal of psychology.
In 1961, the artist Maurits Escher (Holland) created one of his most popular lithographs, Waterfall. It was created under the impression that was caused by the article about impossible figures.
In the eighties of the last century, the tribar and other impossible figures were depicted on state postage stamps of Sweden. This went on for several years.
At the end of the last century (or rather, in 1999), an aluminum sculpture was created in Australia, depicting the impossible Penrose triangle. She reached a height of 13 meters. Similar sculptures, only smaller in size, are 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 represents the three faces 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. Visually combines the near and far angles from the beholder.
If you be careful, you can guess that the tribar is nothing more than an illusion. The real appearance of the figure can give out a shadow from it. It shows that in fact the corners do not connect. Well, of course, everything becomes clear if you pick up the figure.
DIY figure making
The Penrose Triangle can be assembled independently. For example, from paper or cardboard. And help with this scheme. They just need to be printed and glued. There are two schemes on the Internet. One of them is a little easier, the other is more complicated, but more popular. Both are shown in the figures.
The Penrose Triangle will be an interesting product that guests will love. He certainly will not go unnoticed. The first step in creating it is to prepare the circuit. It is transferred to paper (cardboard) using a printer. And then it’s still easier. It just needs to be cut along the perimeter. The diagram already has all the necessary lines. It will be more convenient to work with thicker paper. If the scheme is printed on thin paper, but you want something denser, the workpiece is simply applied to the selected material and cut along the contour. So that the circuit does not move, it can be attached with paper clips.
Next, you need to determine the lines along which the workpiece will be bent. As a rule, in the diagram it is represented by a dashed line. Bend the part. Next, we determine the places to be glued. They are coated with PVA glue. The detail is connected into a single figure.
The item can be painted. And you can initially use colored cardboard.
Draw an impossible figure
The Penrose Triangle can also be drawn. First, a simple square is drawn on the sheet. Its size does not matter. With a base on the underside of the square, a triangle is drawn. In its corners, small rectangles are drawn inside. Their sides will need to be erased, leaving only those that are 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 a little shorter, is drawn from the lower left corner. Parallel to the base of the triangle, a line is drawn out from the right corner. It turns out the second dimension.
By the principle of the second, the third dimension is drawn. Only in this case, all the lines are based on the corners of the figure, not the first, but the second dimension.