HomelinessDo it yourself

What do you need to know about the Penrose triangle?

Impossible is still possible. And a vivid confirmation of this is the impossible triangle of Penrose. Opened in the last century, it is still often found in the scientific literature. And no matter how amazing it may sound, you can make it yourself. And it's not difficult to do this. Many lovers of drawing or collecting origami have long been able to do this.

The value of Penrose's 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".

Under these definitions one understands one of the main impossible figures. If to judge by the name, then it is impossible to get such a figure in reality. But in practice it has been proved that it is still possible to do this. 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 is the three cube edges. And to make such a construction is easy.

History of the discovery

The Penrose triangle was discovered in 1934 by Oscar Reutersvard, an artist from Sweden. The figure was presented in the form of cubes together. Later, the artist was called "the father of impossible figures."

Perhaps Reutersvard's design would have remained little-known. But in 1954, the Swedish mathematician Roger Penrose wrote an article about impossible figures. This was the second birth of the triangle. True, the scientist presented it in a more familiar form. He used not cubes, but beams. Three beams joined together at an angle of 90 degrees. The difference was also that Reutersvard used a parallel perspective during drawing. And Penrose used a linear perspective, which made the drawing even more impossible. Such a triangle was published in 1958 in a British journal on psychology.

In 1961, the artist Maurits Esher (Holland) created one of his most popular lithographs "Waterfall". It was created under the impression, which was caused by the article about impossible figures.

In the eighties of the last century, tribar and other impossible figures were portrayed on Swedish state stamps. It continued for several years.

At the end of the last century (or, more precisely, in 1999), an aluminum sculpture was created in Australia, depicting the impossible triangle of Penrose. It 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 the cube. But if you look from a certain angle, you get the illusion of a triangle due to the fact that on the plane there are 2 angles completely coinciding. Visually, the near from the viewer and the far corners are combined.

If you are careful, you can guess that tribar is nothing but an illusion. The real form of the figure can give a shadow from it. It shows that in fact the corners do not unite. And, of course, everything becomes clear if the figure is taken in hand.

Making a figure yourself

The Penrose triangle can be collected independently. For example, from paper or cardboard. And help in this scheme. They need only be printed and glued. There are two schemes on the Internet. One of them is slightly lighter, the other is more complicated, but more popular. Both are presented in the figures.

The Penrose triangle will be an interesting product, which the guests will surely like. He definitely will not go unnoticed. The first stage for its creation is the preparation of the scheme. It is transferred to paper (cardboard) using a printer. And then everything is even simpler. You just need to cut it around the perimeter. The diagram already has all the necessary lines. It will be more convenient to work with more dense paper. If the circuit is printed on thin paper, but you want something more dense, the workpiece is simply applied to the selected material and cut out 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 bend. As a rule, on the diagram it is represented by a dashed line. Bend the part. Next, we determine the places that are to be glued together. They are smeared with PVA glue. The item is connected in a single shape.

The detail can be colored. And you can initially use colored cardboard.

Draw the impossible shape

The Penrose triangle can also be drawn. To begin with, a simple square is drawn on the sheet. Its size does not matter. With a bottom on the bottom side of the square, a triangle is drawn. In its corners, small rectangles are drawn inside. Their sides will have 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. In parallel with the base of the triangle, a line extending from the right corner is drawn. The second dimension is obtained.

By the principle of the second, the third dimension is drawn. Only in this case, all straight lines are based on the angles of the figure not of the first, but of the second dimension.

Similar articles

 

 

 

 

Trending Now

 

 

 

 

Newest

Copyright © 2018 en.birmiss.com. Theme powered by WordPress.