Penrose triangle

The Penrose triangle, also called Tribar, is a so-called " impossible figure ". It shows three bars that are mutually at right angles and are still connected to form a triangle. Thus, it violates several laws of Euclidean geometry, for example against that which states that the sum of interior angles in a triangle is always 180 °. The viewer a Tribar representation is confronted with the difficulty of having to reinterpret its distance to the parts of Tribars and their location in the space shown again and again.

The invention of the Tribars

The Tribar was invented in 1934 by the Swedish artist Oscar Reutersvärd, whose works, however, until the 1980s, the public remained largely unknown.

Another time it was invented by the mathematician Roger Penrose, after which it is named. He had participated in the International Congress of Mathematicians in Amsterdam in 1954, to its occasion an exhibition of paintings by the Dutch graphic artist MC Was organized Escher. Inspired by the illustrations of Escher he tried himself in designing impossible figures. Most clearly the principle of impossible figures seemed realized in Tribar. Together with his father, Lionel Penrose, who was inspired by the designs of his son to design the infinite Penrose stairs, he published in 1958 an article about the Tribar in the British Journal of Psychology.

The Tribar in art

Figures, which are formed on similar principles to that of the Tribars, there was in art since the invention of perspective. One example is the " Carceri " by Italian artist Giovanni Battista Piranesi, where a partially impossible architecture is shown.

In the 20th century Reutersvärd had experimented with the presentation of impossible figures since 1934, including those of the Tribars. His work, however, won only in the eighties the attention of the crowd. At that time the Swedish Post has also published three stamps with impossible objects Reutersvärds that are based on similar principles as that of the Tribars.

Escher was made by Penrose attention to the Tribar. He already had his picture "Belvedere" designed as Penrose sent him a copy of his article. This inspired him to his picture " steps on the staircases " to where he took over the infinite staircase of Lionel Penrose without major changes, and a little later his picture " waterfall " of a waterfall showing the viewer that feeds itself and its representation on the Tribar based.

Is an impossible object as the Tribar possible?

Penrose gives in his article on the simplest answer: "Every single part of a figure is acceptable as a representation of an object which is normally in space; the acceptance of the whole object, but as a result performs incorrect connections between the individual parts to the deceptive effect of an impossible structure. "

An impossible figure thus fulfills two conditions: 1 It consists of individual parts that are possible in the image space without contradiction. These second parts are connected in such a way that on the two-dimensional image surface in three dimensional space, however, is impossible, although shown possible.

For the explanation of these figures, the findings of Gestalt psychology play an important role, especially that seeing is not a passive process, but always also the active interpretation of what is seen, that the whole of perception is something else than the sum of its parts and that we are the illusion can not escape, even if it is something seemingly impossible.