PENROSE TRIAGLE

Inspired by an Escher exhibition at a mathematics congress in 1954, the mathematician Roger Penrose and his father, the geneticist Lionel Penrose, became interested in the so-called impossible figures (the triangle, the ladder, etc.), and published their findings in a British psychology journal in 1958. Escher himself simultaneously began to create his own figures and turned the idea into art.

This piece you see, in general, as it appears above.

Now try to position yourself, closing one of your eyes, to see it as it appears below.

The title of "father" of the impossible figures, however, is given to the late artist Oscar Reutersvärd, who had been drawing them since 1934, when he was not yet 20-years-old, during his Latin classes. Reutersvärd never thought they would have artistic recognition, so he did not release them until he saw the Penrose article and Escher's work.

USEFUL LINKS

This Wikipedia page talks about impossible objects, also called undecidable figures. In it, the main examples are discussed (allowing access to other links with specific figures), about their history and about some impossible objects that were built in the form of sculpture.

This ichi.pro page talks about what makes a figure impossible. In this process, some of these figures are made explicit, such as Penrose's triangle and ladder, and the impossible cube. Some paintings that portray the idea of impossibility are also used as a reference.

If you are specifically interested in the Penrose Triangle, this Dinamática page provides a brief summary of it. After that, you can use an online application that allows you to rotate and tilt an impossible triangle for an optical illusion. It is also possible to disassemble it to see its parts.

Continuing on the theme of the Penrose triangle, this Matemática Rio com Prof. Rafael Procopio's channel video teaches you how to draw an impossible triangle using just a pen and string. Although it doesn't create as perfect an illusion as the piece itself, it is possible to use it to explain the concept behind it.

Roger Penrose's biggest inspiration was M.C. Escher, and it's precisely about him that this A.Muse.Arte page talks. In addition to offering a brief biography, it shows some of his main "impossible" works, explaining how each one was thought and built, including a Möbius strip.                                                                                        

Finally, this Super Interessante's article also talks about M.C. Escher, from a more biographical and historical point of view. It is discussed how he did not do well in school and did not understand academic arts classes very well, and also about the main concepts involved in his works.