The Penrose triangle

Impossible Triangle sculpture, East Perth, Australia

The Penrose triangle, also known as the tribar, is an impossible object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. The mathematician Roger Penrose independently devised and popularised it in the 1950s, describing it as "impossibility in its purest form". It is featured prominently in the works of artist M.C. Escher, whose earlier depictions of impossible objects partly inspired it. It is used as a symbol in the religion of Empirical Universalism, asserting the need to transcend any system of belief. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Image File history File linksMetadata Download high resolution version (1995x1155, 548 KB) Summary Impossible Triangle sculpture by Brian MacKay & Ahmad Abas, Claisebrook roundabout, East Perth, Western Australia. ... Image File history File linksMetadata Download high resolution version (1995x1155, 548 KB) Summary Impossible Triangle sculpture by Brian MacKay & Ahmad Abas, Claisebrook roundabout, East Perth, Western Australia. ... East Perth is a suburb of Perth, Western Australia, located within close proximity to the Perth CBD. It was in the early twentieth century the location of a gas works, a power station, railway yard, and sheds. ... Two famous undecidable figures, the Penrose triangle and devils pitchfork. ... The Stockholm-born artist Oscar Reutersvärd (1915–2002), the father of the impossible figure, pioneered the art of impossible objects. ... 1934 (MCMXXXIV) was a common year starting on Monday (link will take you to calendar). ... Leonhard Euler is considered by many to be one of the greatest mathematicians of all time A mathematician is the person whose primary area of study and research is the field of mathematics. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. ... // Recovering from World War II and its aftermath, the economic miracle emerged in West Germany and Italy. ... Hand with Reflecting Sphere (Self-Portrait in Spherical Mirror), 1935. ...

The tribar appears to be a solid object, made of three straight beams of square cross-section which meet pairwise at right angles at the vertices of the triangle they form. In jewelry, a solid gold piece is the alternative to gold-filled or gold-plated jewelry. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...

This combination of properties cannot be realized by any 3-dimensional object. Nevertheless, there do exist 3-dimensional solid shapes each of which, when viewed from a certain angle, has the appearance of possessing all the qualities mentioned in the above paragraph. That is, it appears the same as the purple, green, and yellow 2-dimensional depiction of the Penrose triangle on this page.

M.C. Escher's lithograph Waterfall depicts a watercourse that flows in a zigzag along the long sides of two elongated Penrose triangles, so that it ends up two stories higher than it began. The resulting waterfall, forming the short sides of both triangles, drives a water wheel. Escher helpfully points out that in order to keep the wheel turning some water must occasionally be added to compensate for evaporation. Lithography is a method for printing on a smooth surface, as well as a method of manufacturing semiconductor and MEMS devices. ... Waterfall is a lithograph print by the Dutch artist M.C. Escher which was first printed in October, 1961. ... An overshot water wheel standing 42 feet high powers the Old Mill at Berry College in Rome, Georgia A water wheel (also waterwheel, Norse mill, Persian wheel or noria) is a hydropower system; a system for extracting power from a flow of water. ... This article or section is in need of attention from an expert on the subject. ...

The concept can be extended to other polygons, making, for example the "Penrose square", but the visual effect is not as striking. Look up polygon in Wiktionary, the free dictionary. ... In plane (Euclidean) geometry, a square is a polygon with four equal sides, four right angles, and parallel opposite sides. ...

There exists some terminological confusion over whether "Penrose triangle" refers to the 2-dimensional depiction of an impossible 3-dimensional object, or that impossible object itself. (Philosophically, it is unclear what "that impossible object" refers to, other than a set of conditions that cannot be satisfied.)

If a line is traced around the Penrose triangle, a 3-loop Möbius strip is formed. A Möbius strip made with a piece of paper and tape. ...

Other Penrose polygons

While it is possible to construct a Penrose triangle with other regular polygons to create a Penrose polygon, the visual effect is not as striking, and as the sides increase, the image seems to be warped or twisted.

Penrose rectangle Image File history File links No higher resolution available. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ...

Penrose pentagon Image File history File links No higher resolution available. ... Look up pentagon in Wiktionary, the free dictionary. ...

Penrose hexagon Image File history File links No higher resolution available. ... A regular hexagon. ...

Penrose octagon Image File history File links No higher resolution available. ... For other uses, see Octagon (disambiguation). ...

External links

Wikimedia Commons has media related to:

Penrose triangle

• Escher for Real constructions
• The impossible triangle made possible