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The Penrose triangle, also known as the Penrose 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.
The tribar appears to be a solid object, made of three straight beams of square crosssection which meet pairwise at right angles^{[citation needed]} at the vertices of the triangle they form.
This combination of properties cannot be realized by any 3dimensional object in ordinary Euclidean space. Such an object can exist in certain Euclidean 3manifolds.^{[1]} There also exist 3dimensional solid shapes each of which, when viewed from a certain angle, appears the same as the purple, green, and yellow 2dimensional depiction of the Penrose triangle on this page. The term "Penrose triangle" can refer to the 2dimensional depiction or the impossible object itself.
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.
If a line is traced around the Penrose triangle, a 3loop Möbius strip is formed.
Contents
Other Penrose polygons
While it is possible to construct analogies to the Penrose triangle with other regular polygons to create a Penrose polygon, the visual effect is not as striking, and as the sides increase, the object seems merely to be warped or twisted.
Penrose square
Penrose pentagon
Penrose hexagon
Penrose octagon
See also
References
External links
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