Penrose triangle
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Penrose_triangle.png
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 invented and popularised it in the 1950s, describing it as "impossibility in its purest form". It features prominently in the works of artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it.
The tribar can only exist as a 2-dimensional drawing, since it exploits the overlapping of parallel lines drawn in different perspectives. It appears as a solid object, made of three beams of square cross-section. All the beams are mutually perpendicular, yet join to form a triangle.
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 storeys 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.
The concept can be extended to other polygons, making, for example the "Penrose square", but the visual effect is not as striking.
It is possible to create a solid object which looks like a Penrose Triangle. Such shapes can be either curved or have a break in them, but when viewed from a certain angle give the illusion of the complete triangle.
External link
- Escher for Real constructions (http://www.cs.technion.ac.il/~gershon/EscherForReal/)
- Escher in LEGO creations (http://www.lipsons.pwp.blueyonder.co.uk/lego.htm)de:Penrose-Dreieck