The Penrose triangle, also known as the Penrose tribar, the impossible tribar,[1] or the impossible triangle,[2] is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing. It cannot exist as a solid object in ordinary three-dimensional Euclidean space, although its surface can be embedded isometrically (bent but not stretched) in five-dimensional Euclidean space.[3] It was first created by the Swedish artist Oscar Reutersvärd in 1934.[4] Independently from Reutersvärd, the triangle was devised and popularized in the 1950s by psychiatrist Lionel Penrose and his son, the mathematician and Nobel Prize laureate Roger Penrose, who described it as "impossibility in its purest form".[5] It is featured prominently in the works of artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it.
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brorubwas invoked but never defined (see the help page). - ^ Zeng, Zhenbing; Xu, Yaochen; Yang, Zhengfeng; Li, Zhi-bin (2021). "An isometric embedding of the impossible triangle into the Euclidean space of lowest dimension" (PDF). In Corless, Robert M.; Gerhard, Jürgen; Kotsireas, Ilias S. (eds.). Maple in Mathematics Education and Research: 4th Maple Conference, MC 2020, Waterloo, Ontario, Canada, November 2–6, 2020, Revised Selected Papers. Springer International Publishing. pp. 438–457. doi:10.1007/978-3-030-81698-8_29. ISBN 9783030816988.
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