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- Q58914 subject Q6966800.
- Q58914 subject Q8543434.
- Q58914 subject Q8790080.
- Q58914 abstract "The Penrose stairs or Penrose steps, also dubbed the impossible staircase, is an impossible object created by Lionel Penrose and his son Roger Penrose. A variation on the Penrose triangle, it is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher. This is clearly impossible in three dimensions.The "continuous staircase" was first presented in an article that the Penroses wrote in 1959, based on the so-called "triangle of Penrose" published by Roger Penrose in the British Journal of Psychology in 1958. M.C. Escher then discovered the Penrose stairs in the following year and made his now famous lithograph Klimmen en dalen (Ascending and Descending) in March 1960. Penrose and Escher were informed of each other's work that same year. Escher developed the theme further in his print Waterval (Waterfall), which appeared in 1961.In their original article the Penroses noted that "each part of the structure is acceptable as representing a flight of steps but the connexions are such that the picture, as a whole, is inconsistent: the steps continually descend in a clockwise direction."".
- Q58914 thumbnail Impossible_staircase.svg?width=300.
- Q58914 wikiPageExternalLink impossible_staircase.html.
- Q58914 wikiPageExternalLink Acoustics_Today_2010_Jul.pdf.
- Q58914 wikiPageExternalLink books?id=iKleTxffj5IC&pg=PA172.
- Q58914 wikiPageWikiLink Q11461.
- Q58914 wikiPageWikiLink Q1191396.
- Q58914 wikiPageWikiLink Q12141.
- Q58914 wikiPageWikiLink Q1470.
- Q58914 wikiPageWikiLink Q193803.
- Q58914 wikiPageWikiLink Q2032939.
- Q58914 wikiPageWikiLink Q25188.
- Q58914 wikiPageWikiLink Q254.
- Q58914 wikiPageWikiLink Q2635126.
- Q58914 wikiPageWikiLink Q278053.
- Q58914 wikiPageWikiLink Q2864650.
- Q58914 wikiPageWikiLink Q339375.
- Q58914 wikiPageWikiLink Q378145.
- Q58914 wikiPageWikiLink Q4096602.
- Q58914 wikiPageWikiLink Q601362.
- Q58914 wikiPageWikiLink Q6966800.
- Q58914 wikiPageWikiLink Q8543434.
- Q58914 wikiPageWikiLink Q860611.
- Q58914 wikiPageWikiLink Q8790080.
- Q58914 wikiPageWikiLink Q9418.
- Q58914 comment "The Penrose stairs or Penrose steps, also dubbed the impossible staircase, is an impossible object created by Lionel Penrose and his son Roger Penrose. A variation on the Penrose triangle, it is a two-dimensional depiction of a staircase in which the stairs make four 90-degree turns as they ascend or descend yet form a continuous loop, so that a person could climb them forever and never get any higher.".
- Q58914 label "Penrose stairs".
- Q58914 depiction Impossible_staircase.svg.