Editing M. C. Escher (section)

=== Geometries ===

{{further|Perspective (geometry)|Curvilinear perspective}}

[[File:The Artist - Maurits Cornelis Escher - working at his Atelier (50385403156).jpg|thumb|Escher at work on ''Sphere Surface with Fish'' (1958) in his workshop, using a [[mahlstick]] for support, late 1950s]]
<!--blank lines are for readability when editing-->

Although Escher did not have mathematical training – his understanding of mathematics was largely visual and intuitive – his [[mathematics and art|art had a strong mathematical component]], and several of the worlds that he drew were built around impossible objects. After 1924 Escher turned to sketching landscapes in Italy and [[Corsica]] with irregular [[perspective (geometry)|perspectives]] that are impossible in natural form. His first print of an impossible reality was ''[[Still Life and Street]]'' (1937); impossible stairs and multiple visual and gravitational perspectives feature in popular works such as ''[[Relativity (M. C. Escher)|Relativity]]'' (1953).{{efn|See [[Relativity (M. C. Escher)]] article for image.}} ''[[House of Stairs]]'' (1951) attracted the interest of the mathematician [[Roger Penrose]] and his father, the biologist [[Lionel Penrose]]. In 1956, they published a paper, "Impossible Objects: A Special Type of Visual Illusion" and later sent Escher a copy. Escher replied, admiring the Penroses' [[Penrose stairs|continuously rising flights of steps]], and enclosed a print of ''[[Ascending and Descending]]'' (1960). The paper contained the tribar or [[Penrose triangle]], which Escher used repeatedly in his lithograph of a building that appears to function as a [[perpetual motion]] machine, ''[[Waterfall (M. C. Escher)|Waterfall]]'' (1961).{{efn|See [[Waterfall (M. C. Escher)]] article for image.}}<ref name=Seckel2004>{{cite book |last=Seckel |first=Al |title=Masters of Deception: Escher, Dalí & the Artists of Optical Illusion |url=https://archive.org/details/mastersofdecepti00alse |url-access=registration |year=2004 |publisher=Sterling |isbn=978-1-4027-0577-9 |pages=[https://archive.org/details/mastersofdecepti00alse/page/81 81]–94, 262}} Chapter 5 is on Escher.</ref><ref>{{cite journal |last1=Penrose |first1=L.S. |last2=Penrose |first2=R. |title=Impossible objects: A special type of visual illusion |journal=[[British Journal of Psychology]] |year=1958 |volume=49 |issue=1 |pages=31–33 |doi=10.1111/j.2044-8295.1958.tb00634.x | pmid=13536303}}</ref><ref>{{cite book | last1=Kirousis | first1=Lefteris M. | last2=Papadimitriou | first2=Christos H. | title=26th Annual Symposium on Foundations of Computer Science (SFCS 1985) | chapter=The complexity of recognizing polyhedral scenes | author2-link=Christos Papadimitriou | doi=10.1109/sfcs.1985.59 | pages=175–185 | year=1985| isbn=978-0-8186-0644-1 | citeseerx=10.1.1.100.4844 }}</ref><ref>{{cite book | last=Cooper | first=Martin | title=Inequality, Polarization and Poverty | contribution=Tractability of Drawing Interpretation | doi=10.1007/978-1-84800-229-6_9 | isbn=978-1-84800-229-6 | pages=217–230 | publisher=Springer-Verlag | year=2008}}</ref>

Escher was interested enough in [[Hieronymus Bosch]]'s 1500 triptych ''[[The Garden of Earthly Delights]]'' to re-create part of its right-hand panel, ''Hell'', as a lithograph in 1935. He reused the figure of a [[Middle Ages|Mediaeval]] woman in a two-pointed headdress and a long gown in his lithograph ''[[Belvedere (M. C. Escher)|Belvedere]]'' in 1958; the image is, like many of his other "extraordinary invented places",<ref name=Poole>{{cite news |last1=Poole |first1=Steven |title=The impossible world of MC Escher |url=https://www.theguardian.com/artanddesign/2015/jun/20/the-impossible-world-of-mc-escher |newspaper=The Guardian |access-date=2 November 2015 |date=20 June 2015}}</ref> peopled with "[[jester]]s, [[wikt:knave|knaves]], and contemplators".<ref name=Poole /> Thus, Escher not only was interested in possible or impossible geometry but was, in his own words, a "reality enthusiast";<ref name=Poole /> he combined "formal astonishment with a vivid and idiosyncratic vision".<ref name=Poole />

Escher worked primarily in the media of [[Lithography|lithographs]] and [[woodcut]]s, although the few [[mezzotint]]s he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures, and space. Integrated into his prints were mirror images of cones, spheres, cubes, rings, and spirals.<ref>{{cite web |url=http://www.mcescher.com/Biography/biography.htm |title=The Official M.C. Escher Website – Biography |access-date=7 December 2013 |archive-url=https://web.archive.org/web/20130702184317/http://www.mcescher.com/Biography/biography.htm |archive-date=2 July 2013 |url-status=dead }}</ref>

Escher was fascinated by mathematical objects such as the [[Möbius strip]], which has only one surface. His wood engraving ''Möbius Strip II'' (1963) depicts a chain of ants marching forever over what, at any one place, are the two opposite faces of the object—which are seen on inspection to be parts of the strip's single surface. In Escher's own words:<ref name=NGC>{{cite web |title=Möbius Strip II, February 1963 |url=https://www.gallery.ca/en/see/collections/artwork.php?mkey=21164 |website=Collections |publisher=National Gallery of Canada |access-date=2 November 2015 |archive-url=https://web.archive.org/web/20150719142225/http://www.gallery.ca/en/see/collections/artwork.php?mkey=21164 |archive-date=19 July 2015 |url-status=dead }} which cites {{cite book |last1=Escher |first1=M. C. |title=M. C. Escher, the Graphic Work |date=2001 |publisher=Taschen}}</ref>

{{blockquote|An endless ring-shaped band usually has two distinct surfaces, one inside and one outside. Yet on this strip nine red ants crawl after each other and travel the front side as well as the reverse side. Therefore the strip has only one surface.<ref name=NGC />}}

The mathematical influence in his work became prominent after 1936, when, having boldly asked the Adria Shipping Company if he could sail with them as travelling artist in return for making drawings of their ships, they surprisingly agreed, and he sailed the [[Mediterranean Sea|Mediterranean]], becoming interested in order and symmetry. Escher described this journey, including his repeat visit to the Alhambra, as "the richest source of inspiration I have ever tapped".<ref name=StAndrews>{{cite web |last1=O'Connor |first1=J. J. |last2=Robertson |first2=E. F. |title=Maurits Cornelius Escher |url=http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Escher.html |website=Biographies |publisher=University of St Andrews |access-date=2 November 2015 |date=May 2000 |archive-url=https://web.archive.org/web/20150925235220/http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Escher.html |archive-date=25 September 2015 |url-status=dead }} which cites {{cite news |author=Strauss, S. |title=M C Escher |work=The Globe and Mail |date=9 May 1996}}</ref>

Escher's interest in [[curvilinear perspective]] was encouraged by his friend and "kindred spirit",<ref name=ErnstinEmmerSchattschneider2007>{{cite book |last1=Emmer |first1=Michele |last2=Schattschneider |first2=Doris|last3=Ernst |first3=Bruno |title=M.C. Escher's Legacy: A Centennial Celebration |url=https://books.google.com/books?id=5DDyBwAAQBAJ&pg=PA16 |year=2007 |publisher=Springer |isbn=978-3-540-28849-7 |pages=10–16}}</ref> the art historian and artist Albert Flocon, in another example of constructive mutual influence. Flocon identified Escher as a "thinking artist"<ref name=ErnstinEmmerSchattschneider2007 /> alongside [[Piero della Francesca]], [[Leonardo da Vinci]], [[Albrecht Dürer]], [[Wenzel Jamnitzer]], [[Abraham Bosse]], [[Girard Desargues]], and [[Père Nicon]].<ref name=ErnstinEmmerSchattschneider2007 /> Flocon was delighted by Escher's ''Grafiek en tekeningen'' ("Graphics and Drawings"), which he read in 1959. This stimulated Flocon and André Barre to correspond with Escher and to write the book ''La Perspective curviligne'' ("[[Curvilinear perspective]]").<ref>{{cite book |author1=Flocon, Albert |author2=Barre, André | title=La Perspective curviligne |publisher=Flammarion |year=1968}}</ref>