Waterfall

M. C. Escher, 1961

lithograph, 38 × 30 cm

Waterfall is a lithograph print by the Dutch artist M.C. Escher which was first printed in October, 1961. It shows an apparent paradox where water from the base of a waterfall appears to run downhill before reaching the top of the waterfall. Image File history File links Download high resolution version (865x1080, 357 KB)http://people. ... Maurits Cornelis Escher (June 17, 1898 – March 27, 1972), usually referred to as M. C. Escher, was a Dutch graphic artist known for his often mathematically inspired woodcuts, lithographs and mezzotints which feature impossible constructions, explorations of infinity, architecture, and tessellations. ... 1961 (MCMLXI) was a common year starting on Sunday (the link is to a full 1961 calendar). ... Lithography stone and mirror-image print of a map of Munich. ... Lithography stone and mirror-image print of a map of Munich. ... Hand with Reflecting Sphere (Self-Portrait in Spherical Mirror), 1935. ... 1961 (MCMLXI) was a common year starting on Sunday (the link is to a full 1961 calendar). ... Look up paradox in Wiktionary, the free dictionary. ... This article does not adequately cite its references or sources. ...

While most two-dimensional artists use relative proportions to create an illusion of depth, Escher here and elsewhere uses conflicting proportions to create the visual paradox. Waterfall has the structure of a Penrose triangle, an impossible object designed independently by Roger Penrose and Oscar Reutersvärd. The Penrose triangle Impossible Triangle sculpture, East Perth, Australia The Penrose triangle, also known as the tribar, is an impossible object. ... Two famous undecidable figures, the Penrose triangle and devils pitchfork. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. ... The Stockholm-born artist Oscar Reutersvärd (1915–2002), the father of the impossible figure, pioneered the art of impossible objects. ...

The image depicts a village or part of a small city with an elevated aqueduct and waterwheel as the main focus. The aqueduct begins at the waterwheel and flows behind it. The walls of the aqueduct step downward, suggesting that it slopes downhill. The aqueduct turns sharply three times, first to the left, then straight forward and finally to the left again. We are looking down at the scene diagonally, which means that from our perspective the aqueduct appears to be slanted upward. We are also looking across it diagonally from the lower right, which means from our perspective the two left-hand turns are directly in line with each other, while the waterwheel, the forward turn and the end of the aqueduct are all in line. The second left-hand turn is supported by pillars from the first, while the other two corners are supported by a tower of pillars that begins at the waterwheel. The water falls off the edge of the aqueduct and over the waterwheel in an infinite cycle. (In his notes on the picture, Escher points out that some water must be periodically added to this apparent perpetual motion machine to compensate for evaporation.) The two support towers continue above the aqueduct and are topped by two compound polyhedra. The one on the left is a compound of three cubes. The one on the right is a stellation of a rhombic dodecahedron (or a compound of three octahedrons). Pont du Gard, France, a Roman aqueduct built circa 19 BC. It is one of Frances top tourist attractions and a World Heritage Site. ... An overshot water wheel standing 42 feet high powers the Old Mill at Berry College in Rome, Georgia A water wheel (also waterwheel, Norse mill, Persian wheel or noria) is a hydropower system; a system for extracting power from a flow of water. ... This article or section should include material from Parallel Path See also Perpetuum mobile as a musical term Perpetual motion machines (the Latin term perpetuum mobile is not uncommon) are a class of hypothetical machines which would produce useful energy in a way science cannot explain (yet). ... This article or section is in need of attention from an expert on the subject. ... In mathematics, there are three related meanings of the term polyhedron: in the traditional meaning it is a 3-dimensional polytope, and in a newer meaning that exists alongside the older one it is a bounded or unbounded generalization of a polytope of any dimension. ... A cube[1] is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. ... Stellation is a process of constructing new polygons (in two dimensions), new polyhedra in three dimensions, or in general new polytopes in n dimensions. ... This shape is a Rhombus In geometry, a rhombus (also known as a rhomb) is a parallelogram in which all of the sides are of equal length. ... A dodecahedron is any polyhedron with twelve faces, but usually a regular dodecahedron is meant: a Platonic solid composed of twelve regular pentagonal faces, with three meeting at each vertex. ... An octahedron (plural: octahedra) is a polyhedron with eight faces. ...

Below the mill is a garden of bizarre, giant plants. This is actually a magnified view of a cluster of moss and lichen which Escher drew in ink as a study in 1942. Subclasses Sphagnidae Andreaeidae Tetraphidae Polytrichidae Archidiidae Buxbaumiidae Bryidae Mosses are small, soft plants that are typically 1–10 cm tall, though some species are much larger. ... Lichenes from Ernst Haeckels Artforms of Nature, 1904 Lichens are symbiotic associations of a fungus (the mycobiont) with a photosynthetic partner (the photobiont also known as the phycobiont) that can produce food for the lichen from sunlight. ... 1942 (MCMXLII) was a common year starting on Thursday (the link is to a full 1942 calendar). ...

The background seems to be an endlessly climbing expanse of terraced farmland. Terraced vineyards near Lausanne The Incan terraces at Písac are still used today. ...

A stylised version of the channel in Waterfall with ambiguous 3-dimensional detail added