| Belvedere | |
|---|---|
 | |
| Artist | M. C. Escher |
| Year | 1958 |
| Type | Lithograph |
| Dimensions | 46.2 cm× 29.5 cm(18.2 in× 11.6 in) |
Belvedere is a lithograph print by the Dutch artist M. C. Escher, first printed in May 1958. It shows a plausible-looking belvedere building that is an impossible object, modelled after an impossible cube.
In this lithograph, Escher uses two-dimensional images to depict objects free of the confines of the three-dimensional world. The image is of a rectangular, three-story building. The upper two floors are open at the sides, with the top floor and roof supported by pillars. From the viewer's perspective, all the pillars on the middle floor are the same size at both the front and back, but the pillars at the back are set higher. The viewer also sees by the corners of the top floor that it is at a different angle than the rest of the structure. All these elements make it possible for all the pillars on the middle floor to stand at right angles, yet the pillars at the front support the back side of the top floor while the pillars at the back support the front side. This paradox also allows a ladder to extend from the inside of the middle floor to the outside of the top floor.
There is a man seated at the foot of the building holding an impossible cube. He appears to be constructing it from a diagram of a Necker cube at his feet, with the intersecting lines circled. The window next to him is closed with an iron grille that is geometrically valid, but practically impossible to assemble.
The woman about to climb the steps of the building is modeled after a figure from the right-hand panel of Hieronymus Bosch's 1500 triptych The Garden of Earthly Delights . This panel is individually titled Hell; a portion of it was recreated by Escher as a lithograph in 1935. [1]
The ridge in the background is part of the Morrone Mountains in Abruzzo, that Escher had visited several times when living in Italy during the 1920s and 1930s.
In 2012, Prof. Gershon Elber of Israel's Technion University, using specially designed CAD software and a 3D printer, created a 3D model of Belvedere and other impossible Escher structures, viewable only from one angle. [2]
Maurits Cornelis Escher was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for most of his life neglected in the art world, even in his native Netherlands. He was 70 before a retrospective exhibition was held. In the late twentieth century, he became more widely appreciated, and in the twenty-first century he has been celebrated in exhibitions across the world.
Technical drawing, drafting or drawing, is the act and discipline of composing drawings that visually communicate how something functions or is constructed.
The Penrose triangle, also known as the Penrose tribar, the impossible tribar, or the impossible triangle, is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing, but cannot exist as a solid object. It was first created by the Swedish artist Oscar Reutersvärd in 1934. Independently from Reutersvärd, the triangle was devised and popularized in the 1950s by psychiatrist Lionel Penrose and his son, prominent Nobel Prize-winning mathematician Sir Roger Penrose, who described it as "impossibility in its purest form". It is featured prominently in the works of artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it.
An impossible object is a type of optical illusion that consists of a two-dimensional figure which is instantly and naturally understood by the retina as representing a projection of a three-dimensional object.
The impossible cube or irrational cube is an impossible object invented by M.C. Escher for his print Belvedere. It is a two-dimensional figure that superficially resembles a perspective drawing of a three-dimensional cube, with its features drawn inconsistently from the way they would appear in an actual cube.
An engineering drawing is a type of technical drawing that is used to convey information about an object. A common use is to specify the geometry necessary for the construction of a component and is called a detail drawing. Usually, a number of drawings are necessary to completely specify even a simple component. The drawings are linked together by a master drawing or assembly drawing which gives the drawing numbers of the subsequent detailed components, quantities required, construction materials and possibly 3D images that can be used to locate individual items. Although mostly consisting of pictographic representations, abbreviations and symbols are used for brevity and additional textual explanations may also be provided to convey the necessary information.
The Penrose stairs or Penrose steps, also dubbed the impossible staircase, is an impossible object created by Oscar Reutersvärd in 1937 and later independently made popular 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-dimensional Euclidean geometry.
Reptiles is a lithograph print by the Dutch artist M. C. Escher first printed in March 1943. It touches on the theme found in much of his work of mathematics in art.
Magic Mirror is a lithograph print by the Dutch artist M. C. Escher first printed in January, 1946.
Another World II, also known as Other World II, is a woodcut print by the Dutch artist M. C. Escher first printed in January 1947.
Convex and Concave is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1955.
Waterfall is a lithograph by the Dutch artist M. C. Escher, first printed in October 1961. It shows a perpetual motion machine where water from the base of a waterfall appears to run downhill along the water path before reaching the top of the waterfall.
The Droste effect, known in art as an example of mise en abyme, is the effect of a picture recursively appearing within itself, in a place where a similar picture would realistically be expected to appear. This produces a loop which mathematically could go on forever, but in practice only continues as far as the image's resolution allows.
Anamorphosis is a distorted projection requiring the viewer to occupy a specific vantage point, use special devices, or both to view a recognizable image. It is used in painting, photography, sculpture and installation, toys, and film special effects. The word is derived from the Greek prefix ana-, meaning "back" or "again", and the word morphe, meaning "shape" or "form". Extreme anamorphosis has been used by artists to disguise caricatures, erotic and scatological scenes, and other furtive images from a casual spectator, while revealing an undistorted image to the knowledgeable viewer.
In geometry, the rhombille tiling, also known as tumbling blocks, reversible cubes, or the dice lattice, is a tessellation of identical 60° rhombi on the Euclidean plane. Each rhombus has two 60° and two 120° angles; rhombi with this shape are sometimes also called diamonds. Sets of three rhombi meet at their 120° angles, and sets of six rhombi meet at their 60° angles.
Ascending and Descending is a lithograph print by the Dutch artist M. C. Escher first printed in March 1960.
Cube with Magic Ribbons is a lithograph print by the Dutch artist M. C. Escher first printed in 1957. It depicts two interlocking bands wrapped around the frame of a Necker cube. The bands have what Escher called small "nodules" or "buttonlike protuberances" that make use of the dome/crater illusion, an optical illusion characterized by shifting perception of depth from concave to convex depending on direction of light and shadow. Escher's interest in reversible perspectives, as seen in Cube with Magic Ribbons, can also be noted in an earlier work, Convex and Concave, first printed in 1955.
In technical drawing and computer graphics, a multiview projection is a technique of illustration by which a standardized series of orthographic two-dimensional pictures are constructed to represent the form of a three-dimensional object. Up to six pictures of an object are produced, with each projection plane parallel to one of the coordinate axes of the object. The views are positioned relative to each other according to either of two schemes: first-angle or third-angle projection. In each, the appearances of views may be thought of as being projected onto planes that form a six-sided box around the object. Although six different sides can be drawn, usually three views of a drawing give enough information to make a three-dimensional object. These views are known as front view, top view and end view. Other names for these views include plan, elevation and section. When the plane or axis of the object depicted is not parallel to the projection plane, and where multiple sides of an object are visible in the same image, it is called an auxiliary view.
Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Stereoscopic depth rendition specifies how the depth of a three-dimensional object is encoded in a stereoscopic reconstruction. It needs attention to ensure a realistic depiction of the three-dimensionality of viewed scenes and is a specific instance of the more general task of 3D rendering of objects in two-dimensional displays.