Hand with Reflecting Sphere, also known as Self-Portrait in Spherical Mirror, is a lithograph by Dutch artist M. C. Escher, first printed in January 1935. The piece depicts a hand holding a reflective sphere. In the reflection, most of the room around Escher can be seen, and the hand holding the sphere is revealed to be Escher's.[citation needed]
Self-portraits in reflective, spherical surfaces are common in Escher's work. In much of his self-portraiture of this type, Escher is in the act of drawing the sphere, whereas in this image he is seated and gazing into it. On the walls there are several framed pictures, one of which appears to be of an Indonesian shadow puppet.[citation needed]
Maurits Cornelis Escher was a Dutch graphic artist who made woodcuts, lithographs, and mezzotints, many of which were inspired by mathematics. Despite wide popular interest, for most of his life Escher was 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 around the world.
A mirror, also known as a looking glass, is an object that reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the direction of the image in an equal yet opposite angle from which the light shines upon it. This allows the viewer to see themselves or objects behind them, or even objects that are at an angle from them but out of their field of view, such as around a corner. Natural mirrors have existed since prehistoric times, such as the surface of water, but people have been manufacturing mirrors out of a variety of materials for thousands of years, like stone, metals, and glass. In modern mirrors, metals like silver or aluminium are often used due to their high reflectivity, applied as a thin coating on glass because of its naturally smooth and very hard surface.
A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians.
A retroreflector is a device or surface that reflects radiation back to its source with minimum scattering. This works at a wide range of angle of incidence, unlike a planar mirror, which does this only if the mirror is exactly perpendicular to the wave front, having a zero angle of incidence. Being directed, the retroflector's reflection is brighter than that of a diffuse reflector. Corner reflectors and cat's eye reflectors are the most used kinds.
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. A list of the spherical harmonics is available in Table of spherical harmonics.
Curvilinear perspective, also five-point perspective, is a graphical projection used to draw 3D objects on 2D surfaces. It was formally codified in 1968 by the artists and art historians André Barre and Albert Flocon in the book La Perspective curviligne, which was translated into English in 1987 as Curvilinear Perspective: From Visual Space to the Constructed Image and published by the University of California Press.
Still Life with Spherical Mirror is a lithography print by the Dutch artist M. C. Escher first printed in November 1934. It depicts a setting with rounded bottle and a metal sculpture of a bird with a human face seated atop a newspaper and a book. The background is dark, but in the bottle can be seen the reflection of Escher's studio and Escher himself sketching the scene.
Magic Mirror is a lithograph print by the Dutch artist M. C. Escher first printed in January, 1946.
Three Spheres II is a lithograph print by the Dutch artist M. C. Escher first printed in April 1946.
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 Western art history, mise en abyme, literally "placement in abyss", is a formal technique of placing a copy of an image within itself, often in a way that suggests an infinitely recurring sequence. In film theory and literary theory, it refers to the technique of inserting a story within a story. The term is derived from heraldry and means "placed into abyss". It was first appropriated for modern criticism by the French author André Gide.
In computer graphics, environment mapping, or reflection mapping, is an efficient image-based lighting technique for approximating the appearance of a reflective surface by means of a precomputed texture. The texture is used to store the image of the distant environment surrounding the rendered object.
A curved mirror is a mirror with a curved reflecting surface. The surface may be either convex or concave. Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices. The most common non-spherical type are parabolic reflectors, found in optical devices such as reflecting telescopes that need to image distant objects, since spherical mirror systems, like spherical lenses, suffer from spherical aberration. Distorting mirrors are used for entertainment. They have convex and concave regions that produce deliberately distorted images. They also provide highly magnified or highly diminished (smaller) images when the object is placed at certain distances.
A self-portrait is a portrait of an artist made by themselves. Although self-portraits have been made since the earliest times, it is not until the Early Renaissance in the mid-15th century that artists can be frequently identified depicting themselves as either the main subject, or as important characters in their work. With better and cheaper mirrors, and the advent of the panel portrait, many painters, sculptors and printmakers tried some form of self-portraiture. Portrait of a Man in a Turban by Jan van Eyck of 1433 may well be the earliest known panel self-portrait. He painted a separate portrait of his wife, and he belonged to the social group that had begun to commission portraits, already more common among wealthy Netherlanders than south of the Alps. The genre is venerable, but not until the Renaissance, with increased wealth and interest in the individual as a subject, did it become truly popular.
The Hockney–Falco thesis is a theory of art history, advanced by artist David Hockney and physicist Charles M. Falco. Both argued that advances in realism and accuracy in the history of Western art since the Renaissance were primarily the result of optical instruments such as the camera obscura, camera lucida, and curved mirrors, rather than solely due to the development of artistic technique and skill. Nineteenth-century artists' use of photography had been well documented.
A plane mirror is a mirror with a flat (planar) reflective surface. For light rays striking a plane mirror, the angle of reflection equals the angle of incidence. The angle of the incidence is the angle between the incident ray and the surface normal. Therefore, the angle of reflection is the angle between the reflected ray and the normal and a collimated beam of light does not spread out after reflection from a plane mirror, except for diffraction effects.
In computer graphics, sphere mapping is a type of reflection mapping that approximates reflective surfaces by considering the environment to be an infinitely far-away spherical wall. This environment is stored as a texture depicting what a mirrored sphere would look like if it were placed into the environment, using an orthographic projection. This texture contains reflective data for the entire environment, except for the spot directly behind the sphere.
A null corrector is an optical device used in the testing of large aspheric mirrors. A spherical mirror of any size can be tested relatively easily using standard optical components such as laser, mirrors, beamsplitters, and converging lenses. One method of doing this using a Shack cube is shown at the right, and many other setups are possible. An interferometer test such as this one generates a contour map of the deviation of the surface from a perfect sphere, with the contours in units of half the wavelength used. This is called a null test because when the mirror is perfect, the result is null. If the result is not null, then the mirror is not perfect, and the pattern shows where the optician should polish the mirror to improve it.
In geometry, the order-6 square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,6}.
Dragon is a wood engraving print created by Dutch artist M. C. Escher in April 1952, depicting a folded paper dragon perched on a pile of crystals. It is part of a sequence of images by Escher depicting objects of ambiguous dimension, including also Three Spheres I, Doric Columns, Drawing Hands and Print Gallery.
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