Perspective (visual) in the context of "Mathematics and art"

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⭐ Core Definition: Perspective (visual)

Linear or point-projection perspective (from Latin perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. It is based on the optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was.

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👉 Perspective (visual) in the context of Mathematics and art

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.

Mathematics and art have a long historical relationship. Artists have used mathematics since the 4th century BC when the Greek sculptor Polykleitos wrote his Canon, prescribing proportions conjectured to have been based on the ratio 1:2 for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient art and architecture, without reliable evidence. In the Italian Renaissance, Luca Pacioli wrote the influential treatise De divina proportione (1509), illustrated with woodcuts by Leonardo da Vinci, on the use of the golden ratio in art. Another Italian painter, Piero della Francesca, developed Euclid's ideas on perspective in treatises such as De Prospectiva Pingendi, and in his paintings. The engraver Albrecht Dürer made many references to mathematics in his work Melencolia I. In modern times, the graphic artist M. C. Escher made intensive use of tessellation and hyperbolic geometry, with the help of the mathematician H. S. M. Coxeter, while the De Stijl movement led by Theo van Doesburg and Piet Mondrian explicitly embraced geometrical forms. Mathematics has inspired textile arts such as quilting, knitting, cross-stitch, crochet, embroidery, weaving, Turkish and other carpet-making, as well as kilim. In Islamic art, symmetries are evident in forms as varied as Persian girih and Moroccan zellige tilework, Mughal jali pierced stone screens, and widespread muqarnas vaulting.

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Perspective (visual) in the context of Les Demoiselles d'Avignon

Les Demoiselles d'Avignon (The Young Ladies of Avignon, originally titled The Brothel of Avignon) is a large oil painting created in 1907 by the Spanish artist Pablo Picasso. Part of the permanent collection of the Museum of Modern Art in New York, it portrays five nude female prostitutes in a brothel on Carrer d'Avinyó, a street in Barcelona, Spain. The figures are confrontational and not conventionally feminine, being rendered with angular and disjointed body shapes, some to a menacing degree. The far left figure exhibits facial features and dress of Egyptian or southern Asian style. The two adjacent figures are in an Iberian style of Picasso's Spain, while the two on the right have African mask-like features. Picasso said the ethnic primitivism evoked in these masks moved him to "liberate an utterly original artistic style of compelling, even savage force" leading him to add a shamanistic aspect to his project.

Drawing from tribal primitivism while eschewing central dictates of Renaissance perspective and verisimilitude for a compressed picture plane using a Baroque composition while employing Velazquez's confrontational approach seen in Las Meninas, Picasso sought to take the lead of the avant-garde from Henri Matisse. John Richardson said Demoiselles made Picasso the most pivotal artist in Western painting since Giotto and laid a path forward for Picasso and Georges Braque to follow in their joint development of cubism, the effects of which on modern art were profound and unsurpassed in the 20th century.

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Perspective (visual) in the context of Three Dialogues Between Hylas and Philonous

Three Dialogues between Hylas and Philonous, or simply Three Dialogues, is a 1713 book on metaphysics and idealism written by George Berkeley. Taking the form of a dialogue, the book was written as a response to the criticism Berkeley experienced after publishing A Treatise Concerning the Principles of Human Knowledge.

Three important concepts discussed in the Three Dialogues are perceptual relativity, the conceivability/master argument and Berkeley's phenomenalism. Perceptual relativity argues that the same object can appear to have different characteristics (e.g. shape) depending on the observer's perspective. Since objective features of objects cannot change without an inherent change in the object itself, shape must not be an objective feature.

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Perspective (visual) in the context of Station point

A station point is a location or vantage point from which an artist or exhibitor intends an observer to experience an artwork.

In photography, the station point is the location of the camera at the point in time when the camera records a view to a recording medium.

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Perspective (visual) in the context of Illusionistic tradition

Illusionistic tradition is a style of theatre that was created in Italy during the Renaissance. Its focus was primarily centered on grandiose spectacle in theatrical performance. Stages made use of Italianate scenery, including Proscenium arch, perspective, border flats, and a raked stage to create a visual image that had never before been used.

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Perspective (visual) in the context of Hologram

Holography is a technique that allows a wavefront to be recorded and later reconstructed. It is best known as a method of generating three-dimensional images, and has a wide range of other uses, including data storage, microscopy, and interferometry. In principle, it is possible to make a hologram for any type of wave.

A hologram is a recording of an interference pattern that can reproduce a 3D light field using diffraction. In general usage, a hologram is a recording of any type of wavefront in the form of an interference pattern. It can be created by capturing light from a real scene, or it can be generated by a computer, in which case it is known as a computer-generated hologram, which can show virtual objects or scenes. Optical holography needs a laser light to record the light field. The reproduced light field can generate an image that has the depth and parallax of the original scene. A hologram is usually unintelligible when viewed under diffuse ambient light. When suitably lit, the interference pattern diffracts the light into an accurate reproduction of the original light field, and the objects that were in it exhibit visual depth cues such as parallax and perspective that change realistically with the different angles of viewing. That is, the view of the image from different angles shows the subject viewed from similar angles.

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Perspective (visual) in the context of Real projective line

In geometry, a real projective line is a projective line over the real numbers. It is an extension of the usual concept of a line that has been historically introduced to solve a problem set by visual perspective: two parallel lines do not intersect but seem to intersect "at infinity". For solving this problem, points at infinity have been introduced, in such a way that in a real projective plane, two distinct projective lines meet in exactly one point. The set of these points at infinity, the "horizon" of the visual perspective in the plane, is a real projective line. It is the set of directions emanating from an observer situated at any point, with opposite directions identified.

An example of a real projective line is the projectively extended real line, which is often called the projective line.

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Perspective (visual) in the context of Worm's-eye view

A worm's-eye view, also known as a frog's-eye view is a description of the view of a scene from below that a worm might have if it could see. It is the perspective inverse of a bird's-eye view.

It can give the impression that an object is tall and strong while the viewer is childlike or powerless.

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