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M. C. Escher
WaterfallEscher worked primarily in the media of lithographs and woodcutsalthough the few mezzotints 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. In Escher's own words: 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. Escher described this journey, including his repeat visit to the Alhambra, as "the richest source of inspiration I have ever tapped".
Dante Alighieri - Wikipedia
In the print Reptileshe combined two- and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality: The flat shape irritates me—I feel like telling my objects, you are too fictitious, lying there next to each other static and frozen: So I make them come out of the plane. Escher had used this solid in his woodcut Starswhich also contains all five of the Platonic solids and various stellated solids, representing stars; the central solid is animated by chameleons climbing through the frame as it whirls in space.
His interest in the multiple levels of reality in art is seen in works such as Drawing Handswhere two hands are shown, each drawing the other.
The critic Steven Poole commented that It is a neat depiction of one of Escher's enduring fascinations: In Drawing Hands, space and the flat plane coexist, each born from and returning to the other, the black magic of the artistic illusion made creepily manifest.
Both Roger Penrose and H. Coxeter were deeply impressed with Escher's intuitive grasp of mathematics. Inspired by Relativity, Penrose devised his tribarand his father, Lionel Penrose, devised an endless staircase. Roger Penrose sent sketches of both objects to Escher, and the cycle of invention was closed when Escher then created the perpetual motion machine of Waterfall and the endless march of the monk-figures of Ascending and Descending.
Circle Limit IIIEscher carefully studied Coxeter's figure, marking it up to analyse the successively smaller circles [d] with which he deduced it had been constructed. He then constructed a diagram, which he sent to Coxeter, showing his analysis; Coxeter confirmed it was correct, but disappointed Escher with his highly technical reply.
All the same, Escher persisted with hyperbolic tilingwhich he called "Coxetering". The poster shows a detail from Day and Night, Escher's special way of thinking and rich graphics have had a continuous influence in mathematics and art, as well as in popular culture. In art collections The Escher intellectual property is controlled by the M.
Escher Company, while exhibitions of his artworks are managed separately by the M. The image is based on Hand with Reflecting Sphere These are the classification of regular tilings using the edge relationships of tiles: By Averroes was in Marrakesh in present-day Moroccothe capital of the Almohad caliphateto perform astronomical observations and to support the Almohad project of building new colleges.
The Encyclopaedia of Islam said the caliph distanced himself from Averroes to gain support from more orthodox ulema, who opposed Averroes and whose support al-Mansur needed for his war against Christian kingdoms. Monfredo de Monte Imperiali Liber de herbis, 14th century. List of works by Averroes Averroes was a prolific writer and his works, according to Fakhry, "covered a greater variety of subjects" than those of any of his predecessors in the East, including philosophy, medicine, jurisprudence or legal theory, and linguistics.
Aristotle's works are the subject of extensive commentaries by Averroes. Averroes wrote commentaries on nearly all of Aristotle's surviving works. He also wrote several polemics: Fasl al-Maqal "The Decisive Treatise" is a treatise that argues for the compatibility of Islam and philosophy.
It combines ideas in his commentaries and stand alone works, and uses them to respond to al-Ghazali. Unsourced material may be challenged and removed. December Learn how and when to remove this template message Not much is known about Dante's education; he presumably studied at home or in a chapter school attached to a church or monastery in Florence. It is known that he studied Tuscan poetry and that he admired the compositions of the Bolognese poet Guido Guinizelli —whom in Purgatorio XXVI he characterized as his "father"—at a time when the Sicilian school Scuola poetica Sicilianaa cultural group from Sicilywas becoming known in Tuscany.
Dante's experience of such love was typical, but his expression of it was unique. It was in the name of this love that Dante left his imprint on the dolce stil novo sweet new style, a term which Dante himself coinedand he would join other contemporary poets and writers in exploring never-before-emphasized aspects of love Amore.
Love for Beatrice as Petrarch would show for Laura somewhat differently would be his reason for poetry and for living, together with political passions.
In many of his poems, she is depicted as semi-divine, watching over him constantly and providing spiritual instruction, sometimes harshly. When Beatrice died inDante sought refuge in Latin literature.
He then dedicated himself to philosophical studies at religious schools like the Dominican one in Santa Maria Novella. He took part in the disputes that the two principal mendicant orders Franciscan and Dominican publicly or indirectly held in Florence, the former explaining the doctrines of the mystics and of St. Bonaventurethe latter expounding on the theories of St. Nor speaking less on that account I go With Ser Brunetto, and I ask who are his most known and most eminent companions.
Other studies are reported, or deduced from Vita Nuova or the Comedy, regarding painting and music. December Further information: Guelphs and Ghibellines Dante, like most Florentines of his day, was embroiled in the Guelph—Ghibelline conflict. To further his political career, he became a pharmacist. He did not intend to practice as one, but a law issued in required nobles aspiring to public office to be enrolled in one of the Corporazioni delle Arti e dei Mestieri, so Dante obtained admission to the Apothecaries' Guild.
This profession was not inappropriate since at that time books were sold from apothecaries' shops.
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As a politician, he accomplished little but held various offices over some years in a city rife with political unrest. Although the split was along family lines at first, ideological differences arose based on opposing views of the papal role in Florentine affairs, with the Blacks supporting the Pope and the Whites wanting more freedom from Rome.
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The Whites took power first and expelled the Blacks. But the city's government had treated the Pope's ambassadors badly a few weeks before, seeking independence from papal influence.
It was believed that Charles had received other unofficial instructions, so the council sent a delegation to Rome to ascertain the Pope's intentions.
Dante was one of the delegates. Exile and death[ edit ] Pope Boniface quickly dismissed the other delegates and asked Dante alone to remain in Rome. At the same time November 1,Charles of Valois entered Florence with the Black Guelphs, who in the next six days destroyed much of the city and killed many of their enemies. In MarchDante, a White Guelph by affiliation, along with the Gherardini familywas condemned to exile for two years and ordered to pay a large fine.
Florence under the Black Guelphs therefore considered Dante an absconder.