Melencolia I in the context of "German Renaissance"

Saint Jerome in His Study (German: Der heilige Hieronymus im Gehäus) is a copper engraving of 1514 by the German artist Albrecht Dürer. Saint Jerome is shown sitting behind his desk, engrossed in work. The table, on the corner of which is a cross, is typical of the Renaissance. An imaginary line from Jerome's head passing through the cross would arrive at the skull on the window ledge, as if contrasting death and the Resurrection. The lion in the foreground is part of the traditional iconography of St. Jerome, and near it is a sleeping dog, an animal found frequently in Dürer's works, symbolizing loyalty. Both creatures are part of Jerome's story in the Golden Legend (c. 1260), which contained fanciful hagiographies of saints.

St. Jerome in His Study is often considered as part of a group of three Dürer engravings (his Meisterstiche), the other two being the well-known Melencolia I (1514) and Knight, Death and the Devil (1513). Together they have been viewed as representing the three spheres of activity recognized in medieval times: Knight, Death, and the Devil belongs to the moral sphere and the "active life"; Melencolia I represents the intellectual; and St. Jerome the theological and contemplative life.

A claw hammer is a hammer primarily used in carpentry for driving nails into or pulling them from wood. Historically, a claw hammer has been associated with woodworking, but is also used in general applications. It is not suitable for heavy hammering on metal surfaces (such as in machining work), as the steel of its head is somewhat brittle; the ball-peen hammer is more suitable for such metalwork.

An early claw hammer is seen in Albrecht Dürer's etching "Melencolia I," dated 1514, halfway up the left side. There are several nails in the lower right corner.

The Meisterstiche ("master prints") by Dürer are three of his most famous engravings. They are Knight, Death and the Devil (1513), Melencolia I (1514) and St. Jerome in His Study (1514). These three large prints (about 7 by 10 inches (18 by 25 cm)) are often grouped together because of their perceived quality and unity of meaning, although this latter is a matter of scholarly dispute.

Art historian Erwin Panofsky has described them as showing meticulous care in execution and also having complexity and significance in terms of iconography. Panofsky, while recognising that these are Durer's "most famous engravings" and are "not unjustly, known as his 'Meisterstiche'", notes that they "have no appreciable compositional relationship with one another" and should not, in any technical sense, be "considered as 'companion pieces'". They do, Panofsky argues, form "a spiritual unity". Here, Panofsky refers to Friedrich Lippmann's noticing of the scholastic classification of the virtues they represent: the moral, the theological and the intellectual. The Knight showing "the life of the Christian in the practical world of decision and action"; St. Jerome showing "the life of the Saint in the spiritual world of sacred contemplation"; and Melencolia I showing the "life of the secular genius in the rational and imaginative worlds of science 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.