How to Write Fractions as Decimals

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fra angelico, annunciation The Annunciation (Fig. 38.12) by Dominican friar and painter Fra Angelico (c. 1400– 1455) reveals a much more modest image than Gentile’s painting. In 1436, Fra Angelico moved to the monas- tery of San Marco. Soon thereafter Cosimo de’ Medici commissioned him to paint a series of frescoes there. The Annunciation fresco, located in the upstairs corridor of the monks’ dormitory, presents a simplified version of the story, in which the Archangel Gabriel informs the Virgin Mary that she is to be the mother of Jesus. The spare setting is rendered in perspective and with minimal, vernacular (everyday) details. The angel Gabriel kneels before a young Virgin Mary, who is seated on a simple wooden stool in the loggia of an enclosed garden. The thin, elegantly posed figures have calm facial expressions. They humble themselves with arms crossed and a slight bow toward each other. Their drapery is modeled in a limited color palette illumi- nated by a light source coming from behind Gabriel. There is a modest use of gold in Gabriel’s pink robe, while the Virgin’s cloak is an azurite blue over an off- white dress that blends into her skin tone. Gabriel’s beautiful wings in stripes of rich color lead the eye to the dark-green meadow behind him. The architecture frames the scene with whitewashed walls and slim Corinthian columns braced together with iron bars to reinforce the linear perspective of the cubed space, cre- ating a sense of harmony and order. A door opens into a dormitory cell beyond the portico; the cell is empty except for one window set high on the wall. The monastery had formerly belonged to Benedictines, followers of the early medieval St. Benedict who estab- lished the rules of monastic life, and was transferred to the Dominicans and rebuilt by Michelozzo di Bartolommeo under the sponsorship of Cosimo de’ Medici as part of the expansion of the area that also included Michelozzo’s Medici Palace (see Fig. 38.1). Michelozzo’s renovated mon- astery shows a spare Classicism similar to Fra Angelico’s frescoes, appropriate for the monks, who had taken a vow of poverty, as well as for Cosimo, who maintained a private cell to escape his worldly affairs. Because the friars—not the general public—were the primary intended audi- ence for the frescoes, no didactic details were needed to tell the story they already knew. Instead, the images were meant to inspire piety within the silence of a clois- tered monastery. The Language of Classicism The revival of Classicism not only played an impor- tant role in art patronage and the greater emphasis on naturalism, but it also expanded the artistic language to include a fuller symbolic and aesthetic repertoire. The humanist scholar Giovanni Pico della Mirandola (1463–1494) wrote Oration on the Dignity of Man in 1486 to explain humankind’s capacity for greatness through a quest for knowledge. Pico sought to bring together diverse branches of thought including Platonism, tied to the ancient philosopher Plato, and Christianity, which he argued held similar truths, and these ideas promoted an intellectual approach to art in the Renaissance. brunelleschi, the old sacristy During the period in which Brunelleschi was working on the Florence Cathedral dome, he also constructed several churches, chapels, and a hospital in Florence. Citizens marveled at the new Classical style he introduced. The Old Sacristy (Fig. 38.13), commissioned in 1421 by Cosimo de’ Medici, is an excellent example of Brunelleschi’s interest in Classicism adapted for a Christian building. This small, square room where priests prepared for services, accessed from inside the church of San Lorenzo, was designed with a dome set on top of a cube, in which the altar wall is subdivided into three rectangular sections of equal length by Corinthian fluted pilasters and molding made from pietra serena, a gray-green stone. Stone gridlines divide the floor into smaller squares. An elevated, square altar is located on the wall opposite the entrance, while an umbrella, or ribbed, dome with twelve ribs rises above the room. Triangular pendentives spring from the entablature to create arches that mark the transition from the square plan to the circular dome. In Classical antiquity, domes symbolized the heavenly realm, and they were used for mausolea, imperial homes, and civic buildings such as bath houses. The same sym- bolism appears in the Old Sacristy, which was used for Medici family tombs. Donatello completed the interior painted stucco reliefs, including corner medallions with scenes of the Four Evangelists (Matthew, Mark, Luke, and John, authors of the New Testament Gospels) above the Medici family coat-of-arms. The numbers three, four, and twelve are embedded in the chapel’s design principles in the form of the triangle, square, and ribs of the dome circle. These numbers also symbolize the Trinity (the Father, the Son, and the Holy Ghost), the Four Evangelists, and the Twelve Apostles (the disciples of Jesus). According to the ancient Greek philosopher Pythagoras (c. 570–c. 495 BCE), who was a major influence on Plato, numbers have symbolic meaning that can generate harmony, as found in musical ratios and proportion studies. For Brunelleschi, Classical numerology, together with medieval number symbolism, could be used to create a rich symbolic architectural language where harmony is achieved through numbers. donatello, david Art had long been commissioned by religious institutions, wealthy families, and civic groups for the public promotion of their ideology, but the rise of domestic art came about with the development of larger private family homes in the Renaissance. Historians studying household inventories have noted an increase in material possessions for the home during this time. One such possession is Donatello’s bronze David (Fig. 38.14), probably made in the 1440s for the courtyard of the Medici Palace. It was the first freestanding nude sculpture since antiquity, and it reflects Cosimo de’ Medici’s Classical interests. In the Old Testament, the young shepherd David, who eventually became King of the Israelites, was challenged to fight the undefeated Philistine giant warrior Goliath. David was victorious, and this story became a popular subject in Florence, a city that championed its morals and intellect over brute strength and its cultural superiority over the lingering feudal-era military rule epitomized by rivals such as Milan. Vasari noted an inscription beneath the figure, now gone, that stated: “Behold, a boy overcame the great tyrant. Conquer, o citizens!” David stands in a Classical curvilinear pose, looking down upon the severed head of Goliath lying sideways on the ground in front of his sandaled feet. The scene is not violent. The nude David wears a cap decorated with laurel (denoting both victory and perseverance) and holds a heavy sword in one hand while anchoring his other hand against his swayed hips. A feather from Goliath’s helmet rests sensually against the inside of David’s thigh. Rather than a heroic, victorious nude, here David is young, with soft flesh, and many scholars have speculated on the rationale for such a seemingly erotic version of this biblical hero. It is possible that Donatello was inspired by Plato, who argued in his Symposium that a person’s physical beauty can inspire the viewer to contemplate divine love, which is represented in the supreme, ideal beauty of the youthful male figure. 38.14 Donatello, David, c. 1440. Bronze, height 5 ft. 2⅛ in. (1.58 m). Museo Nazionale del Bargello, Florence, Italy. zanobi di domenico, nerli cassone In addition to sculptures, artists created and decorated a wide range of objects for the home, including furniture, tapestries, and ceramics. Leon Battista Alberti’s text On the Family (Libri della famiglia) from 1440 provides a description of the life of a wealthy homeowner and, more importantly, a glimpse into the elusive private lives of women at this time when men dominated public spaces and shaped cultural discourse. A young woman brought a dowry into her arranged marriage and was responsible for the upkeep of the home and the early moral education of the children, while her husband oversaw the family business. A wooden marriage chest for the personal goods of a bride is called a cassone. In September 1472, the Florentine merchant Lorenzo Morelli paid Zanobi di Domenico (active c. 1464–74) 21 florins to create a pair of cassoni in anticipation of his arranged marriage to Vaggia Nerli, who brought a large dowry from her wealthy family. This cassone (Fig. 38.15, p. 639) was painted by Zanobi and two other artists. It is a rare surviving example, with its spal- liera (backboard) intact, as well as documentation of its original ownership. Such rich furnishings were often decorated with hunting scenes, jousting tournaments, and stories from Classical antiquity, and this cassone illustrates a scene from a history book of ancient Rome written by Titus Livius, known as Livy (c. 64 BCE–c. 17 CE), which highlights an example of brave patriotism. Such scenes provided a new repertoire of moralizing stories to remind the bride and groom of the importance of family and societal loyalty. antonio del pollaiuolo, hercules and antaeus Another domestic work, this one found in the Palazzo Medici, is Antonio del Pollaiuolo’s (c. 1431–1498) Hercules and Antaeus (Fig. 38.16), from around 1475. Standing about 18 inches tall, this small bronze statuette is a versatile, portable object that can be turned and viewed from all sides. Pollaiuolo was interested in movement, specifically of the human body, and here he shows the Greco-Roman mythological wrestling match between Antaeus, the son of an earth goddess, and Hercules, the son of Zeus. Both were known for their physical strength, but Antaeus derived his strength from the earth, so Hercules had to hoist him off the ground to gain the upper hand. Hercules’ spine bends dramatically as he adjusts his weight backward and wraps his arms around Antaeus, while Antaeus cries in agony and tries to push Hercules away. Their bodies are tense and angular, with bulging calf muscles and exaggerated poses. Antaeus’s legs flail in the air, encouraging viewers to look at the sculpture from multiple vantage points, thereby solving the problem of the one-point view. Such statuettes reflect a growing interest in small domestic art, featuring Classical sub- jects, that could be collected, studied, and displayed in various locations in the home. sandro botticelli, birth of venus Classical sub- jects also appear in Sandro Botticelli’s (1444–1510) Birth of Venus (Fig. 38.17), dated around 1482. This large painting of Venus, the goddess of love and beauty, was created in tempera on canvas, and may have been commissioned by the Medici. Canvas paintings were rare at this time, and generally they were found not in urban palaces but in villas (country houses), where this painting could have functioned as a less expensive alternative to a tapestry. Although its original location is not known, Vasari saw this painting at a Medici villa in the 1530s. Large mythological paintings and nude female images were unprecedented in Italy, yet they provide a subject suited to wealthy families such as the Medici, who sought to promote their humanist aspirations through such art- works: In Birth of Venus, the display of this nude, Classical figure expresses Platonic notions about the elevation of physical love into a higher spiritual or divine love, through an artistic idealization of the female form. Thus, while a naked female figure would have been unacceptable by Renaissance standards, a nude goddess of love, with its detachment from earthly concerns, was deemed intel- lectually uplifting. The scene in Birth of Venus, perhaps taken from a poem written by humanist scholar Angelo Poliziano (1454–1494) and described in an ancient Greek Homeric hymn, shows Venus (named Aphrodite in ancient Greece), after she is born full-grown, standing on a large shell that washes up on the shore of the Mediterranean island of either Cyprus or Cythera, guided by the wind, blown by Zephyrus, who holds the nymph Chloris. A goddess of spring, sometimes identified as the Roman garden goddess Pomona, pre- pares to cover Venus with a floral robe, a suggestion of her modesty. Venus was frequently depicted in antiquity, and Botticelli echoes the modest pose of the Aphrodite of Knidos by Praxiteles of Athens (see Fig. 15.1), a copy of which he could have seen in Rome. Botticelli was less interested in the spatial developments of the Renaissance and more focused on graceful, lyrical figures set against a flat background to create a perfect harmony of parts, epitomizing Platonic ideas of love and beauty. While Florence was the center of the artistic inno- vations that characterize the Renaissance, many other city-states began to use art to assert political power and cultural authority, resulting in rich artistic communities across all of Europe.

donatello, saint mark Following Brunelleschi, artists began to adjust their measurements by shortening or elongating figures to be viewed from different angles and distances, an idea that was adapted to sculptural com- missions as well. One such major sculptural program was found at Orsanmichele, a rectangular building near the Duomo that had served as a granary and then as a church, with administrative offices for the guilds upstairs. These guilds were asked to fill the building’s exterior niches with public sculpture, and guild leaders considered it their civic duty to beautify the city with public art commis- sions. In 1411, Donatello received a commission from the of its heavier weight and its tendency to shear or shift laterally under stress. All of these materials, including more than four million bricks, were hoisted up the side scaffolding using a reversible hoist invented by Brunelleschi and powered by pairs of oxen that moved in a circle. The hoist was devised in a way that allowed the ropes to go up and down without workers having to rehitch and reverse the oxen for each delivery. After Brunelleschi’s death, Michelozzo di Bartolommeo built a lantern on top of the dome, and in 1469 a copper ball made by the Florentine sculptor Andrea del Verrocchio (c. 1435–1488) was raised to the top of the lantern using one of Brunelleschi’s pulley systems. The end result was a magnificent dome 375 feet tall, built with a sophisticated understanding of construction practices realized in Florence, made possible through access to both Classical knowledge and new technical advances. Perspective and the Viewer Brunelleschi was also interested in perspective drawing, and he devised a mathematical method of rendering three-dimensional images onto a flat surface with a con- vincing spatial realism. Artists throughout history have found ways to depict space in painting, as in the more intuitive orthogonal lines visible in the ancient Roman wall murals at Boscoreale (see Fig. 18.18) and, much later, in the Virgin’s throne in Giotto’s Madonna and Child Enthroned, c. 1305–10 (see Fig. 37.14). Brunelleschi’s goals were different, however. Using a grid, he analyzed the way orthogonal lines converge at a vanishing point on the horizon line, creating an illusion of space and depth that better approximates how the eye sees objects in the Arte dei Linaioli (linen-weavers' guild) to carve a marble sculpture of its patron saint, St. Mark. Donatello carved St. Mark (Fig. 38.5, p. 631) standing on a soft pillow with a linen cover held together with buttons—a nod to the guild that financed the sculpture. His imposing and realistic figure fills the niche; a robe draped across his shoulders falls across his arms and down his legs in a display of billowing fabric. Because the sculpture was to be placed in a niche several feet above street level, Donatello elon- gated the torso and enlarged the head slightly to take into account the angle of the viewer’s line of sight. This manipulation caused the guild to reject the sculpture aspoorly proportioned—until they saw it in its intended location, where the proportions appeared correct. Classical artists had observed that human bodies are constantly in movement and that harmony can be achieved through counterbalance. Donatello’s St. Mark stands on his right leg with his left leg relaxed, creating the Classical contrapposto. His legs are counterbalanced with his arms, as his right arm hangs down and his left arm carries the weight of a book. Donatello reveals the shape of St. Mark’s body beneath the drapery that flows in a straight line down the tense right leg, while fabric pools around the bent knee of the relaxed left leg. lorenzo ghiberti, gates of paradise Naturalistic developments also appeared in relief sculpture. After Ghiberti finished his first set of bronze doors for the baptistery of San Giovanni, he was hired in 1425 to com- plete another set. These doors were placed on the east side, facing the cathedral, and his first set of doors was moved to the north side. The new doors came to be called the Gates of Paradise (Fig. 38.6), perhaps because the area between the baptistery and the earlier church was the site of a cemetery. The Gates of Paradise features ten large relief panels flanked by medallions. Each scene reveals a sophisticated use of depth, with larger figures in high relief used in the foreground, diminishing to various degrees of low relief and smaller figures in the background to give the impres- sion of distance. In the panel featuring the story of Jacob and Esau (Fig. 38.7), from the biblical Book of Genesis, the Classically inspired space includes an arched portico that appears to recede backward into space with a grid of floor tiles that create orthogonal lines to a vanishing point through the central arch. This system of organization allows for a clear movement between the seven separate scenes that appear on the panel in a compressed-narra- tive format (see box: Looking More Closely: Finding the Narrative in Ghiberti’s Jacob and Esau). Ghiberti included a self-portrait head among the medallions of prophets that flank the reliefs, one of the earliest artist self-portraits in the Renaissance. Ghiberti also wrote Commentaries, an art treatise that focuses on the importance of Classical art and includes an autobiography, one of the earliest in art history. This self-referencing is an example of the emerging impor- tance of the individual during the Renaissance, where a self-conscious, public display of one’s worth was con- sistent with civic virtue. masaccio, holy trinity The mathematical language found in Brunelleschi’s studies of perspective and propor- tion also had a profound impact on painters, including Tommaso “Masaccio” di Ser Giovanni di Simone (1401– 1428). In his short career, Masaccio moved away from the Late Medieval style of painting—with gold backgrounds and two-dimensional surface patterns—toward a greater realism of space and form. Masaccio’s Holy Trinity (Fig. 38.8), c. 1425–27, is a fresco on the nave wall of the Dominican church of Santa Maria Novella in Florence and was perhaps commissioned by the wealthy merchant and writer Domenico Lenzi as a painted funerary monument. Lenzi and his wife appear opposite each other at the outer edges of the fresco, kneeling in profile with their hands clasped together in prayer at a painted altar, which was originally an actual altar ledge attached to the wall. Beneath the altar and tilted toward the viewer is a painted sarcophagus with a skeleton above that reminds us in a memento mori: “I once was what now you are, and what I am, you shall yet be.” The sarcophagus appears to project forward into the real space of the nave, where viewers of the painting would be standing. Above the altar, the figures around the central Crucifixion scene are set into a single unified space—a Classical chapel with Ionic columns and Corinthian pilasters, and a barrelvaulted space that appears to recede. Masaccio used the new system of linear perspective to measure orthogonal lines that can be traced from the bottom of the cross up through the square coffers to create the painted illusion of an eight-foot-deep chapel. Four figures are arranged in a triangular composition. John the Evangelist (gospel writer) and an elderly Virgin Mary flank Christ, who is elevated on the cross with the white dove of the Holy Spirit above his head. God stands at the top of the triangle on the platform, supporting the cross with his hands. Light emanates from Christ’s body and reflects off the donors’ robes, modeling their forms. The viewer must stand directly in front of the fresco to observe the convergence of orthogonal lines at the vanishing point in the middle of the horizon line at the base of the cross, located at the viewer’s eye level. This fresco reveals Masaccio’s fusion of linear perspec- tive and religious symbolism, which helped to expand the iconographic language of art in the Renaissance. The triangular composition creates solidity and stabil- ity, while the number three,implied by the composition, reinforces the symbolism of the Trinity (Father, Son, and Holy Spirit). paolo uccello, battle of san romano A series of three wood panels by Paolo Uccello (1397–1475), a painter born outside Florence who studied with Ghiberti, com- memorates the Florentine military victory in 1432 over its rival, the neighboring city-state of Siena. In one panel, Battle of San Romano (Fig. 38.9), the Florentine condottiero (mercenary soldier) Niccolò da Tolentino, confident in his large red hat, leads his men into victory on a white horse. On the viewer’s right, his colleague, Micheletto Attendolo Sforza, dressed in full armor, pushes forward on his dark horse to clash with an opposing soldier. Clean, bright colors draw the viewer’s eye around the painting. Uccello offers an unusual interpretation of linear perspective, with lances broken on the ground at ninety- degree angles to impose a grid. At the viewer’s left, a foreshortened soldier lies face down on the ground, and his body recedes into space parallel to the lance next to him, showing us a man who has died in perfect linear perspective. The ground seems to glow, allowing us to see the lances that otherwise would have been hidden in the meadow foliage, and the background tilts up rather than backward to form a tapestry-like backdrop that again directs our eyes to the battle in the foreground. Uccello seems to acknowledge the paradox of linear perspective, as spatial constructions are ultimately artificial arrange- ments on a two-dimensional surface. Documents show that the three panel paintings originally belonged to two Bartolini Salimbeni broth- ers. Lorenzo de’ Medici (1449–1492) convinced one of them to sell the paintings to him, but when the other refused, Lorenzo considered the contract broken and sent an armed guard to steal the paintings from the Bartolini palace. He then had the panels cut down to fit his bedroom—an action that somewhat tarnishes Lorenzo’s image as a generous art patron who sought to protect and preserve the cultural heritage of Florence. Color and Light In addition to perspective, Renaissance artists were inter- ested in optics (the study of sight), and they studied ancient writings on light and vision. The ancient Greek mathematician Euclid (300s BCE) identified the law of reflection, where a surface reflects light, while the ancient Roman scholar Ptolemy (100–170 CE) observed and described the law of refraction (which states that a light wave changes direction when it enters a medium, such as a glass prism, at an angle). A complete theory of optics was first introduced in western Europe by Ibn al-Haytham (known as Alhazen, 965–1040) in his Book of Optics, which Muslim traders brought to the Spanish caliphate of Al-Andalus. The book was then brought to Italy in the thirteenth century and translated into Latin. Alhazen was the first to describe accurately how percep- tion occurs and how the eye functions. The ancient Greek philosopher Aristotle’s (384–322 BCE) ideas about the per- ception of color and light also influenced the Renaissance color palette and how artists modeled with light and dark. Renaissance artists sought to create figures with color and light that could better replicate how we experience things in the natural world. masaccio, tribute money Masaccio was interested not only in linear perspective (for more about the linear per- spective used in Tribute Money, see: Seeing Connections: The World in Perspective), but also in modeling his figures in shading and color. He was hired to assist Masolino da Panicale (c. 1383–1447) in painting the Brancacci Chapel in Santa Maria del Carmine, and he took over the project when Masolino left for Hungary. Masaccio’s Tribute Money (Fig. 38.10, p. 636) features a story from the life of St. Peter. This fresco compresses three parts of the story into one scene. The story begins in the middle, where a tax collector facing away from the viewer confronts Christ. Christ, wearing a bright blue robe, points to St. Peter in an orange-yellow drape, directing him to Lake Galilee. Peter also points in that direction to lead the viewer’s eye left, where Peter appears again, having removed his robe as he bends down to extract a coin from the mouth of a fish. On the right side of the scene, Peter appears a third time, back in his robe, thrusting a coin into the hand of the tax collector. Masaccio uses color as a visual tool to identify the figures that repeat through the compressed narrative. In addition, he begins the story in the middle to balance the need for visual hierarchy with the eye’s natural movement, as in Ghiberti’s Jacob and Esau panel. The figures stand out against the bare, muted land- scape. The colors of their robes include a deep yellow, an orange, and red vermillion, while Christ’s blue robe is an ultramarine made from lapis lazuli, a semi-precious stone, imported from Afghanistan, that was ground into powder. Masaccio modeled his figures, mimicking the effects of light reflecting off an object to give them a solid physical presence, unlike the flattened figures of medieval art. The figures also cast shadows, confirming their volume and providing depth to the foreground. While the building to the right provides orthogonal lines that pull the space backward, the landscape reveals a different method of depicting depth, called atmospheric perspective. Found in ancient Roman wall murals, this perspective relies not on straight lines but on the type of curves found in nature. The mountains are painted in a light gray-blue pigment made from carbon soot. The hue is similar to the color seen when viewing mountains from a great distance, a result of the scattering of light. The mountains also appear smaller, less saturated in color, and less detailed than the foreground figures. With this fresco, Masaccio took Giotto di Bondone's naturalism (see Fig. 37.14) a step further, to include a type of atmos- pheric depth not seen since antiquity. gentile da fabriano, adoration of the magi While Masaccio and Ghiberti experimented with naturalism and spatial developments, the contemporary painter Gentile da Fabriano (c. 1370–1427) created a unique style of paint- ing that demonstrates the magnificent effects of light on color, showing not only reflection but also refraction, which makes colors seem to shimmer. His Adoration of the Magi altarpiece from 1423 was commissioned by Palla Strozzi for his family chapel in Santa Trinità in Florence, and Gentile was paid the unprecedented sum of 300 gold florins for this public work, six times the medieval artist's annual salary. This fee included the cost of the extensive use of gold leaf throughout the work. Panel paintings made from attached wood boards, such as in this altarpiece, were the most common form of painting before canvases were introduced later in the Renaissance. Dense hardwoods such as poplar and oak were typically used, and the boards were sanded and coated with a priming mixture of glues, resin, and linen before gesso was applied in as many as fifteen sanded layers to create a smooth surface. The design was then sketched in with pencil or charcoal before painting. Adoration of the Magi depicts three distinguished foreigners, the Magi, visiting Jesus after his birth; the work comprises a large altarpiece with an elaborate gold frame, a predella below, and medallions above (Fig. 38.11). On the left side of the altarpiece, the Virgin Mary holds the Christ Child, and the Star of Bethlehem that signaled Christ’s birth shines above Joseph’s head. At the center, the three richly robed Magi kneel before the Holy Family in front of a crowd of courtiers, while a royal procession curves through the landscape back to a distant castle, creating a long, undulating line through the painting. The Magi and their entourage, some of whom are thought to depict Strozzi family members, wear ornate robes and golden crowns. Gentile painted these robes in saturated colors with the appearance of gold brocade and jeweled inlay. He also included horses, donkeys, a dog, and monkeys and falcons in the crowd. The predella scenes depict the Night Nativity (featuring the birth of Jesus), the Flight into Egypt (in which Joseph, Mary, and Jesus flee Bethlehem to avoid persecution by King Herod), and the Presentation in the Temple (in which the baby Jesus is brought to the temple forty days after his birth). In the Night Nativity, light emanates directly from the body of Christ to illu- minate the dark sky like a twinkling star.