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  3. In math, simple relationships can often take on critical roles. One such relationship, the Golden Ratio, has captivated the imag

In math, simple relationships can often take on critical roles. One such relationship, the Golden Ratio, has captivated the imag

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问题     In math, simple relationships can often take on critical roles. One such relationship, the Golden Ratio, has captivated the imagination and appealed to mathematicians, architects, astronomers, and philosophers alike. The Golden Ratio has perhaps had more of an effect on civilization than any other well-known mathematical constant. To best understand the concept, start with a line and cut it into two pieces (as seen in the figure). If the pieces are cut according to the Golden Ratio, then the ratio of the longer piece to the length of the shorter piece (A:B) would be the same as the ratio of the length of the entire line to the length of the longer piece (A+B=A). Rounded to the neatest thousandth, both of these ratios will equal 1. 618:1.
    The first recorded exploration of the Golden Ratio comes from the Greek mathematician Euclid in his 13-volume treatise on mathematics, Elements: published in approximately 300 BC. Many other mathematicians since Euclid have studied the ratio. It appears in various elements of certain regular geometric figures, which are geometric figures with all side lengths equal to each other and all internal angles equal to each other. Other regular or nearly regular figures that feature the ratio include the pentagram (a five-side star formed by five crossing line segments, the center of which is a regular pentagon) and three-dimensional solids such as the dodecahedron (whose 12 faces are all regular pentagons).
    The Fibonacci sequence, described by Leonardo Fibonacci, demonstrates one application of the Golden Ratio. The Fibonacci sequence is defined such that each term in the sequence is the sum of the previous two terms, where the first two terms are 0 and 1. The next term would be 0+1 = 1, followed by 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, etc. this sequence continues: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on. As the sequence progresses, the ratio of any number in the sequence to the previous number gets closer to the Golden Ratio. This sequence appears repeatedly in various applications in mathematics.
    The allure of the Golden Ratio is not limited to mathematics, however. Many experts believe that its aesthetic appeal may have been appreciated before it was ever described mathematically. In fact, ample evidence suggests that many design elements of the Parthenon building in ancient Greece beat a relationship to the Golden Ratio. Regular pentagons, pentagrams, and decagons were all used as design elements in its construction. In addition, several elements of the fade of the building incorporate the Golden Rectangle, whose length and width are in proportion to the Golden Ratio. Since the Parthenon was built over a century before Elements was published, the visual attractiveness of the ratio, at least for the building’s designers, may have played a role in the building’s engineering and construction.
    Numerous studies indicate that many pieces of art now considered masterpieces may also have incorporated the Golden Ratio in some way. Leonardo da Vinci created drawings illustrating the Golden Ratio in numerous forms to supplement the writing of De Divina Proportione. This book on mathematics, written by Luca Pacioli, explored the application of various ratios, especially the Golden Ratio, in geometry and art. Analysts believe that the Golden Ratio influenced proportions in some of da Vinci’s other works, including his Mona Lisa and Annunciation paintings. The ratio is also evident in certain elements of paintings by Raphael and Michelangelo. Swiss painter and architect Le Corbusier used the Golden Ratio in many design components of his paintings and buildings. Finally, Salvador Dali intentionally made the dimensions of his work Sacrament of the Last Supper exactly equal to the Golden Ratio, and incorporated a large dodecahedron as a design element in the painting’s background.
    The Golden Ratio even appears in numerous aspects of nature. Philosopher Adolf Zeising observed that it was a frequently occurring relation in the geometry of natural crystal shapes. He also discovered a common recurrence of the ratio in the arrangement of branches and leaves on the stems of many forms of plant life. Indeed, the Golden Spiral, formed by drawing a smooth curve connecting the corners of Golden Rectangles repeatedly inscribed inside one another, approximates the arrangement or growth of many plant leaves and seeds, mollusk shells, and spiral galaxies.
Why does the author mention that Dali incorporated a large dodecahedron as a design element in the painting’s background?
选项 A、To demonstrate Dali’s frequent use of geometric shapes.
B、To illustrate the extent to which the Golden Ratio has influenced some works of art.
C、To argue that certain style elements in art are more effective than others.
D、To refer to works by other artists such as da Vinci and Le Corbusier.
答案B
解析 事实细节题。根据Dali定位到第五段最后一句。该段第一句提到，许多现在被认为是杰作的艺术品也可能在某种程度上包含了黄金比例；接着以达.芬奇、米开朗基罗、达利等著名画家及其作品为例子说明。由此可知，作者提到达利的画作背景中出现了一个正十二面体，意在说明该段第一句的观点，即黄金比例在艺术创作中被广泛应用，故答案为B项。
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