Each time I hear someone say, "Do the math," I grit my teeth. The phrase rei

游客2024-08-05 37

问题 Each time I hear someone say, "Do the math," I grit my teeth. The phrase reinforces how little awareness there is about the breadth and scope of the subject. Imagine, if you will, using " Do the lit" as an exhortation to spell correctly.
【R1】______Ideas that inform our existence, that permeate our universe and beyond, that can surprise and enthrall. Perhaps the most intriguing if there is the way infinity is harnessed to deal with the infinite range of decimal numbers—a wonder product offered by mathematics to satisfy any measurement needed, down to an arbitrary number of digits.

【R2】______One can develop a fairly good understanding of the power and elegance of calculus, say, without actually being a-ble to use it to solve scientific or engineering problems. Think of it this way: you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. Math also deserves to be enjoyed for its own sake.
【R3】______So what math idea can be appreciated without calculation or formulas? One candidate is the origin of numbers. Think of it as a magic trick: harnessing emptiness to create the number zero, then demonstrating how from any whole number, one can create its successor. One from zero, two from one, three from two—a chain reaction of numbers erupts into existence. I still remember when I first experienced this Big Bang of numbers. The walls of my Bombay classroom seemed to blow away, as nascent cardinal numbers streaked through space.
【R4】______I can almost imagine a yoga instructor asking a class to mediate on what would happen if the number of sides kept increasing indefinitely. Eventually, the sides shrink so much that the kinks start flattering out and the perimeter begins to appear curved. And then you see it: what will emerge is a circle, while at the same time the polygon can never actually become one. The realization is exhilarating—it lights up pleasure centres in your brain. This underlying concept of a limit is one upon which all of calculus is built.
【R5】______For instance, enjoying the eye candy of fractal images—those black, amoeba like splotches surrounded by brands of psychedelic colors—hardly qualifies as making a math connection. But suppose you knew that such an image depicts a mathematical rule that plucks every point from its spot and moves it. Imagine this rule applied over and over again, so that every point hops from location to location. The "amoeba" comprises those well-behaved points that remain hopping around within this black region, while the colored points are more adventurous, loping off toward infinity. Not only does the picture acquire more richness and meaning with this knowledge, it suddenly churns with drama, with activity.
Would you be intrigued enough to find out more—for instance, what the different shades of color signified? Would the Big Bang example make you wonder where negative numbers came from? Could the thrill of recognizing the circle as a limit of polygons lure you into visualizing the sphere as a stack of its circular cross sections, as Archimedes did over 2, 000 year ago?
Questions 61 to 65
Choose from the sentences A-G the one which best fits each gap of 61-65. There are two extra sentences, which you do not need to use.
A. As a mathematician, I can attest that my field is about ideas above anything else.
B. Perhaps just as significant, priority can decide who reaps the financial benefits of a new discovery.
C. The more deeply you engage with such ideas, the more rewarding the experience is.
D. For a more contemplative example, gaze at a sequence of regular polygons: a hexagon, an octagon, a decagon, and so on.
E. Sadly, few avenues exist in our society to expose us to mathematical beauty.
F. Despite what most people suppose, many profound mathematical ideas don’t require advanced skills to appreciate.
G. As a scientist, I have seen many erroneous "discoveries"—including one of my own—greeted with substantial publicity. [br] 【R3】

选项

答案 E

解析本段主要列举了哪些数学概念可以不通过演算和公式即能被欣赏。比如，数字的起源。由本段第二句的问句及上下文内容得知，此处是过渡句。E项表示，遗憾的是，社会上很少有明示出可以怎么领会数学的美。E项过渡自然。

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