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把数学烘焙成一道美味甜点
添加时间:2016-05-07 09:11:55 浏览次数: 作者:未知
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  • CHICAGO — We had just finished the mathematician1 Eugenia Cheng’s splendid demonstration2 of nonassociativity where the order of operations counts — as it does in, say, subtraction3.

    芝加哥——我们刚刚听完了数学家尤金妮娅·郑(Eugenia Cheng)关于非结合律的精彩讲解:运算的顺序会影响运算结果,比如在减法中。

    Now she wanted to forge ahead with the next lesson, in knot theory.

    现在,她想开始下一课:纽结理论(knot theory)。

    I suggested we wait until later. “Why?” she asked.

    我建议等一下。“为什么?”她问。

    “Well, we shouldn’t eat two desserts before dinner, should we?” I said, and giggled4 nervously5.

    “这个,正餐之前总不能吃两道甜点吧,对不对?”我不安地笑道。

    “Why not?” she replied, not giggling6. She tightened7 her apron8 strings9 and walked over to her stove.

    “为什么不能呢?”她没有笑,系紧腰上的围裙,走向烤炉。

    Of course. What was I thinking? Hadn’t Dr. Cheng already made clear her conviction that in mathematics, rules are like eggs: meant to be broken, stirred, flipped10 over and taste-tested? And that day, we had broken a lot of eggs.

    当然啦。我想什么呢?郑博士不是早就阐明了自己的理念吗——在数学中,规则就像鸡蛋一样,就是用来打破、搅拌、翻转和尝试的。那一天,我们已经打破了不少鸡蛋了。

    “You’re absolutely right,” I said, rushing to her side for the grand unveiling of another mathematically themed confection.

    “你是对的,”我快速走到她身边,等待她郑重展示下一道数学主题的甜点。

    Dr. Cheng pulled from the oven a perfectly11 baked specimen12 of what she calls Bach pie, named for the great composer beloved by mathematicians13 everywhere: an oblong rectangle of creamy dark chocolate studded with banana slices and topped by an Escher-like braid of four glazed14 pastry15 plaits that followed divergent trajectories16, never quite crisscrossing where you expected them to.

    郑博士从烤箱中拿出一份完美烘焙的样本,她称之为“巴赫派”(Bach pie),以那位全世界数学家都深深喜爱的伟大作曲家命名。它是一块长方形的奶油黑巧克力蛋糕,点缀着香蕉切片,顶上是一个发辫一样的埃舍尔式图案:四股糖麻花呈放射状分布,在看似纵横相交的地方却并不相交。

    The filling was a clever concatenation — “BAnana added to CHocolate gives you Bach,” Dr. Cheng said. The braiding illustrated17 the structure of a Bach prelude18 and the sorts of patterns that knot theorists study “to see how looped up the braids are,” Dr. Cheng said, “and whether you can transform one braid into another by wiggling the different strings.”

    馅料别具匠心——“香蕉(BAnana)和巧克力(CHocolate)的前两个字母加起来就是巴赫(Bach),”郑博士说。这个编织图案展示了巴赫一首序曲的结构,也是纽结理论所研究的那种图形,为了“研究麻花辫子结构是如何纽结起来的”,她说,“以及你是否可以通过扭动不同的辫股,把一条辫子变形为另一条辫子”。

    The pie was a true union of art and math, too beautiful to besmirch19, and besides, you’re not supposed to untie20 knots with your teeth, are you?

    这个派真是艺术与数学的结合,美到让人不敢亵玩,另外,也不应该用牙齿解开绳结呀,对不对?

    Another rule, easily broken.

    不过这个规则是很容易打破的。

    Dr. Cheng, 39, has a knack21 for brushing aside conventions and edicts, like so many pie crumbs22 from a cutting board. She is a theoretical mathematician who works in a rarefied field called category theory, which is so abstract that “even some pure mathematicians think it goes too far,” Dr. Cheng said.

    39岁的郑博士惯于抛弃惯例与成规,就像信手拂去砧板上的糕点碎屑一样。她是个理论数学家,研究范畴论(category theory)这个罕为人知的领域,它非常抽象,“甚至许多纯数学家都觉得它走得太远了,”郑博士说。

    At the same time, Dr. Cheng is winning fame as a math popularizer, convinced that the pleasures of math can be conveyed to the legions of numbers-averse humanities majors still recovering from high school algebra23. She has been featured on shows like “Late Night With Stephen Colbert,” and her online math tutorials have been viewed more than a million times.

    与此同时,郑博士还以数学科普者而闻名。她坚信, 大批在高中数学课上留下后遗症、至今看到数字就头痛的文科生也可以领略到数学的乐趣。她上过“科尔伯特晚间秀”(Late Night With Stephen Colbert)等电视节目,她的在线数学课访问量超过了100万次。

    The hardcover edition of her first book, “How to Bake π: An Edible24 Exploration of the Mathematics of Mathematics,” has sold about 25,000 copies in this country and been translated into six languages, a surprising hit for a text visibly if judiciously25 seasoned with numbers, graphs and equations. The book is being released in paperback26 this month.

    她的第一本书名为《怎样烘焙π:对数学中的数学的可食用探险》(How to Bake π: An Edible Exploration of the Mathematics of Mathematics),其精装版在美国售出了2.5万册,并被翻译成六种语言。对于一本满篇(虽说是慎重使用的)数字、图表和等式的书籍来说,真是惊人的成功。这本书的平装版本月也将上市。

    “I spend a lot of time explaining mathematics on blogs, and I try to cut through the technicalities and make things easier to understand,” said John Baez, a professor of math at the University of California, Riverside (and yes, a cousin of Joan). Still, his posts are aimed at scientists and others with some quantitative27 background.

    “我花费了很多时间在博客上解释数学,试着迈过学术性,把问题弄得简单易懂,”加州大学河滨分校(University of California, Riverside)的数学教授约翰·贝兹(John Baez)说(没错,他是琼·贝兹的亲戚)。不过,他在网上的帖子还是针对科学家和其他有定量研究背景的人的。

    “Eugenia has gone all the way in,” he said. “She’s trying to explain math to everybody, with or without pre-existing expertise28, and I think she’s doing wonderfully.”

    “尤金妮娅则是彻底投入,”他说。“她试着向所有人解释数学,不管对方是不是已经具备了专业知识,而且我觉得她干得很棒。”

    So committed is Dr. Cheng to mass math demystification that she recently left a tenured professorship at the University of Sheffield in Britain to take a position at the School of the Art Institute of Chicago, where she teaches math to art students, lectures widely and continues her research in category theory on the side.

    郑博士是如此专注于大众数学启蒙工作,她前不久辞去了英国谢菲尔德大学(University of Sheffield)的终身教授职位,来到芝加哥艺术学院(Art Institute of Chicago),向学艺术的学生们教授数学,四处讲座,同时继续自己在范畴论领域的研究。

    Dr. Cheng adopts a literal approach to making math more appetizing. “Math is about taking ingredients, putting them together, seeing what you can make out of them, and then deciding whether it’s tasty or not,” she said.

    郑博士采用一种直接的方式让数学更“开胃”。“数学就是使用各种元素,把它们放在一起,看看能得到什么结果,然后判断它是不是美味可口,”她说。

    Every chapter in “How to Bake π” offers recipes for desserts and other dishes that encapsulate mathematical themes. To demonstrate how math seeks to identify underlying29 similarities across a broad set of problems, for example, Dr. Cheng starts with a recipe that can be readily tweaked to make mayonnaise instead of hollandaise sauce.

    怎样烘焙π》中的每一章都提供甜点菜谱和其他菜谱,都包含数学的主题。比如,为了展示数学是如何在一组广泛的问题中发现潜在的相似性,郑博士从一份便于调整的食谱入手,不调制荷兰酱,而代之以普通蛋黄酱。

    “Books might tell you that hollandaise sauce needs to be done differently,” she writes, “but I ignore them to make my life simpler. Math is also there to make things simpler, by finding things that look the same if you ignore some small detail.”

    “书本会告诉你,荷兰酱有另一种做法,”她写道,“但是我忽略了它们,好让自己的生活简单点。数学在这里也发挥了作用,找出相同点,帮助你把小的细节忽略掉,让一切变得简单。”

    Her recipe for lasagna illuminates30 the importance of context to math. Dr. Cheng lists among the basic ingredients “fresh lasagna noodles,” and then points out that another cookbook might deem the noodles not truly basic and instead describe their preparation from scratch.

    她的千层面菜谱显示出背景条件在数学中的重要性。郑博士把“新鲜千层面”列为这道菜所需的基本原料,并指出,另一本菜谱或许并不把面条视为做这道菜的基本原料,而是从零开始,描述了面条的制作方法。

    So, too, do numbers change their character and degree of basicness depending on context. The number 5, for example, when viewed among the natural, or counting, numbers is one of those elemental creatures: a prime number, divisible only by 1 and itself.

    同理,根据背景条件,数字的特性及其基本程度也会改变。比如数字5,在自然数或计数中,它是一个基本的数字:质数,只能被1或它自身整除。

    But in the context of the so-called rational numbers, which include fractions, 5 loses its prime identity and gains versatility31, able to be divided into ever tinier slivers32, like a cake at a dieters’ convention.

    然而,如果把“5”放在包括分数在内的有理数中考虑,它就失去了质数的特性,有了更多用途,可以被划分为更小的部分,就像节食者的蛋糕。

    The number 1 in its multiplicative identity is practically bedridden, leaving other numbers unchanged: 6 times 1 equals 6. In its additive33 capacity, however, 1 is unstoppable: if you keep adding 1 to itself, Dr. Cheng noted34, you can generate all the natural numbers, out to infinity35.

    数字“1”在乘法中起一种限制作用,就是让其他数字保持不变:6乘以1还等于6。而在加法中,1的作用是不可遏制的:郑博士指出,如果在1上面持续再加1,就会得到所有的自然数,直到无穷大。

    Context can prod36 numbers to defy grade-school verities37: 2 plus 2 equals 4, and that’s that. But not if you’re talking about a clock face with only three numbers: 1, 2 and 3. In that case, 2 plus 2 equals 1 – if you start at the 2 and move clockwise by 2, you reach 1.

    背景条件可以令数字违背学校里教的“2加2等于4”之类公理。如果一个表盘上只有1、2、3这3个数字,在这种情况下,2加2就等于1——如果你从2开始,把指针顺时针移动2次,你就可以得到1。

    “I admit I was skeptical38 at first about her analogies to cooking, but I ended up being completely sold,” said Steven Strogatz, a professor of applied39 mathematics at Cornell University who also writes popular books.

    “我承认,对于她把数学和烹饪做类比的方法,我一开始感到怀疑,但最后我完全被她说服了,”同样撰写通俗书籍的康奈尔大学(Cornell University)应用数学教授史蒂芬·斯特朗盖茨(Steven Strogatz)说。

    “She conveys the spirit of inventiveness and creativity in math that all mathematicians feel but do a very poor job communicating when teaching math. Refreshing40 is the word that keeps coming to mind.”

    “她传达了数学中的创新精神与创造性,所有数学家都能体会到,但是在教授数学的时候,却很难同学生沟通这一点。看她的书不断让人感觉耳目一新。”

    Dr. Cheng insists that the public has it all wrong about math being difficult, something that only the gifted mathletes among us can do. To the contrary, she says, math exists to make life smoother, to solve those problems that can be solved by applying math’s most powerful tool: logic41.

    郑博士坚持说,公众认为数学很难、只有天才才能搞数学的看法是错误的。相反,她说,数学就是为了让生活更简单;凭借数学当中最强大的工具:逻辑,可以解决各种问题。

    Science may depend on forming hypotheses, doing experiments and gathering42 evidence that support or refute your hypothesis, but math is simply a matter of stating the terms of your argument and then defending those statements using logic.

    科学或许要依靠提出假设、做实验、收集证据,以此支持或否定自己的假设,但数学就只需要摆出论点的条件,然后使用逻辑,支持自己的论述。

    “The great thing about math is you don’t need much to start exploring it,” Dr. Baez said. “No expensive equipment, just pencil and paper, and you can start fiddling43 around with patterns and numbers.”

    “数学最棒的一点,就是探索它不需要很多条件,”贝兹博士说。“不需要昂贵的设备,只需要纸和笔,你就可以在各种模型与数字之中摸索。”

    Dr. Cheng recognizes that people can feel uncomfortable with some of the abstractions required by mathematical thinking, by the need to ignore the particulars of, say, this green round pillow and that square purple pillow in favor of an abstract ideal of a pillow that you’re going to call x.

    郑博士发现,有些需要数学思维的抽象概念可能会让人们感觉不舒服,它们需要人们忽略事物的特殊性,比如说这个绿色的圆枕头,那个紫色的方枕头,在数学中,它们都是抽象概念的枕头,可以管它们叫做“x”。

    But it’s just a matter of practice, she said, before the idea starts to feel like a real object that you can manipulate with ease. “You become very good at separating what’s relevant from what isn’t, and that can be very useful in daily life,” she said.

    但这只是个实践问题,她说,渐渐地,抽象概念就变得好像真实存在的物体,你可以轻易操纵它。“你开始擅长把重要的事物从不重要的事物中分辨出来,这在日常生活中非常有用,”她说。

    Sometimes, she finds it “oddly satisfying” to mentally shave a bearded man or imagine how a furry44 dog would look like after a swim in a lake. “That’s what abstraction is,” she said. “You reveal the structure underneath45.”

    有时候,她觉得在想象中给一个留胡子的男人剃须,或是想象一只毛茸茸的狗从湖里湿淋淋地爬上来,会有一种“奇异的满足感”。“这就是抽象,”她说,“揭示出深层的结构。”

     12级    双语 


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    1 mathematician [ˌmæθəməˈtɪʃn] aoPz2p   第8级
    n.数学家
    参考例句:
    • The man with his back to the camera is a mathematician. 背对着照相机的人是位数学家。
    • The mathematician analyzed his figures again. 这位数学家再次分析研究了他的这些数字。
    2 demonstration [ˌdemənˈstreɪʃn] 9waxo   第8级
    n.表明,示范,论证,示威
    参考例句:
    • His new book is a demonstration of his patriotism. 他写的新书是他的爱国精神的证明。
    • He gave a demonstration of the new technique then and there. 他当场表演了这种新的操作方法。
    3 subtraction [səb'trækʃn] RsJwl   第9级
    n.减法,减去
    参考例句:
    • We do addition and subtraction in arithmetic. 在算术里,我们作加减运算。
    • They made a subtraction of 50 dollars from my salary. 他们从我的薪水里扣除了五十美元。
    4 giggled [ˈɡiɡld] 72ecd6e6dbf913b285d28ec3ba1edb12   第7级
    v.咯咯地笑( giggle的过去式和过去分词 )
    参考例句:
    • The girls giggled at the joke. 女孩子们让这笑话逗得咯咯笑。
    • The children giggled hysterically. 孩子们歇斯底里地傻笑。 来自《简明英汉词典》
    5 nervously ['nɜ:vəslɪ] tn6zFp   第8级
    adv.神情激动地,不安地
    参考例句:
    • He bit his lip nervously, trying not to cry. 他紧张地咬着唇,努力忍着不哭出来。
    • He paced nervously up and down on the platform. 他在站台上情绪不安地走来走去。
    6 giggling [ˈɡiɡlɪŋ] 2712674ae81ec7e853724ef7e8c53df1   第7级
    v.咯咯地笑( giggle的现在分词 )
    参考例句:
    • We just sat there giggling like naughty schoolchildren. 我们只是坐在那儿像调皮的小学生一样的咯咯地傻笑。 来自《简明英汉词典》
    • I can't stand her giggling, she's so silly. 她吃吃地笑,叫我真受不了,那样子傻透了。 来自《现代英汉综合大词典》
    7 tightened [ˈtaɪtnd] bd3d8363419d9ff838bae0ba51722ee9   第7级
    收紧( tighten的过去式和过去分词 ); (使)变紧; (使)绷紧; 加紧
    参考例句:
    • The rope holding the boat suddenly tightened and broke. 系船的绳子突然绷断了。
    • His index finger tightened on the trigger but then relaxed again. 他的食指扣住扳机,然后又松开了。
    8 apron [ˈeɪprən] Lvzzo   第7级
    n.围裙;工作裙
    参考例句:
    • We were waited on by a pretty girl in a pink apron. 招待我们的是一位穿粉红色围裙的漂亮姑娘。
    • She stitched a pocket on the new apron. 她在新围裙上缝上一只口袋。
    9 strings [strɪŋz] nh0zBe   第12级
    n.弦
    参考例句:
    • He sat on the bed, idly plucking the strings of his guitar. 他坐在床上,随意地拨着吉他的弦。
    • She swept her fingers over the strings of the harp. 她用手指划过竖琴的琴弦。
    10 flipped [flipt] 5bef9da31993fe26a832c7d4b9630147   第7级
    轻弹( flip的过去式和过去分词 ); 按(开关); 快速翻转; 急挥
    参考例句:
    • The plane flipped and crashed. 飞机猛地翻转,撞毁了。
    • The carter flipped at the horse with his whip. 赶大车的人扬鞭朝着马轻轻地抽打。
    11 perfectly [ˈpɜ:fɪktli] 8Mzxb   第8级
    adv.完美地,无可非议地,彻底地
    参考例句:
    • The witnesses were each perfectly certain of what they said. 证人们个个对自己所说的话十分肯定。
    • Everything that we're doing is all perfectly above board. 我们做的每件事情都是光明正大的。
    12 specimen [ˈspesɪmən] Xvtwm   第7级
    n.样本,标本
    参考例句:
    • You'll need tweezers to hold up the specimen. 你要用镊子来夹这标本。
    • This specimen is richly variegated in colour. 这件标本上有很多颜色。
    13 mathematicians [mæθə'mətɪʃnz] bca28c194cb123ba0303d3afafc32cb4   第8级
    数学家( mathematician的名词复数 )
    参考例句:
    • Do you suppose our mathematicians are unequal to that? 你以为我们的数学家做不到这一点吗? 来自英汉文学
    • Mathematicians can solve problems with two variables. 数学家们可以用两个变数来解决问题。 来自哲学部分
    14 glazed [gleɪzd] 3sLzT8   第8级
    adj.光滑的,像玻璃的;上过釉的;呆滞无神的v.装玻璃( glaze的过去式);上釉于,上光;(目光)变得呆滞无神
    参考例句:
    • eyes glazed with boredom 厌倦无神的眼睛
    • His eyes glazed over at the sight of her. 看到她时,他的目光就变得呆滞。 来自《简明英汉词典》
    15 pastry [ˈpeɪstri] Q3ozx   第8级
    n.油酥面团,酥皮糕点
    参考例句:
    • The cook pricked a few holes in the pastry. 厨师在馅饼上戳了几个洞。
    • The pastry crust was always underdone. 馅饼的壳皮常常烤得不透。
    16 trajectories [trəˈdʒektəri:z] 5c5d2685e0c45bbfa4a80b6d43c087fa   第12级
    n.弹道( trajectory的名词复数 );轨道;轨线;常角轨道
    参考例句:
    • To answer this question, we need to plot trajectories of principal stresses. 为了回答这个问题,我们尚须画出主应力迹线图。 来自辞典例句
    • In the space program the theory is used to determine spaceship trajectories. 在空间计划中,这个理论用于确定飞船的轨道。 来自辞典例句
    17 illustrated ['ɪləstreɪtɪd] 2a891807ad5907f0499171bb879a36aa   第7级
    adj. 有插图的,列举的 动词illustrate的过去式和过去分词
    参考例句:
    • His lecture was illustrated with slides taken during the expedition. 他在讲演中使用了探险时拍摄到的幻灯片。
    • The manufacturing Methods: Will be illustrated in the next chapter. 制作方法将在下一章说明。
    18 prelude [ˈprelju:d] 61Fz6   第9级
    n.序言,前兆,序曲
    参考例句:
    • The prelude to the musical composition is very long. 这首乐曲的序曲很长。
    • The German invasion of Poland was a prelude to World War II. 德国入侵波兰是第二次世界大战的序幕。
    19 besmirch [bɪˈsmɜ:tʃ] NQXyH   第11级
    vt.污,糟蹋
    参考例句:
    • He has accused local people of trying to besmirch his reputation. 他指责当地人企图败坏他的名声。
    • The scandalous remarks in the newspaper besmirch the reputations of every member of the society. 报刊上那些恶意中伤的报道败坏了该社团全体成员的名声。
    20 untie [ʌnˈtaɪ] SjJw4   第9级
    vt.解开,松开;解放
    参考例句:
    • It's just impossible to untie the knot. It's too tight. 这个结根本解不开。太紧了。
    • Will you please untie the knot for me? 请你替我解开这个结头,好吗?
    21 knack [næk] Jx9y4   第9级
    n.诀窍,做事情的灵巧的,便利的方法
    参考例句:
    • He has a knack of teaching arithmetic. 他教算术有诀窍。
    • Making omelettes isn't difficult, but there's a knack to it. 做煎蛋饼并不难,但有窍门。
    22 crumbs [krʌmz] crumbs   第9级
    int. (表示惊讶)哎呀 n. 碎屑 名词crumb的复数形式
    参考例句:
    • She stood up and brushed the crumbs from her sweater. 她站起身掸掉了毛衣上的面包屑。
    • Oh crumbs! Is that the time? 啊,天哪!都这会儿啦?
    23 algebra [ˈældʒɪbrə] MKRyW   第9级
    n.代数学
    参考例句:
    • He was not good at algebra in middle school. 他中学时不擅长代数。
    • The boy can't figure out the algebra problems. 这个男孩做不出这道代数题。
    24 edible [ˈedəbl] Uqdxx   第7级
    n.食品,食物;adj.可食用的
    参考例句:
    • Edible wild herbs kept us from dying of starvation. 我们靠着野菜才没被饿死。
    • This kind of mushroom is edible, but that kind is not. 这种蘑菇吃得,那种吃不得。
    25 judiciously [dʒʊ'dɪʃəslɪ] 18cfc8ca2569d10664611011ec143a63   第9级
    adv.明断地,明智而审慎地
    参考例句:
    • Let's use these intelligence tests judiciously. 让我们好好利用这些智力测试题吧。 来自《简明英汉词典》
    • His ideas were quaint and fantastic. She brought him judiciously to earth. 他的看法荒廖古怪,她颇有见识地劝他面对现实。 来自辞典例句
    26 paperback [ˈpeɪpəbæk] WmEzIh   第8级
    n.平装本,简装本
    参考例句:
    • A paperback edition is now available at bookshops. 平装本现在在书店可以买到。
    • Many books that are out of print are reissued in paperback form. 许多绝版的书籍又以平装本形式重新出现。
    27 quantitative [ˈkwɒntɪtətɪv] TCpyg   第7级
    adj.数量的,定量的
    参考例句:
    • He said it was only a quantitative difference. 他说这仅仅是数量上的差别。
    • We need to do some quantitative analysis of the drugs. 我们对药物要进行定量分析。
    28 expertise [ˌekspɜ:ˈti:z] fmTx0   第7级
    n.专门知识(或技能等),专长
    参考例句:
    • We were amazed at his expertise on the ski slopes. 他斜坡滑雪的技能使我们赞叹不已。
    • You really have the technical expertise in a new breakthrough. 你真正在专业技术上有了一个全新的突破。
    29 underlying [ˌʌndəˈlaɪɪŋ] 5fyz8c   第7级
    adj.在下面的,含蓄的,潜在的
    参考例句:
    • The underlying theme of the novel is very serious. 小说隐含的主题是十分严肃的。
    • This word has its underlying meaning. 这个单词有它潜在的含义。
    30 illuminates [iˈlju:mineits] 63e70c844c6767d7f38403dcd36bb8a5   第7级
    v.使明亮( illuminate的第三人称单数 );照亮;装饰;说明
    参考例句:
    • The light shines on from over there and illuminates the stage. 灯光从那边照进来,照亮了舞台。 来自《简明英汉词典》
    • The sun illuminates the sky. 太阳照亮了天空。 来自《简明英汉词典》
    31 versatility [ˌvɜ:sə'tɪlətɪ] xiQwT   第7级
    n.多才多艺,多样性,多功能
    参考例句:
    • Versatility is another of your strong points,but don't overdo it by having too many irons in the fire.你还有一个长处是多才多艺,但不要揽事太多而太露锋芒。
    • This versatility comes from a dual weather influence.这种多样性是由于双重的气候影响而形成的。
    32 slivers [ˈslɪvəz] b1fe0d3c032bc08f91b6067bea26bdff   第10级
    (切割或断裂下来的)薄长条,碎片( sliver的名词复数 )
    参考例句:
    • Margret had eight slivers of glass removed from her cheek. 从玛格列特的脸颊取出了八片碎玻璃。
    • Eight slivers are drawn together to produce the drawn sliver. 在末道并条机上,八根棉条并合在一起被牵伸成熟条。
    33 additive [ˈædətɪv] BJFyM   第8级
    adj.附加的;n.添加剂
    参考例句:
    • Colour is often an additive in foods. 颜料经常是各种食物中的添加物。
    • Strict safety tests are carried out on food additives. 对食品添加剂进行了严格的安全检测。
    34 noted [ˈnəʊtɪd] 5n4zXc   第8级
    adj.著名的,知名的
    参考例句:
    • The local hotel is noted for its good table. 当地的那家酒店以餐食精美而著称。
    • Jim is noted for arriving late for work. 吉姆上班迟到出了名。
    35 infinity [ɪnˈfɪnəti] o7QxG   第8级
    n.无限,无穷,大量
    参考例句:
    • It is impossible to count up to infinity. 不可能数到无穷大。
    • Theoretically, a line can extend into infinity. 从理论上来说直线可以无限地延伸。
    36 prod [prɒd] TSdzA   第9级
    vt.戳,刺;刺激,激励
    参考例句:
    • The crisis will prod them to act. 那个危机将刺激他们行动。
    • I shall have to prod him to pay me what he owes. 我将不得不催促他把欠我的钱还给我。
    37 verities [ˈveritiz] e8cae4271fa3f5fdf51cd6c5be5c935f   第12级
    n.真实( verity的名词复数 );事实;真理;真实的陈述
    参考例句:
    • the eternal verities of life 生命永恒的真理
    38 skeptical ['skeptɪkəl] MxHwn   第7级
    adj.怀疑的,多疑的
    参考例句:
    • Others here are more skeptical about the chances for justice being done. 这里的其他人更为怀疑正义能否得到伸张。
    • Her look was skeptical and resigned. 她的表情是将信将疑而又无可奈何。
    39 applied [əˈplaɪd] Tz2zXA   第8级
    adj.应用的;v.应用,适用
    参考例句:
    • She plans to take a course in applied linguistics. 她打算学习应用语言学课程。
    • This cream is best applied to the face at night. 这种乳霜最好晚上擦脸用。
    40 refreshing [rɪˈfreʃɪŋ] HkozPQ   第8级
    adj.使精神振作的,使人清爽的,使人喜欢的
    参考例句:
    • I find it so refreshing to work with young people in this department. 我发现和这一部门的青年一起工作令人精神振奋。
    • The water was cold and wonderfully refreshing. 水很涼,特别解乏提神。
    41 logic [ˈlɒdʒɪk] j0HxI   第7级
    n.逻辑(学);逻辑性
    参考例句:
    • What sort of logic is that? 这是什么逻辑?
    • I don't follow the logic of your argument. 我不明白你的论点逻辑性何在。
    42 gathering [ˈgæðərɪŋ] ChmxZ   第8级
    n.集会,聚会,聚集
    参考例句:
    • He called on Mr. White to speak at the gathering. 他请怀特先生在集会上讲话。
    • He is on the wing gathering material for his novels. 他正忙于为他的小说收集资料。
    43 fiddling ['fidliŋ] XtWzRz   第9级
    微小的
    参考例句:
    • He was fiddling with his keys while he talked to me. 和我谈话时他不停地摆弄钥匙。
    • All you're going to see is a lot of fiddling around. 你今天要看到的只是大量的胡摆乱弄。 来自英汉文学 - 廊桥遗梦
    44 furry [ˈfɜ:ri] Rssz2D   第9级
    adj.毛皮的;似毛皮的;毛皮制的
    参考例句:
    • This furry material will make a warm coat for the winter. 这件毛皮料在冬天会是一件保暖的大衣。
    • Mugsy is a big furry brown dog, who wiggles when she is happy. 马格斯是一只棕色大长毛狗,当她高兴得时候她会摇尾巴。
    45 underneath [ˌʌndəˈni:θ] VKRz2   第7级
    adj.在...下面,在...底下;adv.在下面
    参考例句:
    • Working underneath the car is always a messy job. 在汽车底下工作是件脏活。
    • She wore a coat with a dress underneath. 她穿着一件大衣,里面套着一条连衣裙。

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