《三维分形维度中旋转求索的王虹》导学案-2027届高考英语外刊阅读讲练

该高中英语高考复习学案以高考外刊阅读为载体，系统覆盖词汇（含熟词生义）、语法（长难句分析、时态、非谓语动词）、阅读理解（细节理解、主旨大意）及英汉互译等核心考点，通过“语篇讲解—生词词组梳理—长难句解析—专项训练”的层级架构，引导学生以问题为导向自主构建语言知识网络。 亮点在于强化自主学习诊断与语言能力培养，如设置4道阅读理解题和10道英汉互译题作为自测工具，结合长难句解析中的语法方法指导，助力学生精准定位薄弱点。通过任务驱动式学习提升思维品质与学习能力，教师可依据学生自测结果实施针对性指导，有效支持因材施教。

高考外刊讲义&练习 高考外刊阅读讲义 《Hong Wang Twirls in Fractal Dimensions of Three》 （The New York Times 2026.07.23） 第一部分：英文讲解 Hong Wang Twirls in Fractal Dimensions of Three 三维分形维度中旋转求索的王虹 The young mathematician won a prestigious Fields Medal for her work on the so-called Kakeya conjecture. 这位青年数学家因攻克著名的挂谷猜想，斩获极具含金量的菲尔兹奖。 Hong Wang, one of this year’s winners of the Fields Medals, which honor the top mathematicians under the age of 40, once considered giving up on math and becoming an architect instead. 翻译：王虹是本年度菲尔兹奖得主之一。菲尔兹奖用于表彰40岁以下的顶尖数学家，她曾一度考虑放弃数学，转行成为一名建筑师。 【核心生词】 1. architect /ˈɑːkɪtekt/ n. 建筑师；缔造者 【重点词组】 1. give up on 放弃；对……不再抱有希望 例句：You should never give up on yourself when facing temporary failures. 【长难句解析】 Hong Wang, one of this year’s winners of the Fields Medals, which honor the top mathematicians under the age of 40, once considered giving up on math and becoming an architect instead. · 句式解析本句为主谓宾简单句嵌套修饰成分。one of this year’s winners of the Fields Medals 为同位语，用来补充解释主语Hong Wang；which引导非限制性定语从句，先行词为Fields Medals，用于解释该奖项的评选标准。 · 语法解析核心考点为consider doing sth.（考虑做某事），句中giving up on math与becoming an architect为并列动名词结构，共同作consider的宾语。 After graduating from Peking University in 2018, she headed to the United States to pursue doctoral studies. She focused her research on the Kakeya conjecture, a long-standing puzzle in harmonic analysis that had baffled scholars for more than a century. 翻译：2018年从北京大学毕业后，她远赴美国攻读博士学位。她将研究重心聚焦于挂谷猜想，这是调和分析领域一道由来已久的难题，困扰了学界学者一个多世纪。 【核心生词】 1. pursue /pəˈsjuː/ v. 追求；从事；致力于 【熟词生义】攻读（学位、学业） 2. doctoral /ˈdɒktərəl/ adj. 博士的 3. conjecture /kənˈdʒektʃə(r)/ n. （数学、科学）猜想；推测 v. 猜测 4. long-standing /ˌlɒŋ ˈstændɪŋ/ adj. 长期存在的；由来已久的 5. baffle /ˈbæfl/ v. 使困惑；使束手无策；难住 6. scholar /ˈskɒlə(r)/ n. 学者；研究者 【重点词组】 1. head to 前往；动身去往 例句：Most graduates head to big cities to seek better career opportunities. 2. focus…on… 把……集中于……；专注于…… 例句：Top students always focus their attention on key knowledge points. 【长难句解析】 She focused her research on the Kakeya conjecture, a long-standing puzzle in harmonic analysis that had baffled scholars for more than a century. · 句式解析主句+同位语+限制性定语从句结构。主句主谓宾完整；a long-standing puzzle in harmonic analysis 作同位语，解释说明Kakeya conjecture；that引导定语从句，修饰先行词puzzle。 · 语法解析定语从句使用过去完成时，该动作“困扰学者百余年”发生在主句动作focused（过去式）之前，体现动作先后顺序，是高考时态高频考点。 Many mathematicians had made partial progress yet failed to reach a complete proof. By combining innovative geometric methods with rigorous analytical reasoning, Hong eventually cracked the tough conjecture. Her breakthrough immediately drew wide attention across the global mathematical community. 翻译：许多数学家曾取得阶段性进展，却始终未能完成完整论证。王虹通过将创新的几何方法与严谨的分析推理相结合，最终攻克了这一棘手的猜想。她的突破性成果迅速获得了全球数学界的广泛关注。 【核心生词】 1. partial /ˈpɑːʃl/ adj. 部分的；不完全的 2. innovative /ˈɪnəveɪtɪv/ adj. 创新的；新颖的 3. rigorous /ˈrɪɡərəs/ adj. 严谨的；严密的；严格的 4. analytical /ˌænəˈlɪtɪkl/ adj. 分析的；解析的 5. crack /kræk/ v. 破裂 【熟词生义】攻克（难题、谜题）；破解 6. breakthrough /ˈbreɪkθruː/ n. 突破；重大进展 【重点词组】 1. make partial progress 取得阶段性进展 例句：Our team has made partial progress in environmental protection research. 2. combine…with… 将……与……相结合 例句：We should combine practice with theory to improve learning efficiency. 3. draw wide attention 获得广泛关注 例句：The new policy has drawn wide attention from the public. 【长难句解析】 By combining innovative geometric methods with rigorous analytical reasoning, Hong eventually cracked the tough conjecture. · 句式解析介词短语作方式状语前置，后接完整主谓宾主句。状语部分交代主人公攻克难题的方式，主句陈述核心事件，句式简洁高级，是高考写作高分句式。 · 语法解析介词By后必须接动名词形式（combining），表“通过某种方式”；combine A with B为固定搭配，是完形填空、语法填空高频考点。 When receiving the Fields Medal, she shared that persistence and curiosity were the major forces pushing her forward. She also encouraged young learners to dare to face tough problems and keep exploring unknown areas of science. 翻译：在领取菲尔兹奖时，她坦言，坚持与好奇心是推动自己不断前行的核心力量。她同时鼓励青年学习者敢于直面难题，持续探索科学的未知领域。 【核心生词】 1. persistence /pəˈsɪstəns/ n. 毅力；坚持；持之以恒 2. curiosity /ˌkjʊəriˈɒsəti/ n. 好奇心；求知欲 3. explore /ɪkˈsplɔː(r)/ v. 探索；探究；探寻 【重点词组】 1. push sb. forward 推动某人前行；助力某人进步 例句：Positive feedback and self-discipline will push us forward constantly. 2. keep doing sth. 持续做某事；坚持做某事 例句：Keep practicing every day, and you will make steady progress. 【长难句解析】 When receiving the Fields Medal, she shared that persistence and curiosity were the major forces pushing her forward. · 句式解析时间状语省略结构+宾语从句。When receiving…为状语从句省略（省略主语she和be动词）；that引导宾语从句，作shared的宾语；pushing her forward现在分词作后置定语，修饰forces。 · 语法解析状语从句省略条件：主从句主语一致且含be动词，可省略主语和be动词，是高考语法填空、改错高频考点；现在分词后置定语表主动、进行。 阅读理解专项训练 1. Why did Hong Wang once think of abandoning mathematics? A. She failed to finish her doctoral research in America. B. The passage does not mention the specific reason. C. The Kakeya conjecture beat her for many years. D. She preferred architecture to all other subjects. 2. What can we learn about the Kakeya conjecture? A. It belongs to the field of architecture design. B. It has been fully solved over one hundred years ago. C. It confused mathematicians for over a century. D. Scholars had gained complete proof before Hong. 3. Which factor greatly supported Hong Wang’s research work? A. Rich working experience in architecture B. Persistence and curiosity C. Help from architects in Peking University D. Advanced equipment in university labs 4. What is the main idea of the passage? A. An introduction to the famous Kakeya conjecture. B. Basic information about the Fields Medal. C. Suggestions for young scientific researchers. D. Hong Wang wins the Fields Medal after persistent research. 英汉互译专项练习 英译汉 1. Many young researchers pursue advanced studies abroad to explore unknown academic fields. ______________________________________________________________________________________________________ 2. Scientists try to combine creative ideas with rigorous experiments to crack hard problems. ______________________________________________________________________________________________________ 3. This long-standing puzzle has baffled specialists for nearly one hundred years. ______________________________________________________________________________________________________ 4. True persistence and curiosity can always push young scholars forward in scientific research. ______________________________________________________________________________________________________ 5. The innovative research method has drawn wide attention from the international academic community. ______________________________________________________________________________________________________ 汉译英 1. 不要轻易放弃目标，坚持终将推动你不断前行。 ______________________________________________________________________________________________________ 2. 这项重大突破立刻获得了国内外专家的广泛关注。 ______________________________________________________________________________________________________ 3. 我们应当把注意力集中在当前最重要的学习任务上。 ______________________________________________________________________________________________________ 4. 研究者需要将严谨的分析思维与创新方法结合起来攻克学术难题。 ______________________________________________________________________________________________________ 5. 无数学者多年钻研，却始终未能解开这一由来已久的难题。 ______________________________________________________________________________________________________ 学科网（北京）股份有限公司 $高考外刊讲义&练习 高考外刊阅读讲义 《Hong Wang Twirls in Fractal Dimensions of Three》 （The New York Times 2026.07.23） 第一部分：英文讲解 Hong Wang Twirls in Fractal Dimensions of Three 三维分形维度中旋转求索的王虹 The young mathematician won a prestigious Fields Medal for her work on the so-called Kakeya conjecture. 这位青年数学家因攻克著名的挂谷猜想，斩获极具含金量的菲尔兹奖。 Hong Wang, one of this year’s winners of the Fields Medals, which honor the top mathematicians under the age of 40, once considered giving up on math and becoming an architect instead. 翻译：王虹是本年度菲尔兹奖得主之一。菲尔兹奖用于表彰40岁以下的顶尖数学家，她曾一度考虑放弃数学，转行成为一名建筑师。 【核心生词】 1. architect /ˈɑːkɪtekt/ n. 建筑师；缔造者 【重点词组】 1. give up on 放弃；对……不再抱有希望 例句：You should never give up on yourself when facing temporary failures. 【长难句解析】 Hong Wang, one of this year’s winners of the Fields Medals, which honor the top mathematicians under the age of 40, once considered giving up on math and becoming an architect instead. · 句式解析本句为主谓宾简单句嵌套修饰成分。one of this year’s winners of the Fields Medals 为同位语，用来补充解释主语Hong Wang；which引导非限制性定语从句，先行词为Fields Medals，用于解释该奖项的评选标准。 · 语法解析核心考点为consider doing sth.（考虑做某事），句中giving up on math与becoming an architect为并列动名词结构，共同作consider的宾语。 After graduating from Peking University in 2018, she headed to the United States to pursue doctoral studies. She focused her research on the Kakeya conjecture, a long-standing puzzle in harmonic analysis that had baffled scholars for more than a century. 翻译：2018年从北京大学毕业后，她远赴美国攻读博士学位。她将研究重心聚焦于挂谷猜想，这是调和分析领域一道由来已久的难题，困扰了学界学者一个多世纪。 【核心生词】 1. pursue /pəˈsjuː/ v. 追求；从事；致力于 【熟词生义】攻读（学位、学业） 2. doctoral /ˈdɒktərəl/ adj. 博士的 3. conjecture /kənˈdʒektʃə(r)/ n. （数学、科学）猜想；推测 v. 猜测 4. long-standing /ˌlɒŋ ˈstændɪŋ/ adj. 长期存在的；由来已久的 5. baffle /ˈbæfl/ v. 使困惑；使束手无策；难住 6. scholar /ˈskɒlə(r)/ n. 学者；研究者 【重点词组】 1. head to 前往；动身去往 例句：Most graduates head to big cities to seek better career opportunities. 2. focus…on… 把……集中于……；专注于…… 例句：Top students always focus their attention on key knowledge points. 【长难句解析】 She focused her research on the Kakeya conjecture, a long-standing puzzle in harmonic analysis that had baffled scholars for more than a century. · 句式解析主句+同位语+限制性定语从句结构。主句主谓宾完整；a long-standing puzzle in harmonic analysis 作同位语，解释说明Kakeya conjecture；that引导定语从句，修饰先行词puzzle。 · 语法解析定语从句使用过去完成时，该动作“困扰学者百余年”发生在主句动作focused（过去式）之前，体现动作先后顺序，是高考时态高频考点。 Many mathematicians had made partial progress yet failed to reach a complete proof. By combining innovative geometric methods with rigorous analytical reasoning, Hong eventually cracked the tough conjecture. Her breakthrough immediately drew wide attention across the global mathematical community. 翻译：许多数学家曾取得阶段性进展，却始终未能完成完整论证。王虹通过将创新的几何方法与严谨的分析推理相结合，最终攻克了这一棘手的猜想。她的突破性成果迅速获得了全球数学界的广泛关注。 【核心生词】 1. partial /ˈpɑːʃl/ adj. 部分的；不完全的 2. innovative /ˈɪnəveɪtɪv/ adj. 创新的；新颖的 3. rigorous /ˈrɪɡərəs/ adj. 严谨的；严密的；严格的 4. analytical /ˌænəˈlɪtɪkl/ adj. 分析的；解析的 5. crack /kræk/ v. 破裂 【熟词生义】攻克（难题、谜题）；破解 6. breakthrough /ˈbreɪkθruː/ n. 突破；重大进展 【重点词组】 1. make partial progress 取得阶段性进展 例句：Our team has made partial progress in environmental protection research. 2. combine…with… 将……与……相结合 例句：We should combine practice with theory to improve learning efficiency. 3. draw wide attention 获得广泛关注 例句：The new policy has drawn wide attention from the public. 【长难句解析】 By combining innovative geometric methods with rigorous analytical reasoning, Hong eventually cracked the tough conjecture. · 句式解析介词短语作方式状语前置，后接完整主谓宾主句。状语部分交代主人公攻克难题的方式，主句陈述核心事件，句式简洁高级，是高考写作高分句式。 · 语法解析介词By后必须接动名词形式（combining），表“通过某种方式”；combine A with B为固定搭配，是完形填空、语法填空高频考点。 When receiving the Fields Medal, she shared that persistence and curiosity were the major forces pushing her forward. She also encouraged young learners to dare to face tough problems and keep exploring unknown areas of science. 翻译：在领取菲尔兹奖时，她坦言，坚持与好奇心是推动自己不断前行的核心力量。她同时鼓励青年学习者敢于直面难题，持续探索科学的未知领域。 【核心生词】 1. persistence /pəˈsɪstəns/ n. 毅力；坚持；持之以恒 2. curiosity /ˌkjʊəriˈɒsəti/ n. 好奇心；求知欲 3. explore /ɪkˈsplɔː(r)/ v. 探索；探究；探寻 【重点词组】 1. push sb. forward 推动某人前行；助力某人进步 例句：Positive feedback and self-discipline will push us forward constantly. 2. keep doing sth. 持续做某事；坚持做某事 例句：Keep practicing every day, and you will make steady progress. 【长难句解析】 When receiving the Fields Medal, she shared that persistence and curiosity were the major forces pushing her forward. · 句式解析时间状语省略结构+宾语从句。When receiving…为状语从句省略（省略主语she和be动词）；that引导宾语从句，作shared的宾语；pushing her forward现在分词作后置定语，修饰forces。 · 语法解析状语从句省略条件：主从句主语一致且含be动词，可省略主语和be动词，是高考语法填空、改错高频考点；现在分词后置定语表主动、进行。 阅读理解专项训练 1. Why did Hong Wang once think of abandoning mathematics? A. She failed to finish her doctoral research in America. B. The passage does not mention the specific reason. C. The Kakeya conjecture beat her for many years. D. She preferred architecture to all other subjects. 2. What can we learn about the Kakeya conjecture? A. It belongs to the field of architecture design. B. It has been fully solved over one hundred years ago. C. It confused mathematicians for over a century. D. Scholars had gained complete proof before Hong. 3. Which factor greatly supported Hong Wang’s research work? A. Rich working experience in architecture B. Persistence and curiosity C. Help from architects in Peking University D. Advanced equipment in university labs 4. What is the main idea of the passage? A. An introduction to the famous Kakeya conjecture. B. Basic information about the Fields Medal. C. Suggestions for young scientific researchers. D. Hong Wang wins the Fields Medal after persistent research. 阅读理解参考答案与解析 【答案】1.B 2.C 3.B 4.D 1.【解析】原文仅提及主人公曾考虑放弃数学，未交代具体原因，故选B。 2.【解析】定位第二段 a long-standing puzzle…that had baffled scholars for more than a century，该猜想困扰学者百年，对应C选项。 3.【解析】定位最后一段 persistence and curiosity were the major forces pushing her forward，直接锁定答案B。 4.【解析】全文围绕数学家王虹深耕科研、攻克百年难题、斩获菲尔兹奖展开，D选项精准概括文章主旨。 英汉互译专项练习 英译汉 1. Many young researchers pursue advanced studies abroad to explore unknown academic fields. ______________________________________________________________________________________________________ 2. Scientists try to combine creative ideas with rigorous experiments to crack hard problems. ______________________________________________________________________________________________________ 3. This long-standing puzzle has baffled specialists for nearly one hundred years. ______________________________________________________________________________________________________ 4. True persistence and curiosity can always push young scholars forward in scientific research. ______________________________________________________________________________________________________ 5. The innovative research method has drawn wide attention from the international academic community. ______________________________________________________________________________________________________ 汉译英 1. 不要轻易放弃目标，坚持终将推动你不断前行。 ______________________________________________________________________________________________________ 2. 这项重大突破立刻获得了国内外专家的广泛关注。 ______________________________________________________________________________________________________ 3. 我们应当把注意力集中在当前最重要的学习任务上。 ______________________________________________________________________________________________________ 4. 研究者需要将严谨的分析思维与创新方法结合起来攻克学术难题。 ______________________________________________________________________________________________________ 5. 无数学者多年钻研，却始终未能解开这一由来已久的难题。 ______________________________________________________________________________________________________ 英汉互译参考答案 英译汉答案 1. 许多青年研究者远赴海外深造，探索未知的学术领域。 2. 科学家努力将创新想法与严谨的实验相结合，攻克难题。 3. 这个由来已久的难题困扰专家近百年。 4. 真正的坚持与好奇心总能助力青年学者在科研道路上不断前行。 5. 这项创新的研究方法获得了国际学术界的广泛关注。 汉译英答案 1. Never give up on your goals, and persistence will push you forward eventually. 2. This breakthrough immediately drew wide attention from experts at home and abroad. 3. We ought to focus our attention on the most important learning tasks at present. 4. Researchers need to combine rigorous analytical thinking with innovative methods to crack academic problems. 5. Numerous scholars have studied for years but failed to solve this long-standing puzzle. 学科网（北京）股份有限公司 $