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C 跨学科·数学
体裁: 说明文
主题: 科普知识
难度: ★★★★★
建议用时: 8 min
正确率: /4
The Pythagorean theorem is a big maths idea. It tells us that in a right triangle(直角三角形), the square of the longest side is equal(相等) to the sum of the squares of the other two sides. In school, it allows students to work out the length of the third side of a right triangle when the other two are known. In real life, it helps planes find the shortest way to fly. People who design buildings use this maths idea too.
When this idea first appeared, many mathematicians tried to show it was true in different ways, and there are about 370 different ways to do this. In 1927, a mathematician named Elisha Loomis said that proving(证明) this with trigonometry(三角学) was impossible. His reason was that you can't prove an idea is true by using the idea itself. However, a mathematician named Jason Zimba first proved it successfully in 2009. Three years ago, two high school students, Ne'Kiya Jackson and Calcea Johnson, also found a way to prove the Pythagorean theorem based on trigonometry.
In March 2023, the two showed their work at a maths meeting. Publishing their findings was challenging, and they had to learn new skills. Encouraged by Zimba's proof, they developed more proofs. One of them includes filling a large triangle with smaller triangles and using maths to find side lengths. This amazed other mathematicians. Jackson and Johnson also left five proofs for others to explore, which gives a starting point for more research(研究). Their journey shows that exploring maths is timeless and exciting, and the new way of thinking encourages more young mathematicians to be creative and challenge the norm.
1. 新趋势·学科融合 Which of the following calculations follows the Pythagorean theorem?
►► 学科融合题解题策略见 P44 重点精讲
A. If a＝1，b＝1，then c＝2
B. If a＝2，b＝3，then c＝5
C. If a＝4，b＝6，then c＝20
D. If a＝5，b＝12，then c＝13
2. Why was it thought to be impossible to prove the Pythagorean theorem with trigonometry?
A. The theorem doesn't work with trigonometry.
B. Trigonometry is only for working out triangles.
C. Mathematicians didn't know much about triangles.
D. Someone thought you can't use the same idea to prove itself.
3. What does the underlined word “This” in Paragraph 3 refer to?
A. Developing more proofs.
B. Publishing their findings.
C. Using maths to find side lengths.
D. Filling a small triangle with larger triangles.
4. What's the writer's purpose(目的) of writing the passage?
A. To encourage students to explore maths.
B. To tell a story about two students who like maths.
C. To advise people to do more research on triangles.
D. To show the Pythagorean theorem is difficult to prove.
D
体裁: 说明文
主题: 科普知识
难度: ★★★★★
建议用时: 8 min
正确率: /4
The Pythagorean theorem is a big maths idea. It tells us that in a right triangle(直角三角形), the square of the longest side is equal(相等) to the sum of the squares of the other two sides. In school, it allows students to work out the length of the third side of a right triangle when the other two are known. In real life, it helps planes find the shortest way to fly. People who design buildings use this maths idea too.
When this idea first appeared, many mathematicians tried to show it was true in different ways, and there are about 370 different ways to do this. In 1927, a mathematician named Elisha Loomis said that proving(证明) this with trigonometry(三角学) was impossible. His reason was that you can't prove an idea is true by using the idea itself. However, a mathematician named Jason Zimba first proved it successfully in 2009. Three years ago, two high school students, Ne'Kiya Jackson and Calcea Johnson, also found a way to prove the Pythagorean theorem based on trigonometry.
In March 2023, the two showed their work at a maths meeting. Publishing their findings was challenging, and they had to learn new skills. Encouraged by Zimba's proof, they developed more proofs. One of them includes filling a large triangle with smaller triangles and using maths to find side lengths. This amazed other mathematicians. Jackson and Johnson also left five proofs for others to explore, which gives a starting point for more research(研究). Their journey shows that exploring maths is timeless and exciting, and the new way of thinking encourages more young mathematicians to be creative and challenge the norm.
1. 新趋势·学科融合 Which of the following calculations follows the Pythagorean theorem?
►► 学科融合题解题策略见 P44 重点精讲
A. If a＝1，b＝1，then c＝2
B. If a＝2，b＝3，then c＝5
C. If a＝4，b＝6，then c＝20
D. If a＝5，b＝12，then c＝13
2. Why was it thought to be impossible to prove the Pythagorean theorem with trigonometry?
A. The theorem doesn't work with trigonometry.
B. Trigonometry is only for working out triangles.
C. Mathematicians didn't know much about triangles.
D. Someone thought you can't use the same idea to prove itself.
3. What does the underlined word “This” in Paragraph 3 refer to?
A. Developing more proofs.
B. Publishing their findings.
C. Using maths to find side lengths.
D. Filling a small triangle with larger triangles.
4. What's the writer's purpose(目的) of writing the passage?
A. To encourage students to explore maths.
B. To tell a story about two students who like maths.
C. To advise people to do more research on triangles.
D. To show the Pythagorean theorem is difficult to prove.
D
答案
C
【语篇解读】本文是一篇说明文。文章主要介绍了毕达哥拉斯定理的应用和证明历程等。
1. D 推理判断题。根据第一段“It tells us that in a right triangle, the square of the longest side is equal to the sum of the squares of the other two sides.”可知毕达哥拉斯定理指直角三角形最长边的平方等于其他两边的平方和。故选 D。
2. D 细节理解题。根据第二段“His reason was that you can't prove an idea is true by using the idea itself.”可知路明思认为不能用理论本身来证明这个理论。故选 D。
3. A 代词指代题。根据上文“Encouraged by Zimba's proof, they developed more proofs. One of them includes filling a large triangle with smaller triangles and using maths to find side lengths.”可知两名高中生更多的证明让其他数学家惊讶，此处 This 指代上文“they developed more proofs”。故选 A。
4. A 推理判断题。结合文章内容，尤其是最后一段“Their journey shows that exploring maths is timeless and exciting, and the new way of thinking encourages more young mathematicians to be creative and challenge the norm.”可知，本文主要介绍了毕达哥拉斯定理的应用和证明历程等，探索毕达哥拉斯定理鼓励更多年轻数学家创新和挑战常规，由此可知本文的目的是鼓励学生探索数学。故选 A。
【语篇解读】本文是一篇说明文。文章主要介绍了毕达哥拉斯定理的应用和证明历程等。
1. D 推理判断题。根据第一段“It tells us that in a right triangle, the square of the longest side is equal to the sum of the squares of the other two sides.”可知毕达哥拉斯定理指直角三角形最长边的平方等于其他两边的平方和。故选 D。
2. D 细节理解题。根据第二段“His reason was that you can't prove an idea is true by using the idea itself.”可知路明思认为不能用理论本身来证明这个理论。故选 D。
3. A 代词指代题。根据上文“Encouraged by Zimba's proof, they developed more proofs. One of them includes filling a large triangle with smaller triangles and using maths to find side lengths.”可知两名高中生更多的证明让其他数学家惊讶，此处 This 指代上文“they developed more proofs”。故选 A。
4. A 推理判断题。结合文章内容，尤其是最后一段“Their journey shows that exploring maths is timeless and exciting, and the new way of thinking encourages more young mathematicians to be creative and challenge the norm.”可知，本文主要介绍了毕达哥拉斯定理的应用和证明历程等，探索毕达哥拉斯定理鼓励更多年轻数学家创新和挑战常规，由此可知本文的目的是鼓励学生探索数学。故选 A。
解析
【分析】
本题是跨学科英语说明文阅读题，结合数学的毕达哥拉斯定理设置4道题，分别考查对定理的理解、细节查找、代词指代及主旨归纳。解题时，第1题需紧扣毕达哥拉斯定理公式逐一验证选项；第2题需定位原文关于三角学证明不可能的原因；第3题遵循代词就近指代原则找前文核心内容；第4题结合最后一段主旨句判断作者意图。
【解析】
1. 根据第一段毕达哥拉斯定理定义：直角三角形最长边（斜边）的平方等于另外两条边的平方和。逐一验证选项：
A选项：1²+1²=2≠2²=4，不符合；
B选项：2²+3²=13≠5²=25，不符合；
C选项：4²+6²=52≠20²=400，不符合；
D选项：5²+12²=25+144=169=13²，符合，故选D。
2. 定位第二段关键句“His reason was that you can't prove an idea is true by using the idea itself”，可知认为用三角学证明不可能的原因是不能用理论本身证明自身，对应选项D，故选D。
3. 代词指代遵循就近原则，第三段划线词This的前文提到“they developed more proofs”，因此This指代“developed more proofs”，对应选项A，故选A。
4. 结合最后一段主旨句“the new way of thinking encourages more young mathematicians to be creative and challenge the norm”，可知作者目的是鼓励学生探索数学，对应选项A，故选A。
【答案】
1.D 2.D 3.A 4.A
【知识点】
英语阅读理解、细节理解、代词指代、主旨大意
【点评】
本题为跨学科阅读题，融合数学知识考查英语综合能力，涵盖多种阅读题型，需学生结合原文信息与数学定理分析，难度适中，能有效考查学生的阅读理解与知识融合能力。
【难度系数】
0.6
本题是跨学科英语说明文阅读题，结合数学的毕达哥拉斯定理设置4道题，分别考查对定理的理解、细节查找、代词指代及主旨归纳。解题时，第1题需紧扣毕达哥拉斯定理公式逐一验证选项；第2题需定位原文关于三角学证明不可能的原因；第3题遵循代词就近指代原则找前文核心内容；第4题结合最后一段主旨句判断作者意图。
【解析】
1. 根据第一段毕达哥拉斯定理定义：直角三角形最长边（斜边）的平方等于另外两条边的平方和。逐一验证选项：
A选项：1²+1²=2≠2²=4，不符合；
B选项：2²+3²=13≠5²=25，不符合；
C选项：4²+6²=52≠20²=400，不符合；
D选项：5²+12²=25+144=169=13²，符合，故选D。
2. 定位第二段关键句“His reason was that you can't prove an idea is true by using the idea itself”，可知认为用三角学证明不可能的原因是不能用理论本身证明自身，对应选项D，故选D。
3. 代词指代遵循就近原则，第三段划线词This的前文提到“they developed more proofs”，因此This指代“developed more proofs”，对应选项A，故选A。
4. 结合最后一段主旨句“the new way of thinking encourages more young mathematicians to be creative and challenge the norm”，可知作者目的是鼓励学生探索数学，对应选项A，故选A。
【答案】
1.D 2.D 3.A 4.A
【知识点】
英语阅读理解、细节理解、代词指代、主旨大意
【点评】
本题为跨学科阅读题，融合数学知识考查英语综合能力，涵盖多种阅读题型，需学生结合原文信息与数学定理分析，难度适中，能有效考查学生的阅读理解与知识融合能力。
【难度系数】
0.6
