内容概述
传说柏拉图出生那年（或前后），雅典发生瘟疫。为求消灾，雅典人派代表到得洛斯岛阿波罗神殿祈求神谕。神谕说须把阿波罗像前的立方体祭坛体积扩大一倍。雅典人把祭坛边长都扩大一倍，结果体积变成原来的 8 倍，瘟疫并未平息。由此引出著名的“倍立方”几何问题：确定立方体的边，使其体积为已知立方体的 2 倍。这个问题被称为“得洛斯人问题”，后来传到柏拉图和几何学家手中，柏拉图学院、欧多克斯、梅内赫莫斯等都曾研究过它。
中文正文
柏拉图出生那年（或那年前后），雅典发生瘟疫，大多数人都死了。也许是灾难的刻骨铭心，才生出一个著名的古希腊数学难题。据说，一个公民代表来到得洛斯岛的阿波罗神殿，祈求逃避瘟疫的良方。神谕阿波罗像前的立方体祭坛须扩大一倍。于是，雅典人奉命把祭坛的边长都扩大一倍，可瘟疫没有平息下来。人们回到神殿，询问失败的原因。神告诉他们，他们没有执行神的命令；他们没把祭坛加倍，却让它成了原先的 8 倍。这就引出一个几何问题：确定立方体的边，使它的体积是原先的 2 倍。问题一直没解决，据说后来传到了柏拉图，他又把问题转给几何学家。就是这个故事流传着倍立方的问题，人们经常称它为得洛斯人（Delian）问题。不论故事的真假如何，问题是实在的，柏拉图学院研究过它，还有归在欧多克斯（Eudoxus）、梅内赫莫斯（Menaechmus）甚至柏拉图本人（可能是误传）名下的一些高等的几何解法。
英文正文
66° The Delian problem. Plato was born in, or close to, the year of the plague that killed a large portion of the population of Athens. The great impression that this catastrophe made may be the origin of a famous mathematical problem of Greek antiquity. There is a report that a delegation was sent to the oracle of Apollo on the island of Delos to inquire how the plague might be averted. The oracle replied that the cubical altar to Apollo must be doubled in size. The Athenians accordingly doubled the dimensions of the altar, but the plague did not subside. Returning to the oracle for an explanation of the failure, the Athenians were informed that they had not carried out the orders; they had not doubled the size of the altar, but had increased it to eight times its original size. Thus arose the geometry problem: to find the edge of a cube whose volume shall be exactly twice the volume of a given cube. The problem remained refractory and in time was reputedly taken to Plato, who submitted it to the geometers. It is this story that has led the problem of duplicating a cube frequently to be referred to as the Delian problem. Whether the story is true or not, the problem was studied in Plato's Academy, and there are higher geometry solutions attributed to Eudoxus, to Menaechmus, and even (though probably erroneously) to Plato himself.
英语学习拓展
常用词汇
plague音标/pleɪɡ/
瘟疫。
原文用法：the plague that killed a large portion of the population
delegation音标/ˌdelɪˈɡeɪʃn/
代表团。
原文用法：a delegation was sent to the oracle
oracle音标/ˈɒrəkl/
神谕；神使。
原文用法：the oracle of Apollo
altar音标/ˈɔːltə(r)/
祭坛。
原文用法：the cubical altar to Apollo
cubical音标/ˈkjuːbɪkl/
立方体的。
原文用法：the cubical altar to Apollo
accordingly音标/əˈkɔːdɪŋli/
相应地；于是。
原文用法：The Athenians accordingly doubled the dimensions
subside音标/səbˈsaɪd/
平息；减退。
原文用法：the plague did not subside
refractory音标/rɪˈfræktəri/
难处理的；顽固的。
原文用法：The problem remained refractory
reputedly音标/rɪˈpjuːtɪdli/
据说；据传闻。
原文用法：was reputedly taken to Plato
duplicating音标/ˈdjuːplɪkeɪtɪŋ/
使加倍；复制。
原文用法：the problem of duplicating a cube
同义词与近义词
对应核心词汇：plague
对应核心词汇：plague。
辨析：plague 可指具体的历史瘟疫（如黑死病），epidemic 是更通用的“流行病”。
对应核心词汇：duplicating
对应核心词汇：duplicating。
辨析：doubling 更口语化，duplicating 在数学与正式语境中更常用，文中指“使体积加倍”。
常用短语与固定搭配
- a large portion of：大部分。原文用法：a large portion of the population of Athens
- be sent to：被派往。原文用法：a delegation was sent to the oracle
- double in size：体积/大小加倍。原文用法：must be doubled in size
- carry out：执行。原文用法：they had not carried out the orders
- eight times its original size：原来的 8 倍。原文用法：increased it to eight times its original size
- be referred to as：被称为。原文用法：to be referred to as the Delian problem
常用句式
- Thus arose the ... problem: ...：于是产生了……问题：……。原文例句：Thus arose the geometry problem: to find the edge of a cube whose volume shall be exactly twice the volume of a given cube.
- It is ... that ...：强调句。原文例句：It is this story that has led the problem of duplicating a cube frequently to be referred to as the Delian problem.
长难句解析
Returning to the oracle for an explanation of the failure, the Athenians were informed that they had not carried out the orders; they had not doubled the size of the altar, but had increased it to eight times its original size.
- 主干：the Athenians were informed that ...。
- 修饰与从句：Returning to the oracle for an explanation of the failure 为现在分词短语作时间/原因状语；that 引导宾语从句，说明被告知的内容；分号后两个并列分句 they had not doubled ... but had increased ... 进一步解释未执行命令的原因。
- 逻辑关系：先说明雅典人返回神殿询问失败原因，再转述神谕指出他们并未真正将祭坛加倍，而是扩大到 8 倍。
语言使用特点
- 故事叙述中多次使用被动语态（was sent, were informed, was studied），保持客观叙述；reputedly、probably erroneously 等副词体现对传说真实性的谨慎态度。
迁移练习
- 用英文写出倍立方问题的数学表述：已知立方体边长为 a，求新边长 x，使新体积为原体积的两倍。
- 用 It is ... that ... 强调句改写：This story led to the name “Delian problem.”
点击展开参考答案
- Given a cube of edge a, find x such that x³ = 2a³, i.e., x = ³√2 · a.
- It is this story that led to the name “Delian problem.”