内容概述
本文探讨圆周被划分为 360° 这一惯例的起源,将其归功于古巴比伦人。文章依次介绍了三种主要解释:(1)巴比伦人认为一年为 360 天的假说(现已证伪);(2)基于几何事实——圆半径恰可在圆周内排满六根弦——结合六十进制将每根弦的中心角分为 60 等份;(3)学者 Otto Neugebauer 提出的"巴比伦里"时间单位说:一天等于 12 个"时间-里",每个"巴比伦里"再细分为 30 等份,最终得 (12)(30) = 360。
中文正文
18° 角度
今天我们把圆周分为 360°,无疑也该感谢古巴比伦人。为什么选择 360 这个数字呢,人们提出了几种不同的解释。
如果假定古巴比伦人相信一年是 360 天,那他们会自然地把圆划分为 360 个部分,让每个部分代表他们想象的太阳绕着地球走一天的距离。这个解释在今天很值得怀疑,因为我们有证据说明巴比伦人很清楚一年不止 360 天。
当然,巴比伦人也很可能熟悉下面的几何事实:拿圆半径做弦,正好可以在圆周内排满 6 根。于是,在 60 进制的基础上,他们自然想着把每根弦的中心角分为 60 个相等的部分,结果,整个圆也就等分为 360 个部分了。
大学者 O·纽格鲍尔,也是研究古巴比伦数学和天文学的权威,也提出一种有趣的解释。在苏美尔人的时代,有一个很大的距离单位,就像巴比里那样,大约等于今天的 7 英里。巴比伦里用来度量较长的距离,因此自然也可能成为一个时间单位,即走过 1 巴比伦里所需要的时间。后来,大约公元前 1000 年的时候,巴比伦天文学达到了空前的阶段,有了系统的天象记录,那个"巴比伦时间里"就用来度量时间的长度。他们发现,一整天等于 12"里",而一整天也等于天空旋转一周,所以一个圆周被分成 12 个相等的部分。不过,为方便起见,巴比伦里又被划分为 30 个相等的部分。这样,圆周就等分为(12)(30) = 360 个部分了。
英文正文
18° The angular degree. We undoubtedly owe to the ancient Babylonians our present division of the circumference of a circle into 360 equal parts. Several explanations have been put forward to account for the choice of this number.
Thus it has been supposed that the early Babylonians reckoned a year as 360 days, and that this naturally led to the division of the circle into 360 equal parts, each part representing the daily amount of the supposed yearly revolution of the sun about the earth. Today this explanation is discredited, since we now have evidence that the Babylonians very early knew that the year possesses more than 360 days.
Again, the early Babylonians were very likely familiar with the geometric fact that the radius of a circle can be applied exactly six times to its circumference as a chord. Then, having adopted sexagesimal division, it was natural to divide the central angles of these chords into 60 equal parts, resulting in the division of the entire circle into 360 equal parts.
Otto Neugebauer, the great scholar and authority on early Babylonian mathematics and astronomy, has proposed an interesting alternative explanation. In early Sumerian times there existed a large distance unit, a sort of Babylonian mile, equal to about seven of our miles. Since the Babylonian mile was used for measuring longer distances, it was natural that it should also become a time unit, namely the time required to travel a Babylonian mile. Later, sometime in the first millennium b.c., when Babylonian astronomy reached the stage in which systematic records of celestial phenomena were kept, the Babylonian time-mile was adopted for measuring spans of time. Since a complete day was found to be equal to 12 time-miles, and one complete day is equivalent to one revolution of the sky, a complete circuit was divided into 12 equal parts. But, for convenience, the Babylonian mile had been subdivided into 30 equal parts. We thus arrive at (12)(30) = 360 equal parts in a complete circuit.
英语学习拓展
常用词汇
undoubtedly音标/ʌnˈdaʊtɪdli/
毫无疑问地。
原文用法:"We undoubtedly owe to the ancient Babylonians our present division..."
circumference音标/səˈkʌmfərəns/
圆周。
原文用法:"...division of the circumference of a circle into 360 equal parts."
explanation音标/ˌekspləˈneɪʃn/
解释。
原文用法:"Several explanations have been put forward to account for the choice of this number."
reckon音标/ˈrekən/
认为,估算。
原文用法:"...the early Babylonians reckoned a year as 360 days..."
discredit音标/dɪsˈkrɛdɪt/
使……不可信;驳斥。
原文用法:"Today this explanation is discredited, since we now have evidence..."
chord音标/kɔːrd/
弦(几何)。
原文用法:"...the radius of a circle can be applied exactly six times to its circumference as a chord."
sexagesimal音标/ˌsɛksəˈdʒɛzɪməl/
六十进制的。
原文用法:"Then, having adopted sexagesimal division, it was natural to divide..."
authority音标/əˈθɔːrəti/
权威;专家。
原文用法:"Otto Neugebauer, the great scholar and authority on early Babylonian mathematics..."
alternative音标/ɔːlˈtɜːrnətɪv/
替代的;另一种的。
原文用法:"...has proposed an interesting alternative explanation."
millennium音标/mɪˈlɛniəm/
千年。
原文用法:"Later, sometime in the first millennium b.c...."
celestial音标/səˈlɛstʃl/
天的,天上的。
原文用法:"...systematic records of celestial phenomena were kept..."
circuit音标/ˈsɜːrkɪt/
一圈,环行。
原文用法:"a complete circuit was divided into 12 equal parts."
同义词与近义词
对应核心词汇:undoubtedly
对应核心词汇:undoubtedly。
辨析:三者均为"毫无疑问地",undoubtedly 最常用;unquestionably 语气稍强;indubitable 较正式,多用于书面语。
对应核心词汇:explanation
对应核心词汇:explanation。
辨析:explanation 侧重"说明原因";interpretation 侧重"解读意义";account 侧重"叙述经过"(原文中 "account for" 意为"解释")。
对应核心词汇:discredit
对应核心词汇:discredit。
辨析:discredit 指"使失去可信度";refute 指"用证据反驳";debunk 指"揭穿(谬误)",语气更强。
常用短语与固定搭配
- put forward:提出(观点、理论等)。原文用法:"Several explanations have been put forward to account for the choice of this number."
- account for:解释,说明(原因)。原文用法:"...to account for the choice of this number."
- lead to:导致,引起。原文用法:"...this naturally led to the division of the circle into 360 equal parts."
- apply ... to ...:把……应用于……。原文用法:"...the radius of a circle can be applied exactly six times to its circumference as a chord."
- result in:导致,结果是。原文用法:"...resulting in the division of the entire circle into 360 equal parts."
- subdivide into:再细分为。原文用法:"...the Babylonian mile had been subdivided into 30 equal parts."
- arrive at:得出(结论、数字等)。原文用法:"We thus arrive at (12)(30) = 360 equal parts..."
常用句式
- It has been supposed that...:人们曾经假定……(表达已不被认可的旧观点)。原文例句:"Thus it has been supposed that the early Babylonians reckoned a year as 360 days..."
- Since we now have evidence that..., ...:既然我们现在有证据表明……,那么……(证据驱动的论证句式)。原文例句:"Today this explanation is discredited, since we now have evidence that the Babylonians very early knew that the year possesses more than 360 days."
- It was natural that...:……是自然的/合乎情理的(基于前文条件推断合理性)。原文例句:"Then, having adopted sexagesimal division, it was natural to divide the central angles of these chords into 60 equal parts..."
长难句解析
"Later, sometime in the first millennium b.c., when Babylonian astronomy reached the stage in which systematic records of celestial phenomena were kept, the Babylonian time-mile was adopted for measuring spans of time."
- 主干:the Babylonian time-mile was adopted(巴比伦时间-里被采用)
- 修饰与从句:
- "Later, sometime in the first millennium b.c." —— 时间状语 - "when Babylonian astronomy reached the stage..." —— 非限制性定语从句,修饰整个时间背景 - "in which systematic records of celestial phenomena were kept" —— 定语从句,修饰 "the stage" - "for measuring spans of time" —— 目的状语,说明 adopt 的用途
- 逻辑关系:时间背景(when...)→ 条件成熟 → 结果(time-mile 被采用为时间度量单位)
"Since a complete day was found to be equal to 12 time-miles, and one complete day is equivalent to one revolution of the sky, a complete circuit was divided into 12 equal parts."
- 主干:a complete circuit was divided into 12 equal parts(一个完整的圆周被分为 12 等份)
- 修饰与从句:
- "Since a complete day was found to be equal to 12 time-miles," —— 原因状语从句 1 - "and one complete day is equivalent to one revolution of the sky," —— 并列的原因状语从句 2
- 逻辑关系:原因(Since A and B)→ 结论(因此 C),典型的因果论证结构。
语言使用特点
- 本文属于学术性说明文(academic expository prose),语气客观、审慎,频繁使用被动语态("has been put forward", "was found to be", "had been subdivided")来弱化施动者、突出事实本身。
- 使用形式主语 It 结构("it has been supposed that", "it was natural to")使句子平衡、正式。
- 逻辑衔接词丰富:Thus(承接推论)、Again(引入下一假说)、But(转折)、Since(原因)、Later(时间推进)。
迁移练习
- 用 put forward 和 account for 各写一句话,解释一个你熟悉的数学概念(如"为什么 π ≈ 3.14159...")。
- 将以下中文翻译成英文,尽量使用本文出现的句式:"有人曾认为地球是宇宙的中心,但后来的天文观测证据驳斥了这一观点。"
- 根据 Neugebauer 的解释,补全以下推理链:1 天 = [ ? ] 时间-里 → 1 时间-里 = [ ? ] 等份 → 1 圆周 = [ ? ] 等份。
点击展开参考答案
- (示例)A theory was put forward by ancient Greeks to account for why the ratio of circumference to diameter is constant for all circles.
- (示例)It was once supposed that the Earth was the center of the universe, but later astronomical observations discredited this view.
- 1 天 = 12 时间-里 → 1 时间-里 = 30 等份 → 1 圆周 = 360 等份。