内容概述
人类对蜜蜂展现的"几何天才"惊叹已久。最早记录这一奇迹的是约 1600 年前活跃在亚历山大的古希腊几何学家帕普斯（Pappus）。在其名著《数学汇编》（Mathematical Collection）第五卷中，帕普斯记载了一段关于蜂房极值特性的文字：蜜蜂建造紧密相连、全等且相似的六边形蜂房，是因为它们凭"先天的几何直觉"知道——只有正三角形、正方形和正六边形这三种正多边形能无缝铺满平面，而六边形边数最多、等周条件下面积最大（即同样周长时容纳最多蜂蜜）。帕普斯认为蜜蜂选择了最优解。
中文正文
4° 机灵小蜜蜂
人们一直对蜜蜂表现的几何天才感兴趣。头一个记录这个奇迹的，是大约1600年前活跃在亚历山大城的古希腊著名几何学家帕普斯（Pappus）。在他有名的《数学汇编》（Mathematical Collection）第五卷里，我们找到下面一段关于蜂房的极值特性的文字：
[图注：蜂房的结构满足 cosθ = √3/3，即 θ ≈ 57.3°，这样表面积最小，材料最省。]
也许因为它们明白自己肩负着一个大使命，要把那样甘美的食物，从神的身边拿来，奉献给那部分多能的人类，所以它们不愿把它随意倾泻在黄土、树林或其他杂乱丑陋的东西上。它们从大地上最美丽的花朵采摘芬芳，然后，为了聚集蜂蜜，它们用那菁华构筑了我们所调的蜂房，一格紧接一格，相同的六边形，一样的大小。我们猜想，它们是凭着先天的几何感觉来设计意图的。它们一定以为只有那样的图形才能使邻近的格子紧密相连，就是说，两个格子享有共同的边界，这样才不会混入外来的东西，玷污重的纯粹。不过，有三种直边的图形能满足那要求——我说的是等角等边……
英文正文
4° The Ingenious Honey Bees. Man has long shown interest in the seeming geometrical sagacity of the honey bees. The first known man to report on this mathematical acumen was the eminent Greek geometer Pappus, who flourished in Alexandria some sixteen hundred years ago. In Book V of his famous Mathematical Collection we find the following passage concerning the extremum properties of the cells of the bees' honeycombs:
Presumably because they know themselves to be entrusted with the task of bringing from the gods to the accomplished portion of mankind a share of ambrosia in this form, they do not think it proper to pour it carelessly on ground or wood, or any other ugly or irregular material; but first collecting the sweets of the most beautiful flowers which grow upon the earth, they make from them for the reception of the honey, the vessels which we call honeycombs (with cells) all equal and similar, and contiguous to one another, and hexagonal in form. And that they have contrived this by virtue of a certain geometrical forethought, we may infer in this way. They would necessarily think that the figures must be such as to be contiguous to one another, that is to say, to have their sides in common in order that no foreign matter could enter into the interstices between them and so defile the purity of the produce. Now there are three rectilinear figures which are capable of fulfilling this condition, I mean regular figures which are equilateral and equiangular, for bees would have none of figures which are not uniform.... There being then three figures capable by themselves of exactly filling up the space about the same point, the bees by reason of their instinctive wisdom chose for their construction the figure which has most angles, because they conceived it would hold more honey than either of the other two.
英语学习拓展
常用词汇
sagacity音标/səˈɡæsəti/
睿智，聪颖。
原文用法："the seeming geometrical sagacity of the honey bees"
acumen音标/ˈækjʊmən/
敏锐，聪明才智。
原文用法："this mathematical acumen"
eminent音标/ˈemɪnənt/
著名的，杰出的。
原文用法："the eminent Greek geometer Pappus"
flourish音标/ˈflʌrɪʃ/
繁荣，活跃（某时期）。
原文用法："who flourished in Alexandria"
extremum音标/ɪkˈstriːməm/
（数）极值。
原文用法："the extremum properties of the cells"
presumably音标/prɪˈzjuːməbli/
大概，推测起来。
原文用法："Presumably because they know themselves..."
entrust音标/ɪnˈtrʌst/
委托，托付。
原文用法："entrusted with the task of bringing"
accomplished音标/əˈkʌmplɪʃt/
有造诣的，优秀的。
原文用法："the accomplished portion of mankind"
ambrosia音标/æmˈbrəʊziə/
（希神）仙果，美味珍馐。
原文用法："a share of ambrosia in this form"
contiguous音标/kənˈtɪɡjuəs/
相邻的，毗连的。
原文用法："and contiguous to one another"
hexagonal音标/hekˈsæɡənl/
六边形的。
原文用法："and hexagonal in form"
contrive音标/kənˈtraɪv/
设计，设法做到。
原文用法："they have contrived this"
forethought音标/ˈfɔːθɔːt/
深谋远虑，预先规划。
原文用法："by virtue of a certain geometrical forethought"
infer音标/ɪnˈfɜː(r)/
推断，推知。
原文用法："we may infer in this way"
rectilinear音标/ˌrektɪˈlɪniə(r)/
直边的，直线构成的。
原文用法："three rectilinear figures"
equilateral音标/ˌiːkwɪˈlætərəl/
等边的。
原文用法："regular figures which are equilateral and equiangular"
equiangular音标/ˌiːkwiˈæŋɡjʊlə(r)/
等角的。
原文用法同上
interstice音标/ɪnˈtɜːstɪs/
缝隙，空隙。
原文用法："enter into the interstices between them"
defile音标/dɪˈfaɪl/
弄脏，玷污。
原文用法："and so defile the purity of the produce"
instinctive音标/ɪnˈstɪŋktɪv/
本能的。
原文用法："by reason of their instinctive wisdom"
同义词与近义词
对应核心词汇：sagacity
对应核心词汇：sagacity。
辨析：sagacy 文学化，强调"深邃的洞察力"；wisdom 最通用；intelligence 强调认知能力。
对应核心词汇：acumen
对应核心词汇：acumen。
辨析：acumen 强调"在某领域的敏锐判断力"；sharpness 通用；insight 强调"深刻的理解"。
对应核心词汇：eminent
对应核心词汇：eminent。
辨析：eminent 强调"在同行中杰出"；distinguished 强调"地位尊贵"；celebrated 强调"广为人知"。
对应核心词汇：contrived。
辨析：contrive 含"精心策划"意味；devise 较中性；design 最通用。
常用短语与固定搭配
- show interest in...：对……表现出兴趣。原文用法："Man has long shown interest in the seeming geometrical sagacity"
- report on...：报告/记述……。原文用法："to report on this mathematical acumen"
- flourish in...：在……时期活跃/繁荣。原文用法："who flourished in Alexandria some sixteen hundred years ago"
- concerning...：关于……。原文用法："concerning the extremum properties of the cells"
- by virtue of...：凭借，借助。原文用法："they have contrived this by virtue of a certain geometrical forethought"
- in this way：以这种方式。原文用法："we may infer in this way"
- that is to say：也就是说，换言之。原文用法："that is to say, to have their sides in common"
- in order that...：为了使……（引导目的状语从句）。原文用法："in order that no foreign matter could enter"
- fill up the space about...：填满……周围的空间。原文用法："filling up the space about the same point"
- by reason of...：由于，因为。原文用法："the bees by reason of their instinctive wisdom"
常用句式
- The first known man to ... was ..., who ...：引入历史首创者的经典句型。原文例句："The first known man to report on this mathematical acumen was the eminent Greek geometer Pappus, who flourished in Alexandria..."
- In Book V of his famous ... we find the following passage concerning ...：学术引用的标准句式。原文例句："In Book V of his famous Mathematical Collection we find the following passage concerning the extremum properties..."
- Presumably because ..., they do not think it proper to ... but ...：复杂的因果-转折复合句，用于解释行为动机。原文例句："Presumably because they know themselves to be entrusted with..., they do not think it proper to pour it carelessly...; but first collecting..."
- I mean ...：插入语，用于澄清或补充说明术语。原文例句："there are three rectilinear figures which are capable of fulfilling this condition, I mean regular figures which are equilateral and equiangular"
- There being then ..., ... chose ... because ...：独立主格结构 + 因果复合句，用于总结性论述。原文例句："There being then three figures capable by themselves of exactly filling up the space, the bees chose for their construction the figure which has most angles, because they conceived..."
长难句解析
Presumably because they know themselves to be entrusted with the task of bringing from the gods to the accomplished portion of mankind a share of ambrosia in this form, they do not think it proper to pour it carelessly on ground or wood, or any other ugly or irregular material; but first collecting the sweets of the most beautiful flowers which grow upon the earth, they make from them for the reception of the honey, the vessels which we call honeycombs (with cells) all equal and similar, and contiguous to one another, and hexagonal in form.
- 主干：they do not think it proper to pour ... ; but ... they make ... the vessels ...
- 修饰与从句：
- "Presumably because they know themselves to be entrusted with the task of bringing from the gods to the accomplished portion of mankind a share of ambrosia in this form"（原因状语从句，嵌套不定式短语 "to be entrusted with..." 和 "of bringing..."） - "carelessly"（方式副词） - "on ground or wood, or any other ugly or irregular material"（地点/对象并列介词短语） - "first collecting the sweets of the most beautiful flowers which grow upon the earth"（现在分词短语作伴随状语，内嵌定语从句 "which grow upon the earth"） - "from them"（来源状语） - "for the reception of the honey"（目的状语） - "which we call honeycombs (with cells)"（定语从句，修饰 vessels） - "all equal and similar, and contiguous to one another, and hexagonal in form"（并列形容词短语，修饰 vessels/honeycombs）
- 逻辑关系：原因（Presumably because）+ 并列否定（do not think proper）+ 转折（but）+ 并列动作（collecting → making）+ 多重定语/形容词
There being then three figures capable by themselves of exactly filling up the space about the same point, the bees by reason of their instinctive wisdom chose for their construction the figure which has most angles, because they conceived it would hold more honey than either of the other two.
- 主干：the bees chose ... the figure ...
- 修饰与从句：
- "There being then three figures capable by themselves of exactly filling up the space about the same point"（独立主格结构，作原因状语） - "by reason of their instinctive wisdom"（原因状语） - "for their construction"（目的状语） - "which has most angles"（定语从句，修饰 figure） - "because they conceived it would hold more honey than either of the other two"（原因状语从句，内嵌比较结构 "more ... than ..."）
- 逻辑关系：独立主格（背景条件）+ 原因（by reason of）+ 选择（chose）+ 定语从句 + 原因（because）+ 比较
语言使用特点
- 英文正文包含两段文体：第一段是作者的概述（现代学术英语）；第二段是帕普斯原文的英译（古典英语风格，句子冗长、修辞丰富、从句嵌套深）。
- 帕普斯译文使用了大量拉丁源抽象名词（sagacity, acumen, extrema, ambrosia, contiguity, forethought, interstices, defile, instinctive），具有显著的早期现代英语（Early Modern English）特征。
- 中文翻译采用了典雅的半文言风格（"菁华""玷污""纯粹""先天"），与原文的古典气质相匹配。
迁移练习
- 用 The first known person to ... was ... who ... 写一句介绍某领域先驱的话。
- 用 by virtue of 写一句说明某人/物凭借什么特质取得成功。
- 将以下中文翻译成英文："蜜蜂选择的六边形不是巧合——凭借某种几何直觉，它们找到了最优解。"
- 找出帕普斯原文中所有的并列结构（至少三处），并分析其修辞效果。
点击展开参考答案
- The first known person to propose the heliocentric model was Aristarchus of Samos, who lived in the 3rd century BCE.
- She succeeded in solving the problem by virtue of her extraordinary patience and attention to detail.
- The hexagon chosen by the bees is no accident—by virtue of a certain geometric intuition, they found the optimal solution.
- 示例：
- "all equal and similar, and contiguous to one another, and hexagonal in form"（三个并列形容词短语，强调蜂房的三重优良属性） - "equilateral and equiangular"（并列词根，定义正多边形的双重属性） - "on ground or wood, or any other ugly or irregular material"（三层并列递进，强化"任何不当场所都不行"的语气）