内容概述
本篇讲述古印度数学家将算术问题以诗歌形式呈现的传统。由于学生课本为便于记忆多以韵文编写，加之这类问题常被用作社交娱乐中的谜题，印度数学家（如婆什迦罗 Bhāskara、马哈维拉 Mahāvīra）习惯以充满诗意的语言包装数学问题——蜜蜂与荷花、森林与旅人、香蕉与游客。婆罗摩笈多（Brahmagupta）对此评论道：这些问题纯为娱乐而设，能提出并解决问题的人犹如太阳令群星黯然失色。此外，文中还介绍了印度古代独特的"位值符号系统"：用联想事物（月亮代表1、吠陀代表4等）表示数字，使同一数值可用多种方式编码，从而催生了大量以诗歌形式记载的算术法则与科学常数。
中文正文
97° 印度人的诗化数学
印度人喜欢给数学问题披上诗歌的外衣。这部分是因为学生的课文为了方便记忆都写成诗歌的形式，而更重要的是，这些问题被经常拿来做猜谜游戏。我们来看两个例子。一个来自巴什迦罗（约1150年），一个来自马哈维拉（Mahavira）。
一群嗡嗡的蜜蜂，一半的方根落在茉莉花丛，8/9 落在身后；还有一只雌蜂，徘徊在雄蜂的身旁，他昨夜醉卧在荷花的芬芳。迷人的姑娘，告诉我蜜蜂的数量。
明媚清新的森林，花果压弯了树枝，蒲桃、茉莉、大蕉、棕榈、菠萝蜜、海枣、扇椰子、芒果——四季鸟语，百啭千声，杜鹃、鹦鹉争春，蜜蜂沉醉花丛——一群疲惫的游客来到丛林。他们采下63堆香蕉，每堆数量一样，又添加7只相同的水果，恰好均分给23个游客，不少也不多。请你告诉我，一堆香蕉有几个？
婆罗摩笈多在谈这些题目时说："这些问题是纯为娱乐提出的，聪明人可以找出千百个问题，也可以根据这里给出的法则解决别人的问题。犹如太阳的光芒令群星黯然失色，有知识的人，能提出问题、特别能解决问题的人，也将卓尔不群，压倒众人。"
有趣的是印度人早年用过的"位值符号系统"，即数字通过联想的事物来表示。例如，数字1可能牵连着月亮、梵天（Brahma）、造物主或仪式式；而4可能是《吠陀》（因为此书分为4卷）或海洋。我们来看一个例子，它来自5世纪初无名氏的一本天文学著作《太阳系》（Surya Siddhanta）。数1577917828从右向左表示为婆苏（Vasu，8个神的统称¹），2，8，山（7个山系），仪式，数字（9个数字），7，山，半月（15天）。这样一来，同一个数就可能用许多不同的方法来表示，从而大大激发了描写算术法则和科学常数的诗歌，让那些法则和常数更好流传。
英文正文
97° Hindu embroidery. The Hindus often clothed their arithmetic problems in poetic garb. This was partly because school texts were, for purposes of memorization, written in verse, but particularly because the problems were so frequently propounded as puzzles for sheer social amusement. As a couple of examples, consider the following; the first is adapted from Bhaskara (ca. 1150) and the second from Mahavira(ca. 850).
The square root of half the number of bees in a swarm has flown out upon a jasmine bush, ⅔ of the swarm has remained behind; one female bee flies about a male that is buzzing within a lotus flower into which he was allured in the night by its sweet odor, but now imprisoned in it. Tell me, most enchanting lady, the number of bees.
Into the bright and refreshing outskirts of a forest, which were full of numerous trees with their branches bent down with the weight of flowers and fruits, trees such as jambu trees, lime trees, plantains, areca palms, jack trees, date palms, hintala trees, palmyras, punnage trees, and mango trees—outskirts, the various quarters whereof were filled with many sounds of crowds of parrots and cuckoos found near springs containing lotuses with bees roaming about them—into such forest outskirts a number of weary travelers entered with joy. There were 63 numerically equal heaps of plantain fruits put together and combined with 7 more of those same fruits, and these were equally distributed among 23 travelers so as to have no remainder. You tell me now the numerical measure of a heap of plantains.
Brahmagupta, in connection with his problem offerings, says: "These problems are proposed simply for pleasure; the wise man can invent a thousand others, or he can solve the problems of others by the rules given here. As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of
英语学习拓展
常用词汇
cloth音标/kləʊθ/
给……穿上衣服；覆盖。
原文用法："clothed their arithmetic problems in poetic garb"
propound音标/prəˈpaʊnd/
提出（理论、问题等）；正式提议。
原文用法："problems were so frequently propounded as puzzles"
swarm音标/swɔːrm/
一大群（尤指昆虫）；蜂群。
原文用法："the number of bees in a swarm"
allure音标/əˈljʊər/
诱惑；吸引。
原文用法："allured in the night by its sweet odor"
imprison音标/ɪmˈprɪzn/
囚禁；禁锢。
原文用法："now imprisoned in it"
outskirts音标/ˈaʊtskɜːrts/
郊区；边缘地带。
原文用法："the bright and refreshing outskirts of a forest"
weary音标/ˈwɪəri/
疲倦的；疲劳的。
原文用法："a number of weary travelers entered with joy"
brilliancy音标/ˈbrɪliənsi/
光辉；璀璨。
原文用法："As the sun eclipses the stars by his brilliancy"
同义词与近义词
对应核心词汇：cloth
对应核心词汇：cloth。
辨析：clothe 为 cloth 的动词化形式，意为"给…穿衣、覆盖"，近义 dress、cover；文中 "clothed... in poetic garb" 以拟人手法将诗歌比作外衣。
对应核心词汇：propound
对应核心词汇：propound。
辨析：propound 较 propose 更正式，强调"郑重提出供思考"，文中用于"提出谜题"。
对应核心词汇：allure
对应核心词汇：allure。
辨析：allure 兼具"吸引"与"诱惑"义，文学色彩浓；lure 偏贬义诱陷阱，文中指花香引诱蜜蜂。
对应核心词汇：imprison
对应核心词汇：imprison。
辨析：imprison 本义"囚禁"，文中喻指雄蜂被困于荷花中，与 trap 近义但更具文学张力。
对应核心词汇：outskirts
对应核心词汇：outskirts。
辨析：outskirts 指城市或森林的"边缘地带"，常以复数出现，近义 fringe、periphery。
对应核心词汇：weary
对应核心词汇：weary。
辨析：weary 强调因长途跋涉而"疲倦"，比 tired 更具书面与诗意色彩。
常用短语与固定搭配
- in poetic garb：以诗歌形式包装……，文中 "clothed their arithmetic problems in poetic garb" 指用诗歌形式包装算术题。
- as puzzles：把……作为谜题提出，文中 "propounded as puzzles for sheer social amusement" 指作为社交娱乐的谜题提出。
- remain behind：留下、留在原处，文中 "⅔ of the swarm has remained behind" 表示剩余未飞走的蜂群。
- for purposes of memorization：为了记忆的目的，文中说明课本写成韵文便于记诵。
- equally distributed among ...：在…之间平均分配，文中指 63 堆香蕉加 7 只后均分给 23 名旅人。
- so as to have no remainder：以至于没有余数，强调整除关系，对应中文"不少也不多"。
常用句式
- Pattern "This was partly because..., but particularly because..."：先让步后强调的原因分层结构，用于区分诗化数学的两层动因（课本记诵 vs. 社交娱乐）。
- Pattern "As A..., so B..."：as..., so... 明喻结构，文中 "As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others" 喻指智者出众。
长难句解析
句子 1（香蕉问题，超长复杂句）：
"Into the bright and refreshing outskirts of a forest, which were full of numerous trees with their branches bent down with the weight of flowers and fruits, trees such as jambu trees, lime trees, plantains, areca palms, jack trees, date palms, hintala trees, palmyras, punnage trees, and mango trees—outskirts, the various quarters whereof were filled with many sounds of crowds of parrots and cuckoos found near springs containing lotuses with bees roaming about them—into such forest outskirts a number of weary travelers entered with joy."
结构拆解：
- 主句主干：a number of weary travelers entered [into such forest outskirts] with joy.
- 第一层插入（which 引导的非限制性定语从句）：修饰 outskirts，描述森林中树木的种类和状态
- 第二层插入（破折号之间的同位语）：进一步 outskirts 的各个角落（quarters）的景象
- 修辞效果：通过层层嵌套的环境描写，营造出"柳暗花明又一村"式的沉浸感，使读者仿佛身临其境后再引出数学问题。
句子 2（Brahmagupta 引用中的排比）：
"As the sun eclipses the stars by his brilliancy, so the man of knowledge will eclipse the fame of others..."
这是一个 as..., so... 结构的明喻（simile），意为"正如……同样也……"。其中 eclipse 作动词，意为"使……黯然失色"。
语言使用特点
- 正式但富于文学性（formal yet literary）：使用 propounded、allured、imprisoned、outskirts 等较高级词汇，同时保持叙述的流畅性。
- 精确的数学措辞：numerically equal heaps、equally distributed、no remainder 等表达严谨而不失优雅。
- 文化词汇的保留：梵语人名（Bhaskara、Mahavira、Brahmagupta）和植物名（jambu、plantain、palmyra、punnage）保留原貌，体现学术写作的文化尊重态度。
迁移练习
- 用英语复述蜜蜂问题的数量关系（√(x/2) + 2x/3 + 2 = x），并说明为何 x 只能取正整数解。
- 模仿文中 "clothed ... in poetic garb" 的隐喻，用一句话把你熟悉的一个数学公式"诗意化"。
- 将 "As the sun eclipses the stars by his brilliancy, so ..." 句式改写成一句描写"数学之美压过繁复计算"的句子。
点击展开参考答案
- 关系式为 √(x/2) + (2/3)x + 2 = x；因蜜蜂数量只能为整数且根号项须非负，检验增根后得 x = 24（若按中文 8/9 版本则为 x = 72）。
- 示例：Euler clothed his identity e^{iπ}+1=0 in the garb of pure harmony.（欧拉给他的恒等式披上了纯粹和谐的外衣。）
- 示例：As the sun eclipses the stars by his brilliancy, so the elegance of a theorem eclipses the tedium of its computation.