内容概述
本故事讲述了 12 世纪印度数学家巴什迦罗（Bhaskara，约 1114—1185）给出的一种著名的毕达哥拉斯定理分割（拼图）证明。巴什迦罗只画出一幅"将斜边上的正方形分割为四个全等直角三角形加上一个边长为两直角边之差的小正方形"的图，便不再做任何文字解释，只写下一个词——"看哪！"（Behold!）。这正是代数恒等式 $c^2 = 4\!\left(\dfrac{ab}{2}\right) + (b-a)^2 = a^2 + b^2$ 的几何化身。艾夫斯还进一步设想：若把"看"做成一部动态电影（即图 17那五帧连续画面），将斜边正方形连续变换为两直角边正方形之和，便是更好的"看哪"式证明。
中文正文
96° 看哪！
中学生学几何时都见过巴什迦罗用分割的方法来证明毕达哥拉斯定理。像图 16 那样，将斜边的正方形分割为四个全等的三角形加上一个边长为两直角边之差的小正方形。这些分割的图形很容易重新组装成两个直角边的正方形之和。巴什迦罗画了图，但没做进一步的解释，只说"看哪！"当然，一点儿代数计算就能说明。令 $c$ 为斜边，$a$ 和 $b$ 为直角边，那么
c^2 = 4\!\left(\frac{ab}{2}\right) + (b-a)^2 = a^2 + b^2."看"毕达哥拉斯定理的证明，也许最好是动态的电影画面。像图 17 那样，斜边的正方形连续变换成为两个直角边的正方形。
英文正文
96° Behold!
Many students of high school geometry have seen Bhaskara's dissection proof of the Pythagorean theorem, in which the square on the hypotenuse is cut up, as indicated in Figure 16, into four triangles each congruent to the given triangle plus a square with side equal to the difference of the legs of the given triangle. The pieces are easily rearranged to give the sum of the squares on the two legs. Bhaskara drew the figure and offered no further explanation than the word 'Behold!' Of course, a little algebra supplies a proof. For, if $c$ is the hypotenuse and $a$ and $b$ are the legs of the triangle,
c^2 = 4\!\left(\tfrac{1}{2}ab\right) + (b - a)^2 = a^2 + b^2.Perhaps a better 'behold' proof of the Pythagorean theorem would be a dynamical one on movie film wherein the square on the hypotenuse is continuously transformed into the sum of the squares on the legs by passing through the stages indicated in Figure 17.
英语学习拓展
常用词汇
dissection音标/dɪˈsekʃn/
分割，切开。
原文用法：Bhaskara's dissection proof of the Pythagorean theorem
proof音标/pruːf/
证明，论证。
原文用法：a little algebra supplies a proof
congruent音标/ˈkɒŋɡruənt/
全等的。
原文用法：four triangles each congruent to the given triangle
hypotenuse音标/haɪˈpɒtənjuːz/
斜边。
原文用法：the square on the hypotenuse
rearranged音标/ˌriːəˈreɪndʒd/
重新组合。
原文用法：The pieces are easily rearranged to give the sum
algebra音标/ˈældʒɪbrə/
代数。
原文用法：a little algebra supplies a proof
continuously音标/kənˈtɪnjuəsli/
连续地。
原文用法：continuously transformed into the sum
indicated音标/ˈɪndɪkeɪtɪd/
指出，表明。
原文用法：as indicated in Figure 16
同义词与近义词
对应核心词汇：dissection
对应核心词汇：dissection。
辨析：dissection 在几何中指"分割、剖分"；原文 the square ... is cut up 即其口语化同义表达；partition 偏"划分成若干份"，学术语境中可互换使用。
对应核心词汇：proof
对应核心词汇：proof。
辨析：proof 指严格证明；demonstration 偏"演示、示范"（如 dissecting demonstration）；argument 泛指论证过程，语气较弱，不一定达到证明强度。
对应核心词汇：congruent
对应核心词汇：congruent。
辨析：congruent 专指图形"全等"（形状大小皆同）；identical 强调"完全相同"；equal 仅指数量相等，不能描述图形形状一致。
常用短语与固定搭配
- cut up：分割、切碎。原文用法：the square on the hypotenuse is cut up ... into four triangles，此处用被动语态表示"被分割成若干块"。
- the square on the hypotenuse / the square on the legs：斜边上的正方形 / 直角边上的正方形。固定几何表达，介词 on 表示"以……为边"。
- supply a proof：提供一个证明。原文 a little algebra supplies a proof，supply 此处意为"给出、提供"。
- pass through the stages：经过若干阶段。原文 passing through the stages indicated in Figure 17，描述动态变换的连续过程。
常用句式
- Pattern: [S] have seen [O]：现在完成时描述"见过某事"。原文：Many students of high school geometry have seen Bhaskara's dissection proof of the Pythagorean theorem.
- Pattern: [O] is cut up into [C]：被动语态 + into，表示"被分割为……"。原文：the square on the hypotenuse is cut up ... into four triangles each congruent to the given triangle.
长难句解析
Many students of high school geometry have seen Bhaskara's dissection proof of the Pythagorean theorem, in which the square on the hypotenuse is cut up, as indicated in Figure 16, into four triangles each congruent to the given triangle plus a square with side equal to the difference of the legs of the given triangle.
- 主干：Many students of high school geometry have seen Bhaskara's dissection proof of the Pythagorean theorem. - 修饰与从句：in which 引导非限制性定语从句说明 proof；as indicated in Figure 16 为插入状语；each congruent to the given triangle 与 with side equal to the difference of the legs 分别修饰 triangles 与 square。 - 逻辑关系：主句陈述事实，从句以被动结构展开"分割"的具体方式，插入语补充图示依据，整体为由主到次的说明层次。
语言使用特点
- 戏剧性祈使语气：原文以 Behold! 收束，用古老感叹词把全部论证"推到读者眼前"，体现"以图代证"的极简修辞。
- 被动语态高频：is cut up、are easily rearranged、is continuously transformed 多处使用被动，突出"图形被操作"而非"操作者"，符合说明文客观风格。
- 名词化结构：the square on the hypotenuse、the sum of the squares on the legs 用介词短语作后置定语，信息密度高，是数学英语的典型特征。
迁移练习
- 用英语写出"斜边的正方形被分割成四个全等的直角三角形"，模仿原文被动结构。
- 仿照 a little algebra supplies a proof，用 supply 造一个与数学证明相关的句子。
- 将"图 16 展示了分割方式"译为英文，使用 as indicated in Figure 16 结构。
点击展开参考答案
- The square on the hypotenuse is cut up into four triangles each congruent to the given triangle.
- A simple diagram supplies a proof of the theorem.
- The dissection is as indicated in Figure 16.