化圆为方Squaring the Circle

常用词汇

同义词与近义词

常用短语与固定搭配

• equal in area to：面积等于……。原文用法："a square equal in area to a given circle"
• come down to us：流传到我们。原文用法："The earliest attempted solution that has come down to us"
• in all likelihood：很可能。原文用法："In all likelihood, it was obtained by some sort of empirical procedure"
• similar to the following：类似于下面这样。原文用法："empirical procedure similar to the following"
• as uniform in shape and size as possible：尽可能在形状和大小上均匀一致。原文用法："chosen as uniform in shape and size as possible"
• convert ... into ...：把……转换成……。原文用法："convert the collection of pebbles from their circular array into a square array"
• on measuring：一经测量。原文用法："On measuring the side of the square one will find it to be very close to..."

常用句式

• It is an elementary matter to show that ...：表明……是初等的事情/很容易说明。原文例句："It is an elementary matter to show that this solution of the problem is equivalent to taking π = (4/3)⁴ or, approximately, 3.16."
• One naturally wonders how ...：人们自然会想知道……。原文例句："One naturally wonders how the Egyptians arrived at the above approximate solution of the circle-squaring problem."

长难句解析

The earliest attempted solution that has come down to us of the problem of constructing a square equal in area to a given circle is found in the Rhind papyrus of about 1650 B.C.

• 主干：The earliest attempted solution ... is found in the Rhind papyrus.
• 修饰与从句：

- that has come down to us：定语从句，修饰 solution，意为“流传到我们手中的”。 - of the problem of constructing a square equal in area to a given circle：介词短语，修饰 solution/problem，说明是“作一个与已知圆等面积正方形的问题”。 - equal in area to a given circle：形容词短语，修饰 square。 - of about 1650 B.C.：介词短语，修饰 Rhind papyrus。

• 逻辑关系：句子通过多重后置修饰，把“问题—流传—文献”信息层层叠加。

语言使用特点

• 文本使用正式学术英语，被动语态与名词化结构较多（如 "is found", "was obtained"）。
• 数学表达中常用 "equal in area to" 而非 "has the same area as"，体现几何表述的简洁性。
• 描述经验过程时使用祈使句（Draw, cover, convert）使步骤清晰。

迁移练习

1. 用英文简要说明：为什么古埃及人认为直径的 8/9 可以用来“化圆为方”？
2. 用 "It is an elementary matter to show that ..." 句型，写出一条你学过的简单数学结论。
3. 翻译：人们自然会想知道，古埃及人是如何得到那个近似解的。