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mc1-014 · ENGLISH LEARNING

吉萨金字塔The pyramid of Gizeh

英语学习拓展 约 8 分钟阅读 中文English

内容概述

  • 数学故事
  • 数学史 / 建筑工程中的数学
  • 叙事 + 图注

故事介绍吉萨大金字塔的建造规模与精度:约建于公元前2900年,占地13英亩,由200多万块平均重约2.5吨的石块砌成;底边相对误差小于1/14000,直角偏差不超过1/27000。文中还提到埃及人可能用填沙斜坡法把巨石运送到高处,并以底比斯太阳寺前的方尖塔为例,说明古埃及工程面临的巨大挑战。

中文正文

吉萨(Gizeh)大金字塔大约建于公元前2900年,无疑牵涉着一些数学和工程学的问题。整个建筑占地13亩,是由200多万块石头堆砌起来的,石块平均重两吨半,镶嵌恰到好处。这些石块都来自尼罗河对岸的采石场。有些墓室穹顶是54吨重的花岗岩,27英尺长,4英尺厚,它们从600英里外的采石场运来,然后固定在离地面200英尺的地方。据说,金字塔的四边形底边的相对误差不超过一万四千分之一,而每个角与直角的偏离不超过二万七千分之一。

当然,如果想到这项工程是100 000 士兵苦干30年的结果,那些统计数字背后的巧夺天工就会大失光彩。例如,抬升巨石的难题,做起来也许非常简单:当金字塔不断升高时,把它埋进沙里,然后沿着沙堆的斜坡,一点点把巨石滚到塔的高度,最后再把那些沙运走。只要有了足够的时间和劳力,很多技艺都可以通过简单原始的办法来实现。尽管如此,工程问题还是需要这样那样的方式来解决。举例说,为了采集巨石,为了把粉红色花岗岩的巨大方尖塔树立起来,埃及人该遭遇多少工程难题!现存最大的方尖塔耸立在底比斯的太阳寺前,是公元前1500年的杰作,长几乎105英尺,四方形基础宽10英尺,重约430吨!

英文正文

14° The pyramid of Gizeh. The great pyramid of Gizeh was erected about 2900 B.C. and undoubtedly involved some mathematical and engineering problems.

The structure covers thirteen acres and contains over two million stone blocks, averaging two and a half tons in weight, very carefully fitted together. These stone blocks were brought from sandstone quarries located on the other side of the Nile. Some chamber roofs are made of fifty-four-ton granite blocks, twenty-seven feet long and four feet thick, hauled from a quarry six hundred miles away, and set two hundred feet above ground. It is reported that the sides of the square base of the pyramid involve a relative error of less than one fourteen thousandth, and that the relative error in the right angles at the corners does not exceed one twenty-seven thousandth.

Of course, the engineering skill implied by these impressive statistics is considerably diminished when we realize that the task was accomplished by an army of 100,000 laborers working for a period of thirty years. For example, the seemingly difficult problem of raising the great stone blocks to ever higher positions as the structure of the pyramid grew was probably very simply met by constantly keeping the rising pyramid submerged in imported sand, hauling the blocks on rollers up a gradual incline of this sand, and then finally removing all the imported sand. Given sufficient time and sufficient labor power, many difficult feats can be done in a simple and primitive fashion. Nevertheless, the engineering problems had to be overcome one way or another. Consider, for instance, the mammoth engineering problems encountered by the Egyptians in quarrying and setting up some of their huge obelisks of pink granite. The largest existing obelisk appears before the old Temple of the Sun at Thebes; it was quarried about 1500 B.C. and is no less than 105 feet long, nearly 10 feet square at the base, and weighs about 430 tons!

英语学习拓展

常用词汇

重点 · 近义词拓展
erect

音标/ɪˈrekt/

释义与用法

建立,竖立。

原文用法:The great pyramid of Gizeh was erected about 2900 B.C.

查看对应近义词组 ↓
involve

音标/ɪnˈvɒlv/

释义与用法

涉及,包含。

原文用法:involved some mathematical and engineering problems

acre

音标/ˈeɪkə(r)/

释义与用法

英亩。

原文用法:The structure covers thirteen acres

average

音标/ˈævərɪdʒ/

释义与用法

平均为;平均的。

原文用法:averaging two and a half tons in weight(平均重量为2.5吨)。

quarry

音标/ˈkwɒri/

释义与用法

采石场。

原文用法:sandstone quarries located on the other side of the Nile

重点 · 近义词拓展
haul

音标/hɔːl/

释义与用法

拖运,搬运。

原文用法:hauled from a quarry six hundred miles away

查看对应近义词组 ↓

relative error:相对误差。原文用法:a relative error of less than one fourteen thousandth

exceed

音标/ɪkˈsiːd/

释义与用法

超过。

原文用法:does not exceed one twenty-seven thousandth

accomplish

音标/əˈkʌmplɪʃ/

释义与用法

完成,实现。

原文用法:the task was accomplished by an army of 100,000 laborers

重点 · 近义词拓展
feat

音标/fiːt/

释义与用法

功绩,壮举。

原文用法:many difficult feats can be done in a simple and primitive fashion

查看对应近义词组 ↓
mammoth

音标/ˈmæməθ/

释义与用法

巨大的(也常作名词“猛犸象”)。

原文用法:the mammoth engineering problems

obelisk

音标/ˈɒbəlɪsk/

释义与用法

方尖塔。

原文用法:huge obelisks of pink granite

同义词与近义词

erect/build/construct

对应核心词汇:erect

用法辨析

对应核心词汇:erect

erect 更正式,强调“竖立、使直立”;build 最常用;construct 强调按设计建造。

haul/drag/transport

对应核心词汇:haul

用法辨析

对应核心词汇:haul

haul 强调用力拖拉重物;drag 强调在地上拖;transport 泛指运输。

feat/achievement/accomplishment

对应核心词汇:feat

用法辨析

对应核心词汇:feat

feat 常指需要勇气或技艺的壮举;achievement 侧重成就;accomplishment 侧重完成的事情。

常用短语与固定搭配

  • be brought from:来自。原文用法:These stone blocks were brought from sandstone quarries
  • located on the other side of:位于……对岸。原文用法:located on the other side of the Nile
  • above ground:在地面上方。原文用法:set two hundred feet above ground
  • it is reported that:据报道。原文用法:It is reported that the sides of the square base ... involve a relative error ...
  • working for a period of:工作一段时间。原文用法:working for a period of thirty years
  • one way or another:以某种方式,不管怎样。原文用法:the engineering problems had to be overcome one way or another

常用句式

  • Pattern: ... is/are made of ...:由……制成。原文例句:Some chamber roofs are made of fifty-four-ton granite blocks
  • Pattern: ... is considerably diminished when ...:当……时,……大为减弱。原文例句:the engineering skill implied by these impressive statistics is considerably diminished when we realize that ...

长难句解析

For example, the seemingly difficult problem of raising the great stone blocks to ever higher positions as the structure of the pyramid grew was probably very simply met by constantly keeping the rising pyramid submerged in imported sand, hauling the blocks on rollers up a gradual incline of this sand, and then finally removing all the imported sand.

  • 主干:the seemingly difficult problem ... was probably very simply met(这个看似困难的问题可能非常简单地被解决了)。
  • 修饰与从句:of raising the great stone blocks to ever higher positions 为介词短语,修饰 problemas the structure of the pyramid grew 为时间状语从句,表示“随着金字塔不断升高”;by constantly keeping ..., hauling ..., and then finally removing ... 为介词短语,说明解决问题的方式,其中三个动名词短语 keeping ..., hauling ..., removing ... 并列。
  • 逻辑关系:先提出“难题”,再说明条件(金字塔升高),最后给出三种连续操作(填沙、滚石上坡、清沙)作为解决方案。

语言使用特点

  • 文本以数据和事实为主,使用大量具体数字增强说服力。
  • 使用了 diminished, met, overcome 等动词的被动语态,使叙述客观。
  • 通过 of course, nevertheless, for example, consider 等连接词组织论证。

迁移练习

  1. It is reported that ... 造句,描述某一建筑或历史事实。
  2. be made of 描述一种物品的材料。
  3. The structure covers thirteen acres and contains over two million stone blocks. 改写为一句包含具体数字的主动描述。
点击展开参考答案
  1. (示例)It is reported that the Great Wall stretches over 21,000 kilometers.
  2. (示例)The statue is made of bronze.
  3. (示例)Thirteen acres of land and more than two million stone blocks make up the great pyramid.