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数学符号是怎么来的? – 译学馆
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数学符号是怎么来的?

Where do math symbols come from? - John David Walters

“‘所有数学都是符号逻辑’ 这是我们这个时代最伟大的发现之一”
哲学家 罗素 《数学原理》
十六世纪 数学家罗伯特·雷科德
In the 16th century, the mathematician Robert Recorde
写了一本书叫《砺智石》
wrote a book called “The Whetstone of Witte”
让英国的学生了解代数
to teach English students algebra.
但他很厌倦一遍又一遍地写“等于”这个词
But he was getting tired of writing the words “is equal to” over and over.
所以他怎么解决呢?
His solution?
他用两条平行横线段代替了那些字
He replaced those words with two parallel horizontal line segments
因为在他看来
because the way he saw it,
没有比两条横线段更相等的东西了
no two things can be more equal.
那他能用四条横线段代替两条吗?
Could he have used four line segments instead of two?
当然可以
Of course.
他可以用竖直的线段吗?
Could he have used vertical line segments?
实际上 有些人这么做了
In fact, some people did.
我们无法解释为什么今天的等号非得是这个样子
There’s no reason why the equals sign had to look the way it does today.
正如有些人所说 它只是变得流行 有点像个热词
At some point, it just caught on, sort of like a meme.
越来越多的数学家开始使用它
More and more mathematicians began to use it,
最后 它变成了等号的标准符号
and eventually, it became a standard symbol for equality.
数学里到处都是符号
Math is full of symbols.
线条
Lines,
圆点
dots,
箭头
arrows,
英文字母
English letters,
希腊字母
Greek letters,
上标
superscripts,
下标
subscripts.
它可能看起来眼花缭乱
It can look like an illegible jumble.
觉得这堆符号的数量惊人
It’s normal to find this wealth of symbols a little intimidating
想知道它们都是来自何方 是很正常的
and to wonder where they all came from.
有时 正如雷科德对“=”的解释
Sometimes, as Recorde himself noted about his equals sign,
这些符号与其要表达的含义有些相似
there’s an apt conformity between the symbol and what it represents.
另一个例子是加法中的加号
Another example of that is the plus sign for addition,
是来自拉丁语中有叠加意思的”et”
which originated from a condensing of the Latin word et meaning and.
然而 有时 符号选择是随心随欲的
Sometimes, however, the choice of symbol is more arbitrary,
例如 一个叫克里斯蒂安·克兰普的数学家
such as when a mathematician named Christian Kramp
在介绍表示阶乘的“!”时说
introduced the exclamation mark for factorials
这只是因为他需要这样的简略表达
just because he needed a shorthand for expressions like this.
实际上 所有这些符号发明和采用的原因
In fact, all of these symbols were invented or adopted
就是数学家不想重复书写同一内容
by mathematicians who wanted to avoid repeating themselves
或者用过多文字来表达数学
or having to use a lot of words to write out mathematical ideas.
数学运算中使用的大多符号是字母
Many of the symbols used in mathematics are letters,
通常来自拉丁字母或希腊字母
usually from the Latin alphabet or Greek.
字母常用于代表那些未知数
Characters are often found representing quantities that are unknown,
或者它们之间的变量关系
and the relationships between variables.
它们也可表示常用的数
They also stand in for specific numbers that show up frequently
有时要写全这些数 既是繁琐的也是不可能的
but would be cumbersome or impossible to fully write out in decimal form.
数集和方程组也可以用字母表示
Sets of numbers and whole equations can be represented with letters, too.
其他符号则用来表示运算
Other symbols are used to represent operations.
这些运算简写后极其有用
Some of these are especially valuable as shorthand
因为它们把重复的运算转换为单一的表达
because they condense repeated operations into a single expression.
相同数字的重复相加 缩写为乘法运算
The repeated addition of the same number is abbreviated with a multiplication sign
缩小了其所占空间
so it doesn’t take up more space than it has to.
一个数多次相乘用指数来表示
A number multiplied by itself is indicated with an exponent
以表明该运算重复的次数
that tells you how many times to repeat the operation.
一系列有序的数字相加
And a long string of sequential terms added together
缩写为大写的∑
is collapsed into a capital sigma.
这些符号将长运算缩短至一个更短的表达
These symbols shorten lengthy calculations to smaller terms
这样更容易使用
that are much easier to manipulate.
符号也能传达关于如何完成运算的简洁指令
Symbols can also provide succinct instructions about how to perform calculations.
考虑下面的一组运算
Consider the following set of operations on a number.
拿一些你能想到的数字
Take some number that you’re thinking of,
乘2
multiply it by two,
结果减去1
subtract one from the result,
乘上它得到的结果
multiply the result of that by itself,
再把结果除3
divide the result of that by three,
然后加1得最后的结果
and then add one to get the final output.
如果没有我们的符号和公式
Without our symbols and conventions,
我们可能会得出这串文字
we’d be faced with this block of text.
但有了符号 我们有了整洁 简练的表达
With them, we have a compact, elegant expression.
有时 比如等号
Sometimes, as with equals,
这些符号通过形式传达意义
these symbols communicate meaning through form.
但大多数 都是任意的
Many, however, are arbitrary.
理解它们关键在于熟记其意义
Understanding them is a matter of memorizing what they mean
并将其运用于不同场合 直到像一门语言一样烂熟于心
and applying them in different contexts until they stick, as with any language.
如果我们邂逅外星文明
If we were to encounter an alien civilization,
他们可能有一系列完全不同的符号
they’d probably have a totally different set of symbols.
但如果他们想的和我们一样
But if they think anything like us,
他们可能也有符号
they’d probably have symbols.
他们的符号甚至可能和我们的直接相应
And their symbols may even correspond directly to ours.
他们有自己的乘号
They’d have their own multiplication sign,
π的符号
symbol for pi,
当然 还有 等号
and, of course, equals.

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视频概述

本视频介绍了数学中数学符号的来源。

听录译者

收集自网络

翻译译者

陈西瓜

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审核团EM

视频来源

https://www.youtube.com/watch?v=eVm063xmnow

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