《凡事要能够言简意赅的说明白，像表达数学公式一样》
《Everything should be expressed concisely and easy to understood using language, just like expressing mathematical formulas》
一个想法含糊仅用简单的方式表达不清楚，那就说明这个想法应该抛弃。
--- 法国作家 沃夫纳格
If an idea is vague and cannot be expressed clearly in a simple way, it means that the idea should be abandoned.
--- French writer Wolfnag
一个人的说话代表一个人的思维，每个词语是一个概念的抽象，如何清晰的表达，是一门很深的学问，需要不停的总结练习，这篇文章来自于《How to read maths》，重点是后面的英文词汇表格，熟记下来，才能够和老外交流清楚数学表达式，视频译文如下：
A person's speech represents a person's thinking. Each word is an abstraction of a concept. How to express it clearly is a very deep knowledge that requires constant summary practice. This article comes from "How to read maths" , the key point is the English vocabulary table at the back. Only by memorizing it can you clearly communicate mathematical expressions with foreigners. The video translation is as follows:
Mathematical equations can be quite intimidating, if you don’t know how to how to read them, but they don’t need to be. It is possible to learn how to make sense of them even if you don’t know much algebra.So if when you see and equation it looks like a strange alien language, this video is for you.
阅读数学方程通常会让人生畏，但它们其实并不难，即使你不太了解代数，也可以学习如何理解方程式。因此，如果您看到方程像是一种奇怪的外星语言，那么这个视频适合您。
The first rule is you need to find out where these things called variables are. A mathematical equation describes a relationship between things. The most common form is something equals something else. These letters are the variables and are standins for numbers. You can put any number into them but the equation fixes what the other numbers can be. For example, y=x means that the numbers in y and x have to be the same. But in y=2x, the number in y has to be double whatever the number in x is. The best way to visualise this is with a graph, and when you do this each variable in your equation gets an axis. And the line on your graph shows the allowed pairs of values for your equation. Now you can also have equations where the variables appear in multiple different places,but you still only have two axes. Equations with two variables are the simplest you can get, but many equations have multiple variables. So if you wanted to draw a graph of an equation with three variables you would need to have one axis for each of the variables. But often to make it easier to work with we just concentrate on two of the variables and keep the other variables fixed. But you can try different values to see what happens.
第一条规则是您需要找出方程式中的变量在哪里。 数学方程描述了事物之间的关系。 最常见的形式是某物等于另一物。 这些字母是变量，是数字的替代品。 您可以将任何数字放入其中，但方程式会确定其他数字的大小。 例如，y=x 表示 y 和 x 中的数字必须相同。 但在 y=2x 中，无论 x 中的数字是什么，y 中的数字都必须是两倍。 可视化这一点的最佳方法是使用图表，当您这样做时，方程中的每个变量都会获得一个轴。 图表上的线条显示了方程式允许的值对。 现在您还可以拥有其中变量出现在多个不同位置的方程，但你仍然只有两个轴。 具有两个变量的方程是最简单的方程，但许多方程都有多个变量。 因此，如果您想绘制包含三个变量的方程图，则每个变量都需要一个轴。 但通常为了使工作更容易，我们只关注其中两个变量并保持其他变量固定。 但您可以尝试不同的值来看看会发生什么。
The other thing you get in equations are constants. You have to keep an eye out for constants because they look like variables, they are written with a letter, but actually they are just a single number. A famous one is pi, but in science you get many others. So how do you know which letters or symbols are constants or variables? Well you don't. You have to rely on the person writing the equation to tell you what all of the bits mean. Practically when you use equations in science, you have the numbers to put in to all the variables apart from one, and that's the one you are trying to work out. So you plug in all the numbers and find out what the last variable should be. Lets look at an example of an equation and how I would go about reading it. This is Newton’s law of Universal gravitation which looks at the force of gravity between two masses. First thing you do is work out what all the letters mean. F is the gravitational force that you are working out. m1 and m2 are the masses of the two bodies. G is the gravitational constant, and r is the distance between the masses. Now you work out which letters are variables and which ones are constants. This formula just has got one constant: G which is a tiny little number. Now you basically know how to use this formula. If you have the masses of any two objects and the distance between them, you can plug in the numbers and calculate the force of gravity between them. So the force of gravity between an apple and an orange is about the weight of a grain of pollen. Very very small.
方程中得到的另一件事是常数。 你必须留意常量，因为它们看起来像变量，它们是用字母写的，但实际上它们只是一个数字。 圆周率是一个著名的概念，但在科学中还有很多其他的概念。 那么如何知道哪些字母或符号是常量或变量呢？ 您必须依靠编写方程式的人来告诉您所有符号的含义。 实际上，当您在科学中使用方程式时，除了一个变量之外，您还需要将数字放入所有变量中，而这就是您要计算的变量。 因此，您代入所有数字并找出最后一个变量应该是什么。 让我们看一个方程的例子，这就是牛顿万有引力定律，它着眼于两个质量之间的引力。 您要做的第一件事就是弄清楚所有字母的含义。 F 是您正在计算的重力。 m1 和 m2 是两个物体的质量。 G 是万有引力常数，r 是质量之间的距离。 现在您可以找出哪些字母是变量，哪些字母是常量。 这个公式只有一个常数：G，它是一个很小的数字。 现在你基本上知道如何使用这个公式了。 如果您有任意两个物体的质量以及它们之间的距离，您可以代入这些数字并计算它们之间的重力。 所以苹果和橙子之间的重力大约是一粒花粉的重量。 这个力非常非常小。
When you plug numbers in and solve the equation you have to know what order to do things in.And this is the next thing you need to work out after you have identified the variables and constants. Knowing what order you would do the mathematical operations in an equation helps you get your head around them, and there are some rules about how it is done. Any variables that are just next to each other are multiplied with each other, and you do these first. At the same time you do any divisions - but only if it is a single number divided by another number. And then you do the additions and subtractions. If you've got a division, but there is an addition or subtraction at the top or bottom, you need to make sure these are done first before you can do the division. And finally, anything in brackets goes before anything outside of the brackets. There are more rules but this covers you in most situations. When you come across an equation in a book or video, you are probably not going to start putting actual numbers into it. But running through what you would do if you had the numbers is a really useful way to get your head around the equation. In these examples I’ve mostly used normal letters but many equations also use greek letters.
当你代入数字并解方程时，你必须知道按什么顺序做事。这是确定变量和常量后需要解决的下一件事。 知道在方程中进行数学运算的顺序可以帮助您理解它们，并且有一些关于如何完成数学运算的规则。 任何相邻的变量都会相互相乘，并且您首先执行这些操作。 同时您可以进行任何除法 - 但前提是它是一个数字除以另一个数字。 然后你进行加法和减法。 如果您进行了除法，但顶部或底部有加法或减法，则需要确保先完成这些操作，然后才能进行除法。 最后，括号内的任何内容都位于括号外的任何内容之前。 还有更多规则，但这涵盖了大多数情况。 当您在书籍或视频中遇到方程式时，您可能不会开始将实际数字放入其中。 但是，如果你有这些数字，那么想一想你会怎么做是一个非常有用的方法，可以帮助你理解这个等式。 在这些例子中，我主要使用普通字母，但许多方程也使用希腊字母。
I think this is why equations look so weird to people because they are unfamilliar with all these strange symbols. But you should think of them just the same as normal letters, they can be used to represent constants or variables so they are just the same. You also get other notations like subscripts and these are all basically used as labels to identify different constants or variables. Other notation has specific mathematical meanings, and I can’t cover everything in this video, but if you are ever confused about what something means I encourage you to look it up as they normally end up being simpler than you think. But also I've made a handy cheat sheet which I've put in the descripion below so you can also check that out. Now here are some of the other more common weird things that you’ll see. You're all familiar with multiplication, division, adding and subtracting. These are all things call mathematical operations. But they are not the only ones, and here are some of the more common ones that you'll see. This big greek epsilon is a sum operation, and what it means is that you take this thing and repeatedly add it to itself, but put in different numbers each time. This is the number that you start at, and this is the number you end at. It also means that this variable has to be an integer variable, which means that it can only take on whole numbers, zero, one, two, three, four. No numbers in between. So whenever you see a sum, just imagine this thing as a whole series of things being added together, but each having a different value.
我认为这就是为什么方程对人们来说看起来很奇怪，因为他们不熟悉所有这些奇怪的符号。 但您应该将它们视为与普通字母相同，它们可以用来表示常量或变量，因此它们是相同的。您还可以获得其他符号，例如下标，这些符号基本上都用作标签来标识不同的常量或变量。 其他符号具有特定的数学含义，我无法涵盖本视频中的所有内容，但如果您对某些内容的含义感到困惑，我鼓励您查找它，因为它们通常比您想象的要简单。 而且我还制作了一个方便的备忘单，并将其放在下面的描述中，以便您也可以查看。 现在，您将看到一些其他更常见的奇怪事情。 你们都熟悉乘法、除法、加法和减法。 这些都是所谓的数学运算。 但它们并不是唯一的，以下是您会看到的一些更常见的。 这个大希腊 epsilon 是一个求和运算，它的意思是你把这个东西重复地添加到它自己上，但每次放入不同的数字。这是您开始的数字，这是您结束的数字。 它还意味着该变量必须是整数变量，这意味着它只能采用整数，零、一、二、三、四。 中间没有数字。 因此，每当您看到总和时，只需将其想象为一系列事物相加在一起的整体，但每个事物都有不同的值。
Similar to a sum is an integral, which really needs a graph to explain it. It is basically a way of finding the area underneath a line that is defined here. Like a sum it's got a beginning and an end, although these can go from minus infinity to infinity, so you might see that written sometimes too. And finally, related to integration is differentiation which looks like this and is an operation that looks at how the steepness of a line changes, called the gradient of a line. So when you have things like dy/dx, they are looking at the gradients of lines. That's just a quick look at integration and differentiation these make up calculus but that needs a whole video in itself to explain properly.
与和类似的是积分，它确实需要一个图来解释它。 它基本上是一种查找此处定义的线下方区域的方法。 就像总和一样，它有开始和结束，尽管它们可以从负无穷大到无穷大，所以有时你也可能会看到这样的写法。最后，与积分相关的是微分，它看起来像这样，是一种查看线的陡度如何变化的操作，称为线的梯度。 因此，当你有像 dy/dx 这样的东西时，它们会查看线条的梯度。 这只是快速了解微积分的积分和微分，但这本身需要一个完整的视频才能正确解释。
I put the here so that you don't freak out when you see them. So those are the basics of how to read mathematical equations. Step one find the variables and constants and what each one represents. Step two work out what all the weird mathematical operations are. And step three work out what order you would solve the equation in if you put in the numbers. If you want more info check out this cheat sheet I have put together with all of the greek letters and most of the more common mathematical operations, check it out in the link in the description below.
我把它们放在这里，这样你看到它们时就不会惊慌。 这些是如何阅读数学方程的基础知识。 第一步找到变量和常量以及每一个代表什么。 第二步找出所有奇怪的数学运算是什么。 第三步计算出如果输入数字，您将按照什么顺序求解方程。 如果您想了解更多信息，请查看我将所有希腊字母和大多数更常见的数学运算放在一起的备忘单，请在下面描述中的链接中查看。
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绝对值
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absolute value
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加
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plus
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约等于
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approximately equal
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相反数
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opposite number
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减
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minus
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方程
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equation
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函数
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function
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乘
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multiply
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平方
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square
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排列
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permutation
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除
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divided by
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立方
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cube
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组合
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combination
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等于
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equal
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4次方
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the power of four
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分子
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numerator
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不等于
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not equal
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n次方
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the power of n
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分母
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denominator
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大于
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is greater than
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倒数
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reciprocal
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和
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sum
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大于等于
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is greater than or equal
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分数
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fraction
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差
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difference
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小于
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is less than
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对数
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logarithm
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积
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product
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小于等于
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is less than or equal
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指数
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index
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商
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quotient
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根号
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radical sign
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积分
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integral
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比
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ratio
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PS：
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