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Hi. Welcome to www.engvid.com. I'm Adam.
欢迎来到英格威英语学习网。我是亚当。
In today's lesson, we're going to look at some expressions that are used in everyday English, but they come from math. Okay?
在今天的课程中，我们将看一些日常英语中的表达，但是它们是来自数学的。
So, if you know some math terminology, you'll understand these a little bit easier.
所以如果你知道一些数学术语，你就能更容易明白这些词汇了。
We also have... I have a video about math words, you can check that out as well,
我们也有...我们有一期关于数学词汇的视频，你也可以看看。
but let's start with some of these. "Plus" and "minus" or "pluses" and "minuses".
但是让我们从这些词汇开始吧。加和减，或者pluses和minuses。
Now, in math, we use: "One plus one equals", so "plus", there, is more like a verb,
在数学中，我们使用：“一加一等于”，所以“加”更像是一个动词，
but it's more of an equation; it makes the equation move. Here, we're using them as nouns. Okay?
它更像是一个等式，它使等式运动。这里，我们把它们当作名词使用。
So, that's a key feature you have to remember - they are nouns.
这是一个你要记住的主要特征，它们是名词。
And, basically, synonyms to "pluses" and "minuses" are "pros" and "cons".
基本上，pluses与minuses和pros与cons是同义词。
So, when you're looking at a situation, or an action, or an idea, you have to look at the good and the bad side;
所以，当你面对一种情况，或一种行动，或一种观点，你得看它好与不好的一面。
you have to look at the pros and the cons; you have to look at the pluses and the minuses;
你得看看它的优缺点。
the advantages and disadvantages; the positives and the negatives. Okay?
优势和略势，积极的方面和消极的方面。
So, "plus" and "minuses" work the same way, so these give you a little bit of an extra synonym;
plus和minuses也是同样的道理，所以给你一些其他的同义词，
an extra choice, especially in writing, but also in speaking.
其他的选择，尤其是在写作中，也在口语中，
So, if we're looking at... We're looking at this person, this candidate's presidency,
所以，如果我们是看的这个人，这个候选总统，
and we're trying to debate: "What are the good points? What are the bad points?"
我们想要辩论：“好的地方在哪，不好的地方在哪？
So, some of the pluses of his potential presidency are that he will help the economy.
他当选总统的一些好处是他将有助于经济。
The one big minus, though, is that he's a racist and he might destroy harmony in society, for example.
不过，最大的缺点是，他是一个种族主义者，比如，他可能会破坏社会的和谐。
I'm not mentioning any names; I'll leave that to you, but we'll leave it at that as well.
我没有提到任何名字；这个你们自己来想，但我们也会把它放在那里。
So, he has... There are several pluses to his potential presidency; there's one big minus that might outweigh all those pluses.
所以，他成为总统有几个优点；但是有一个大缺点可能会超过所有这些优点。
Now, "exponential". "Exponential" comes from "exponent". Now, you might know this as, like... This is an exponent.
“指数”。Exponential来源于exponent。现在，你可能知道这个，就像...这是指数。
But when we talk about "exponential", we're talking about it to a very large degree. Okay?
但是当我们谈论指数的时候，我们是在很大程度上谈论它。
To a large degree or to a large extent; something that is significant. Okay?
在很大程度上，说的是某件重要的事。
We're talking about growth, so exponential growth; or the opposite, exponential decline; or an exponential spread.
我们讨论的是增长，指数增长；或者相反，指数下降；或者指数分布。
So, it means it's going to... Something is going to increase by many times, or decrease by many times, or spread very quickly.
它的意思就是，某物会增加很多倍，或减少很多倍，或迅速扩散。
Now, when we say: "exponential", there's no number to it.
当我们说指数时，并没有什么数字。
We don't actually have this number, here; we're just saying that it's going to be very fast, very large, etc.
我们实际上没有这个数；我们只是说它会非常快，非常大，等等。
So, after World War II, the economies of most western nations grew exponentially. In this case, I'm using the adverb.
在二战后，多数西方国家的经济呈指数增长。在这里，我使用的是动词。
"Exponential" is an adjective; "exponentially" is an adverb. And most of the countries witnessed exponential growth.
“指数的”是一个名词，“指数地”是一个动词。多数国家都见证了指数地增长。
The use of the internet has spread exponentially around the globe - it means it spread very fast and all over the place.
互联网的使用在全球范围内呈指数级增长-意思是它散播地很快，到处都是。
So, there's no number; just very quickly, very fast. Okay? "Parallel".
所以没有数字，就是很快。平行的。
Now, parallel lines are lines that run along the same path in the same direction, but never meet. Okay?
平行线是沿着同一方向的同一条路径，但从不相交的线。好吧？
So, we say: "It's in line with" or "on a similar path"; these are synonyms to "parallel".
所以我们说：It's in line with或者on a similar path，它们是parallel的同义词。
So, the FBI is conducting an investigation into the event, but the local police department,
联邦调查局正在调查此事，但当地警察局，
although they're going to cooperate with the FBI, are going to run a parallel investigation on their own.
尽管他们要和联邦调查局合作，他们要自己进行平行调查。
So they're going to help the FBI, but they're also going to have their own investigation that's going to go along the same path;
他们将协助联邦调查局，但是他们也要进行他们自己的调查，会走同样的路。
a parallel investigation, meaning in the same direction.
一个平行调查，意思是相同的方向。
"A fraction of". So, a "fraction" is, for example, number over a number - that's a fraction.
一部分。分数就是，比如，数字上面有一个数字-这就是分数。
When we say: "A fraction of", we're saying a small amount of or a partial amount.
当我们说：“一部分”，我们在说一小部分，或者一部分。
So, if you're looking at two companies who create software, let's say...
如果你讨论两家开发软件的公司，
So, this company creates very good software, but my company creates equally good software,
所以，这家公司能开发非常好的软件，但是我的公司也能开发同样好的软件，
but at a fraction of the cost; means much cheaper, much lower. Right?
但是只需花一小部分钱；这意味着更便宜，更便宜。对吧？
A smaller or a partial. So, they charge 1000 bucks; I charge only 600.
更少或者一部分。他们收1000美元，我只收600美元。
It's a partial; it's a fraction of their price; much, much lower. Okay?
只是一部分，只是他们价格的一部分，比他们低得多。
So, so far we have four. Let's look at four more. Okay, let's look at a few more. Now, "angle".
现在我们讲了四个。再来讲四个别的词。再多讲一些。角度。
So, if you're talking about lines or triangles especially, this is the angle.
如果你说的是直线或三角形，这个就是角。
For example: This is a 90-degree angle. But when we talk about "angle" in everyday life,
比如：这是一个90度的角。但是当我们在日常生活中讨论角度时，
we're talking about perspective; the way we view something.
我们讨论的是视角，是看待事情的角度。
So, you can view it from this angle, you can view it from this angle, you can view it from this angle -
你可以在这个角度看待它，你也可以在这个角度看待它，也可以在这个角度看待它-
you're going to have a different perspective; a different way of seeing something from every different angle.
你会有一个不同的视角；从不同角度看事物的不同方式。
And it's also a different approach. The way we want to accomplish something,
它也指一种不同的方法。一种我们想实现什么事情的方式。
we approach it from different angles, we're going to have different results.
我们从不同的角度接近它，我们会得到不同的结果。
So, if we want to solve this problem, we can't just look at it straight on; we have to look at it from different angles.
如果我们想解决这个问题，我们不能直接看它。我们得从不同的角度看待它。
Now, a more slang use... If you ever hear the expression: "Hmm. What's his angle?"
更加俚语化的用法...如果我们听到这个表达：“他要干什么？”
When we use this, it means we... We're suspicious; we don't trust the person. "Suspicious". Right?
我们使用这个的时候，意思是我们...我们怀疑它；我们不相信这个人。怀疑。
"What's his angle? What's he trying to accomplish?" So, we're not sure about his approach to something and we don't trust it.
他要干什么？他想要实现什么？我们不确定他做某件事的方式，我们不相信。
We think he's trying to go this way, so really he can go this way. He has a different target in mind than what we can see.
我们认为他想这样做，他可以这样做。和我们不同，他脑海中有一个不同的目标。
So, we don't trust his angle because we know later he'll come in from this angle and do something different. Okay?
我们不相信他，因为我们知道他会从这个角度进入，做一些不同的事情。
So, it's a bit of a slang use, but again, it basically means the approach or the perspective that someone is taking. Okay.
所以这是偏俚语化的应用，但是再说一次，它的意思就是某人采取的方法或者视角。
"Go off on a tangent". Now, if you think about math, again, here's a circle,
“偏离正题”。现在，如果你想一下数学，这是一个圆，
and you want to maybe measure a point or you might want to measure something,
或许你想测量一个点，或者测量某个事情。
and you think about a line touching the circle... It touches it on one point; not like the way I drew it.
你想象一条接触这个圆圈的线...它和圆交于一点，不像我画的样子。
It touches on one point, and then continues off in the distance; it doesn't go into the circle.
它相交于一点，然后在远处延伸；它没有进入圆。
So, this line is called the tangent. So, if somebody goes off on a tangent,
这条线就叫切线。如果某人离题了，
it means they're getting away from the central point; they're getting away from the circle and going on to something else.
意思就是他们离开了中心点，他们离开了圆，到了别的地方。
So, if we have an interview with a politician and we ask him a very direct question, a lot of them will, you know...
如果我们采访一位政治家，我们问他一个非常直接的问题，他们中的很多人会...
They'll touch on the topic, and then they'll just go off on a tangent and talk about something completely different.
他们会触及这个话题，然后他们就会离题而去，谈论一些完全不同的东西。
So, the politician started to answer the question,
政治家开始回答这个问题，
but then he went off on a tangent and started talking about his dogs, and basically avoided answering the question.
然后，他开始跑题，开始谈论他的狗，基本上避免回答这个问题。
So, go off... Now, we also use this about, like, people who daydream.
我们也在这种情况下使用这个表达，比如，做白日梦的人。
We ask them a question and they start to answer it; they legitimately want to give you an answer,
我们问他们一个问题，他们开始回答；他们想给你一个合理的答案，
but then they mention a word and that gets their mind going,
但是然后他们就提一个词，它让他们的思维活跃起来，
and then they start following that tangent and then they just go off with that tangent,
然后他们就接着这个词聊，然后他们就离题。
and talk about something completely different and unrelated to the original question. Okay?
谈论某件完全不同的事情，和最初的问题无关的东西。
So, they lose focus; they lose track of what they were saying originally. Okay.
他们失去了焦点，忘记了起初讨论的事情。
Now, if something "adds up"... If it adds up, it makes sense. If it doesn't add up, it doesn't make sense.
如果某件事合情理...如果它合情理，就是讲得通。如果不合情理，就是讲不通。
So, we're talking about somebody giving you a story.
我们谈论的是给你讲故事的某个人。
For example, the police are interviewing a witness or they're interviewing a suspect, and the suspect or the witness are saying:
比如，警察在采访一个目击者或者在采访一个嫌疑人，嫌疑人和目击者就会说：
"Oh, this happened, and this happened, and this happened", and the police are going: "Hmm. This doesn't add up."
“发生了这件事，还有这件事，”然后警察说：“这不合情理啊。”
So, this part of the story, plus this part of the story, plus this part of the story
故事的这一部分加上故事的这一部分，还有故事的这一部分，
does not equal this part of the story; something doesn't add up.
和故事的这一部分不一致，这件事情不合理。
Either you're lying, or you missed something, or we missed something in the questions, so it doesn't add up; it doesn't make sense. Okay?
你在说谎，或者你遗漏了什么东西，或者我们在问题中遗漏了什么东西，所以它不合情理，讲不通。
Last: "The lowest common denominator". So, again, we're talking about fractions - this is the numerator; this is the denominator.
最后：“最小公分母”。这是分数，这是分子；这是分母。
Now, when we want to add fractions... For example, if I want to say... I want to add one... One quarter and two-fifths.
当我们想加上分数时...比如，如果我想说，我想加一个...四分之一和五分之二。
So, I can't add one... It's not three over nine; it doesn't work that way. Right?
我不能...结果不是九分之三，不是这样的。
I need to find a common denominator - one that both of these can go into,
我需要找一个公分母-一个它们都能整除的公分母，
and I think the lowest is 20, so you get whatever, 5 over 20 and 10 over... Or, sorry. 8 over 20, and then you make the addition.
我认为最小的是20，然后就是二十分之五和二十分之八，然后再做加法。
So, "the lowest common denominator" in everyday English means the lowest level or the base.
the lowest common denominator在日常英语中的意思是最低水平或者基础。
Now, generally when we talk about the lowest level, we mean the lowest level people; we're talking about an audience or consumers.
通常我们在讨论最低水平的时候，意思是大众，我们讨论的是观众或者消费者。
So, there are very good newspapers in this country, let's say.
比如说，这个国家有非常好的报纸。
In Canada, we have some very good newspapers, but we also have some not so good newspapers.
在加拿大，我们有一些非常好的报纸，但也有一些不太好的报纸。
These not so good newspapers, they cater to or they target the lowest common denominator,
这些不是很好的报纸，它们迎合大众口味为目标，
so they give them very sensationalist headlines, because why?
所以他们给他们起非常耸人听闻的标题，为什么?
Because why? Don't say: "Because why?" Because they want to sell newspapers.
为什么？不要说“因为为什么？”因为他们想卖报纸。
So, they... they create a newspaper, and they target the lowest common denominator with their sensationalist headlines.
所以他们发行了一份报纸，他们以迎合大众口味为目标，使用耸人听闻的标题。
They want to sell more papers to the people who don't really read too much or who don't care about very good reporting. Okay?
他们想把报纸卖给不想阅读太多的人，或者不在意好的报道的人。
So that's: "the lowest common denominator". So, there you go: Eight expressions from math.
那就是迎合大众口味。这就是八个来自数学的表达。
So, it's good to learn math, it's good to learn English, it's good to learn them together.
所以，学习数学很好，学习英语很好，一起学习很好。
You can use these in everyday English. I wouldn't necessarily use these in writing; more for speaking, etc.
你可以在日常英语中使用它们。我不需要在写作中使用它们，更多是用在口语中。
But if you have any questions about these, please go to www.engvid.com and join the forum, and you can ask the questions; I'll be very happy to help you out with these.
但是如果你有任何关于这些词汇的问题，请登录www.engvid.com，并加入论坛，你可以提问问题；我很乐意帮你解决这些问题。
If you like this video, please subscribe to my YouTube channel and see lots more videos like these, or like this or others.
如果你喜欢这个视频，请订阅我的油管频道，观看更多类似的视频，或者其他视频。
Don't forget there's a quiz at www.engvid.com that you can test your knowledge of these expressions.
别忘了在www.engvid.com上有一个小测验，在那里你可以测试你对这些表达的了解程度。
And, again, come back, see more videos; see you again soon. Bye-bye.
再回来看更多的视频吧；再见。再见。
