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So far so good, but we're not done yet.
目前还不错，但是我们还没讲完。
We still have to look at shapes and what to do with them, and angles.
我们还要讲讲形状，怎么表述它们，还有角度。
A lot more interesting stuff coming up. One sec.
接下来会讲更多有趣的东西。
Okay, so actually we're going to look at acouple more symbols and words before we go on to other more complicated things.
所以在讲其他更复杂的东西之前，我们先来看几个符号和单词。
I wanted to just squeeze these in because they're a little bit simple, but still need to understand them.
我想讲一下它们，虽然有点简单，但仍然需要理解它们。
"Average" and "mean", now, "average" and "mean" are synonyms, they essentially mean the same thing.
“Average”和“mean”，“Average”和“mean”是同义词，它们基本上是同一个意思。
We use "mean" more with math. We use "average" more with other things, like everyday things as well.
我们在数学中更多地使用“mean”。我们更多地将“average”用于其他事物，比如日常事物。
But they mean the same thing. So when you're looking for the average or the mean, you're taking all the values.
但它们的意思是一样的。求均值时，需要取所有值。
So in this case we have one, two, three, four values, you add them up, you take the total and then divide it by the number of values you started with.
以此为例，我们有1、2、3、4个值，把它们加起来，然后用总数除以开始时的值的个数。
So the... We have four values, the total 20 divided by 4, and the average of these values is 5.
我们有四个值，用总数20除以4就得到这些值的平均值5。
Okay? So that's "average" or "mean".
这就是平均值。
Now, on the other hand, you want to sometimes look for the "median".
另一方面，有时需要计算“中位数”。
Now, some. In some situations you don't want the meanor the average because the extremes,
在某些情况下，你不想要平均值，因为在极端情况下，
the top or the bottom are so far apart that the average will not give you a right idea of what's going on with whatever values you're looking at,
最大值和最小值相差太大，平均值无法让你正确理解你所看到的数值，
so what you want is the "median".
所以你想要的是中位数。
The "median" is more like the middle number that has an equal number of values above it and an equal number of values below it.
“中位数”更像是中间数，它上面和下面有相同数量的值。
So that's a little bit more representative of the situation you're looking at.
所以中位数更能代表你所看到的情况。
Okay, so now we're going to look at these symbols.
现在我们来看看这些符号。
We got this one, this one, this one, and this one - four of them.
我们有这个，这个，这个，还有这个，总共四个。
Now, this one, when you have the bigger size open and then it goes to the smaller size means y is larger than x.
大的开口指向的是y，另一边指向的是x，意思就是y大于x。
Larger, smaller, right? So, y is larger than x, y is greater than x, y is more than x.
大于，小于。y大于x，“y is greater than x”，“y is more than x”。
Don't forget the "than" because, again, you have a comparative here.
不要忘了“than”，因为这里有一个比较级。
And if you turn it around, y is smaller than x, y is less than x.
如果你换位置，那就是y小于x，y小于x。
Now, sometimes you might see these symbols with a line underneath, in which case: y is greater than or equal to x.
有时你可能会看到这些符号下面有一条线，在这种情况下：y大于或等于x。
Okay? Y is greater than or equal to x, y is less than or equal to.
Y大于等于x, Y小于等于。
Sorry, y is greater. Less than or equal to x. And now, this one you have.
y是更大的。小于等于x，然后是这个。
Basically you have the equal sign, but then you have a squiggly line.
这个是等号，然后这是约等于号。
This means it's approximately equal to, so it's an approximation, not exactly equal.
这意思是它近似等于，所以这是一个近似值，不是完全相等的。
And then you have the equal sign with a strike through, and in this case it's just not equal. Okay, pretty straightforward stuff.
然后有个等号，划线，在这种情况下，它就是不相等。很简单。
Let's move on to some other more complicated things. Okay, let's look at some more math stuff.
让我们来学习其他更复杂的内容。好的，让我们聊聊更多的数学问题。
We're going to look at shapes. Okay? So, first of all we're going to start with our "rectangle", means the two sides.
我们来看看形状。好吧？首先，我们从矩形开始，矩形的意思是两条边，
All four sides are not the same length. You have the "width", you have the "length".
所有的四条边的长度都不一样。有“宽度”，有“长度”。
Okay? Now, when you add a "height" or a "depth", both okay, depending on what you're looking at, then you.
现在，当你添加一个“高度”或“深度”，都可以，这取决于你在说什么，然后，
First of all, you've created a box. So, a rectangle is two-dimensional, a box is three-dimensional.
首先，您创建了一个长方体。矩形是二维的，长方体是三维的。
Width, length, height or depth, both okay. Now, when you measure these, when you measure...
宽度，长度，高度或深度，两个说法都可以。现在，当你测量这些，当你测量，
Like, basically you want to measure the inside space, then you're measuring the area.
基本上，你想测量体积，然后测量面积。
So you do length times width, and then the answer is whatever the number is.
所以你用长度乘以宽度，然后就得到答案。
So let's say you have two feet by four feet, so you have eight, and then the measure.
假设2英尺乘4英尺，答案就是8英尺，然后是度量。
If you're measuring in metres, in feet, in inches, in kilometres, whatever, and then you have the square.
用米，英尺，英寸，公里，等等来测量都可以，然后还有平方。
So, whatever 20 metres square, 20 square metres, etc.
20平方米，20平方米，等等。
When you add the third dimension now you're measuring volume and you're using the 3, the exponent 3 instead of the exponent 2.
当你加入第三维的时候，现在你在测量体积，你用的是立方，立方而不是平方。
Okay? Now, other shapes. We have a "square", all four sides are equal.
现在来看其他形状。我们有一个正方形，所有的四个边都是相等的。
When you put in the extra measure, the extra side, then you have a depth to it, then you have a "cube".
当你加入额外的度量，额外的边，它就会有一个深度，这就是一个“立方体”。
Okay? And, again, another way to think about this: This is two-dimensional, that's why it's squared; this is three-dimensional, cubed.
另一种思考方式是，这是二维的，这就是为什么它是平方的；这是三维的，立方的。
Okay. A "circle" or a "sphere". Now, I can't draw a sphere because I'm not a very good artist, like if I do like this.
来看“圆”或“球体”。现在，我画不了球体，因为我不是一个很好的艺术家。
You know, like a moon, like a ball is a sphere. The flat shape is the circle.
球体就像是月亮，像球一样，是一个球体。平坦的形状是圆。
If you want to measure the outside of the circle then you're looking... You're trying to measure the "circumference".
如果你想测量圆的周围，那么是在试图测量“周长”。
Sorry, I forgot to mention, if you want to measure the outside area of the rectangle, you're measuring the "perimeter", same for square.
抱歉，我忘了说，如果你想测量矩形的外围，你要测量的是周长，正方形也是一样。
For a circle you're measuring the circumference.
对于一个圆，你要测量它的周长。
If you want to measure the volume of a sphere then you're starting to get into things like "radius",
如果你想测量一个球体的体积，那么你就要开始考虑像“半径”这样的概念，
so our radius is from the centre to one side, that's half the distance from side to side.
所以半径是从中心到一边的距离，它是从一边到另一边距离的一半。
If you want to go the full distance, then you have the "diameter".
从一边到另一边的距离就是直径。
"Radius", "diameter", full length, basically cutting it in half, equal points.
“半径”、“直径”，全长，基本上是把它切成两半，等分。
So that's the circle. Then you start.
这就是圆。然后就开始。
If you want to get into the actual measurements then you start having to look at "pi".
如果你想要得到实际的测量值，那么你就必须用到“圆周率”。
Okay? Just that's how it's spelled, "pi", from the... I think Greek, if I'm not mistaken, the letter.
就是这样拼写的，“pi”，如果我没记错的话，它来自希腊文。
Now, we're getting into "triangles". We're going to look at triangles again in a minute, but for now the two-dimensional triangle.
现在，我们来说“三角形”。我们一会儿会再讲三角形，但现在讲的是二维三角形。
Now, three-dimensional you can have a "pyramid", you can have the base and then you have the sides coming up to an apex.
三维的，可以是一个“棱锥”，你可以有底面，然后侧面向上到顶点。
"Apex" means top point of something, or you can have a "prism" where you have the extra side on this side.
“顶点”的意思是某物的顶点，或者你可以有一个“棱柱”，这边有一个侧面。
Okay? So, triangle, pyramid, prism. But then we have other shapes like "oval", this is like a "cone", like an ice cream cone.
这就是三角形，棱锥，棱柱。但是我们还有其他的形状，比如“椭圆形”，就像一个“蛋筒”，就像一个冰淇淋蛋筒。
And there's a bunch of other shapes, there's a "rhombus", there's a "diamond", there's a "heptagon", there's an "octagon", all kinds of shapes.
还有很多其他的形状，有“斜方形”，有“菱形”，有“七边形”，有“八边形”，各种各样的形状。
If you're not sure, basically you can punch in the word you want.
如果你不确定，基本上你可以去查你想要的单词。
Just get a math book or Google "shapes", and you'll see all the different shapes that are available to you, both two-dimensional and three-dimensional.
只要找一本数学书或用谷歌搜索“形状”，你就会看到所有不同的形状，无论是二维的还是三维的。
Okay? There's too many of them to list here. These are the basics, we're going to work with these.
形状太多了，不能在这里一一列举。这些是基本的，我们会用到这些。
We're not done yet, though. There's still some more math stuff to come.
但是我们还没有讲完。还会有更多的数学内容。
We're going to look at the different types of triangles and the different angles that each of them will have.
我们来看看不同类型的三角形以及它们各自的角度。
Okay? Okay, almost done, don't worry. I know you're loving this math stuff, but we're almost done.
快讲完了，别担心。我知道你很喜欢数学，但是我们快讲完了。
We're going to look at some triangles and some angles next. Okay? So there are different types of triangles.
接下来我们要看一些三角形和角。所以这里有不同类型的三角形。
"Isosceles", "isosceles triangle "has two equal sides and one.
“等腰三角形”，“等腰三角形”有两条等边和另外一条边。
Two equal length sides, and one that's different, and "equilateral" has all three sides equal length.
两条等长的边，其中一条是不同的，“等边”三角形的三条边都是等长的。
By the way, just so you know, "lateral" means side, "equi" is equal or even, so "equilateral".
顺便说一下，你们知道，"lateral"的意思是面，“equi”是相等，所以是"equilateral"。
So, equilateral, all three sides are even.
等边三角形，三个边都相等。
And then when you have all three sides different length, we call this a "scalene", "scalene" triangle.
然后当这三条边的长度都不同时，我们叫它“不等边三角形”，“不等边三角形”。
Now, the... For example, the isosceles or the scalene, or really any much either of these two can also be a "right angle triangle".
例如，等腰三角形或不等边三角形，或者这两个中的任何一个都可以是直角三角形。
A "right angle" is this square here, it means 90 degrees.
直角是这里的角，是90度的角。
When you have a 90 degree angle and you want to measure its area,
如果它有一个90度的角，你想计算它的面积，
you have to use this line directly opposite to the right angle, and this line is called the "hypotenuse".
你必须用这条线直接对着直角，这条线叫做斜边。
"Hypotenuse", okay? You use that to calculate.
“斜边”，好吗？你用它来计算。
Now, when we're talking about triangles, or really any shape, like we can.
现在，当我们讨论三角形，或任何形状时，我们可以。
A rectangle in a box, in a rhombus, etc. we have angles and when you're talking about...
长方体中的矩形，菱形，等等。当你说到角的时候，
When we talk about angles we're talking about degrees. So, a circle is 360 degrees.
当我们讨论角时我们讨论的是角度。所以圆是360度。
Now, if I have just a straight line, that's basically like the diameter of a circle.
如果我有一条直线，那基本上就像一个圆的直径。
If you think of this as a circle, this is the diameter, so it's 180 degrees for a straight line.
如果你把它想成一个圆，这是直径，所以直线是180度。
So we have 360, 180, and then we have 90.
所以有360度，180度，然后是90度。
So when you have a line, when you have a square, when you have a straight line and another straight line directly on top of it making a square,
当你有一条直线，当你有一个直角，当你有一条直线，另一条直线在它的正上方形成一个直角，
a right angle, we call this a "perpendicular" line.
一个直角，我们把这条线叫做垂线。
This line is standing perpendicular to this line. Okay? We're going to get back to that in a second.
这条线垂直于这条线。好吧？我们马上就会再讲这个。
Now, let's look at some other angles. If you have an angle that is less than 90 degrees.
让我们看看其他的角度。如果你有一个小于90度的角，
Okay? I hope you can sort of see it in this diagram. Less than 90 degrees it's an "acute angle", "acute".
我希望你们能在这张图中看到它。小于90度是“锐角”。锐角。
Not "cute", "acute". Angle, sorry, not a good one. If you have...
不是“cute”，是“acute”。如果你，
If you have an angle that is more than 90 degrees we call this an "obtuse", "obtuse angle".
如果一个角大于90度的话我们叫它“钝角”，“钝角”。
And then if you have an angle that's more than 180, so for example if I'm measuring thing angle, it's more than 180 degrees, that's a "reflex angle".
如果你有一个大于180度的角，举个例子，如果我测量物体的角度大于180度，这就是“优角”。
So you have all these different angles to work with.
所以有很多不同的角。
Again, very important for those of you who are doing geometry and what not to know the names of these angles.
这对想知道这些角的说法对学几何或其他数学的人很重要。
Now, here we have a perpendicular line, means straight at 90 degrees or at a right angle to another line.
这里有一条垂线，意思是与另一条直线成90度或直角。
If it's not at a 90 degree angle, then it's on a "diagonal".
如果它不是90度角，那么它就是在“对角线”上。
So, diagonal is less or more than 90 degrees, it depends which way you're looking at it.
对角线的角小于或大于90度，这取决于你怎么看它。
Now, one last thing here, if you're looking at graphs.
最后一件事，如果你看图表的话。
Like, I'm not going to get into the details of the math here, but these two lines, they intersect at this point,
我不会在这里讨论数学的细节，但是这两条线，它们在这一点相交，
this is, like, usually the zero point base, whatever, at this point they intersect, cross.
这是，通常以零为底，不管怎样，在这一点它们相交。
Now, generally this is the "x axis", this is the "y axis", and in this graph you have two axes.
通常这是x轴，这是y轴，在这个图中有两个轴。
Singular: "axis", plural: "axes". Okay? So you know these lines. And finally we have "parallel lines".
单数：“axis”，复数：“axes”。好吧？所以你知道这些线。最后还有“平行线”。
Parallel lines are two lines that go in the same direction, but will never meet.
平行线是两条方向相同但永远不会相交的线。
Okay? So there's an equal distance between them, and that equal distance between them continues forever.
所以它们之间的距离相等，而且这个距离会一直保持不变。
They're running along the same direction, the same track apart from each other, they will never meet.
这两条线方向相同，彼此分开，它们永远不会相交。
Okay, so I think we've covered basically everything on this here.
所以我认为我们基本上已经涵盖了这方面的所有内容。
Now, before I finish, I just want to say one thing: I have just scratched the surface of math in this lesson.
在结束之前，我只想说一件事：我这节课讲的内容只触及了数学的皮毛。
I know math is huge, it's a huge field, I don't pretend to know even a bit about it, but I wanted to give this to you as a starting point.
我知道数学很庞大，这是一个很大的领域，我不会假装知道一点点，但我想用这节课给大家开一个头。
From here you can go on and do whatever math you do, whatever specialty you have. If you need to get into more...
从这里开始你可以继续学你的数学，任何你的专长。如果你需要学更多内容的话，
Like in more depth, more detailed math, you're going to have to look that up on your own because,
比如更深入，更详细的数学计算，你必须自己去查，因为，
again, I'm not going to be very helpful with the math part of it.
再说一遍，我不会对数学知识部分有任何帮助。
When you go to the forum at www.engvid.com to ask questions, please don't ask me any math questions.
当你去英格威论坛提问时，请不要问我任何数学问题。
You can ask me about words. Don't ask me to do any equations or anything like that.
你可以问我关于单词的问题。不要让我做任何方程或类似的东西。
Calculus, forget it; algebra, geometry, trigonometry, whatever. Here are your basics.
别问微积分，代数，几何，三角问题，等等。这里是基本的东西。
Okay? If you have any questions, though, of course do come to the engVid forum and ask them.
如果你有任何问题，当然要来engVid论坛问他们。
There's also going to be a quiz where you can practice with some of these words.
这里还有一个小测验，你可以用其中的一些词来练习。
If you like this video, and I hope you did, please subscribe to my YouTube channel.
如果你喜欢这个视频，我希望你喜欢，请订阅我的油管频道。
And again, I hope you enjoyed it and I'll see you again soon. Bye-bye.
再一次，我希望你们喜欢本期课程，我们很快会再见。再见。
