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  • Hi. Welcome to www.engvid.com.

    你好,歡迎訪問www.engvid.com。

  • I'm Adam.

    我是亞當

  • In today's video I'm going to look at some math.

    在今天的視頻中,我將看一些數學知識。

  • Now, I know this is an English site, don't worry, I'm not actually going to do any math.

    現在,我知道這是一個英語網站,別擔心,我其實不會做任何數學。

  • Philosophy and English major, so math not my favourite, but I will give you some math

    哲學和英語專業,所以數學不是我的最愛,但我會給你一些數學。

  • terminology, words that you need if you're going to do math.

    術語,單詞,你需要 如果你要做數學。

  • Now, a lot of you might be engineers or you might be students who came from another country

    現在,你們中的很多人可能是工程師,也可能是來自其他國家的學生。

  • to an English-speaking country, and you go to math class and you know the math, but you're

    到一個英語國家,你去上數學課,你知道數學,但你是

  • not sure of the wording.

    不知道措辭。

  • Okay?

    好嗎?

  • So this is what we're looking at, terminology, only the words that you need to go into a

    所以這就是我們要看的,術語,只有你需要進入的詞,才是

  • math class or to do some math on your own.

    數學課或自己做一些數學題。

  • Okay?

    好嗎?

  • We're going to start with the very basics.

    我們要從最基本的開始。

  • You know all these functions already.

    這些功能你都已經知道了。

  • I'm just going to give you some ways to talk about them, and then we'll move on to some

    我只是給大家講一些關於它們的方法,然後我們再繼續講一些。

  • other functions and other parts.

    其他功能和其他部分。

  • So, you know the four basic functions: "addition", "subtraction", "multiplication", and "division".

    所以,你知道四個基本功能。"加法"、"減法"、"乘法 "和 "除法"。

  • What you need to know is ways to say an equation.

    你需要知道的是方程的說法方法。

  • Right? You know an equation.

    對吧?你知道一個方程式。

  • "1 + 1 = 2", that's an equation.

    "1+1=2",這是一個方程式。

  • "x2 + y3 = znth",

    "x2+y3=znth"。

  • that's also an equation which I'm not even going to get into.

    這也是一個方程式,我甚至不打算進入。

  • So, let's start with addition.

    那麼,我們就從加法開始。

  • The way to talk about addition.

    談到加法的方式。

  • You can say: "1 plus 1", "plus", of course is "+" symbol, that's the plus symbol.

    你可以說:"1加1"。"1加1","加",當然是 "+"號,就是加號。

  • "1 plus 1 equals 2."

    "1加1等於2"

  • 2 means the total, is also called the "sum".

    2是指總數,也叫 "和"。

  • Now, you can also say: "The sum of 1 and 1 is 2."

    現在,你也可以說:"1和1的總和是2。"1和1的總和是2."

  • You can also just say, without this part: "1 and 1 is 2."

    你也可以直接說,沒有這部分,"1和1是2"。"1和1是2"

  • So you don't need the plus, you don't need the equal; you can use "and" and "is", but

    所以你不需要加號,不需要等號,你可以用 "和"、"是",但

  • it means the same thing.

    它的意思是一樣的。

  • Everybody will understand you're making...

    大家都會明白你在做...

  • You're doing addition.

    你在做加法。

  • Sorry. Doing addition, not making.

    抱歉,我是在做加法,不是在做。是做加法,不是做。

  • If you add 1 and 1, you get 2.

    如果你把1和1相加,就會得到2。

  • Okay? So: "add" and "get", other words you can use to express the equation.

    好嗎?那麼,"加 "和 "得","加 "和 "得",你可以用其他詞來表達這個等式。

  • Now, if you're doing math problems, math problems are word problems.

    現在做數學題的話,數學題就是文字題。

  • I know a lot of you have a hard time understanding the question because of the words, so different

    我知道你們很多人很難理解這道題,因為文字,所以不同

  • ways to look at these functions using different words, different verbs especially.

    用不同的詞、不同的動詞,特別是用不同的詞來看這些函數的方法。

  • If we look at subtraction: "10 minus 5 equals 5".

    如果我們看減法。"10減5等於5"。

  • "5", the answer is also called the "difference".

    "5",答案也叫 "差"。

  • For addition it's the "sum", for subtraction it's "difference".

    對於加法是 "和",對於減法是 "差"。

  • "10, subtract 5 gives you 5."

    "10,減去5就得到5。"

  • Or: "10 deduct"-means take away-"5", we can also say: "Take 5 away"...

    或:"十扣"--意思是拿走--"五",我們也可以說。"拿走5"...

  • Oh, I forgot a word here. Sorry.

    哦,我忘了一個詞在這裡。對不起,我忘了一個詞。

  • "Take 5 away from 10, you get", okay?

    "十拿九穩",你懂嗎?

  • "10 subtract 5", you can say: "gives you 5",

    "10減去5",你可以說。"給你5"。

  • sorry, I had to think about that.

    對不起,我不得不考慮這個問題。

  • Math, not my specialty.

    數學,不是我的專長。

  • So: "Take 5 away from 5, you get 5", "Take 5 away from 5, you're left with",

    所以,"從5中取5,你得到5"。"從5中拿走5,你就得到5","從5中拿走5,你就剩下"。

  • "left with" means what remains.

    "剩下的 "是指剩下的東西。

  • Okay, so again, different ways to say the exact same thing.

    好吧,所以再次,不同的方式說完全相同的事情。

  • So if you see different math problems in different language you can understand what they're saying.

    所以,如果你看到不同語言的數學題,你就能明白他們在說什麼。

  • Okay?

    好嗎?

  • Multiplication.

    乘法。

  • "5 times 5", that's: "5 times 5 equals 25".

    "5乘以5",就是。"5乘以5等於25"。

  • "25" is the "product", the answer to the multiplication, the product.

    "25 "是 "積",是乘法的答案,是積。

  • "5 multiplied by 5", don't forget the "by".

    "5乘以5",別忘了 "以"。

  • "5 multiplied by 5 is 25", "is", "gives you", "gets", etc.

    "5乘以5是25","是","給你","得到 "等。

  • Then we go to division.

    然後我們再去分工。

  • "9 divided by 3 equals 3", "3", the answer is called the "quotient".

    "9除以3等於3","3",答案叫做 "商"。

  • This is a "q".

    這是一個 "q"。

  • I don't have a very pretty "q", but it's a "q".

    我的 "q "不是很好看,但它是一個 "q"。

  • "Quotient".

    "商數"。

  • Okay?

    好嗎?

  • "3 goes into... 3 goes into 9 three times",

    "3進..."3進9,3次"。

  • so you can reverse the order of the equation.

    所以你可以把等式的順序倒過來。

  • Here, when...

    在這裡,當...

  • In addition, subtraction, multiplication...

    加法、減法、乘法... ...

  • Well, actually addition and multiplication you can reverse the order and it says the

    嗯,其實加法和乘法你可以把順序反過來,上面寫著

  • same thing.

    同樣的事情。

  • Here you have to reverse the order: "goes into" as opposed to "divided by",

    這裡你要把順序顛倒過來。"進入 "與 "除以 "的順序相反。

  • so pay attention to the prepositions as well.

    所以也要注意介詞。

  • Gives you...

    給你...

  • Sorry. "3 goes into 9 three times", there's your answer.

    對不起,"3進入9的三次",這就是你的答案。"3進入9的三次",這就是你的答案。

  • "10 divided by 4", now, sometimes you get an uneven number.

    "10除以4",現在,有時你會得到一個不均勻的數字。

  • So: "10 divided by 4" gives you 2 with a remainder of 2, so: "2 remainder 2".

    所以:"10除以4 "得2,有餘數為2,所以"10除以4 "得到2,餘數為2,所以:"2除以2"。

  • Sometimes it'll be "2R2", you might see it like that.

    有時會是 "2R2",你可能會看到這樣。

  • Okay?

    好嗎?

  • So these are the basic functions you have to look at.

    所以這些是你必須要看的基本功能。

  • Now we're going to get into a little bit more complicated math things.

    現在我們要進入更復雜一點的數學事情。

  • We're going to look at fractions, exponents, we're going to look at some geometry issues,

    我們要看分數,指數,我們要看一些幾何問題。

  • things like that.

    這樣的事情。

  • Okay, so now we're going to look at something else.

    好了,現在我們要去看看別的東西。

  • We're going to look at fractions, exponents, and decimals.

    我們要研究分數、指數和小數。

  • Again, all of you know these things even from high school, even before high school, primary

    同樣,這些東西你們都知道,甚至從高中開始,甚至在高中之前,小學就知道了

  • school math some of this stuff.

    學校數學這一些東西。

  • A "fraction" is basically a partial number; it's not a whole number.

    "分數 "基本上是一個部分數,它不是一個整數。

  • It's a part of, that's why it's called a fraction.

    它是一部分,所以叫分數。

  • You have two parts to this fraction, you have the "numerator", "nu-mer-a-tor", and then

    這個分數有兩個部分,你有 "分子","nu-mer-a-tor",然後是

  • you have the bottom part which is the "denominator", "de-nom-in-at-or".

    你有最下面的部分,這是 "分母","de-nom-in-at-or"。

  • Numerator, denominator.

    分子,分母。

  • Now, the thing to know about fractions, now, how to add them, how to multiply them, that's

    現在,關於分數,現在要知道的是,如何加法,如何乘法,這是

  • a math lesson, we don't need to know that.

    一堂數學課,我們不需要知道。

  • We just need to know the words.

    我們只需要知道這些話。

  • What you might have some trouble with is pronunciation.

    你可能會有一些問題,就是發音。

  • So: "5 over 12", we don't say: "5 over 12", we say: "Five twelfths",

    所以說:"5比12",我們不說:"5比12",我們不說: "5比12",我們說:"5比12",我們說:"5個12"。

  • "fths", so you have a lot of consonants here.

    "fths",所以你這裡有很多輔音。

  • "Twelfths".

    "十二分"。

  • Now, keep in mind that even native English speakers have a hard time pronouncing this,

    現在,請記住,即使是以英語為母語的人也很難發這個音。

  • so if you find it difficult don't worry.

    所以,如果你覺得困難,不要擔心。

  • In context people will understand you.

    在上下文中,人們會理解你。

  • If you say: "Five twelfs", okay, I get it.

    如果你說:"5個12",好吧,我明白了。

  • If you say: "Five twelfth-th-th", I'll get it, I'll know what you're trying to say.

    如果你說,"五十二三",我就會明白,我就知道你想說什麼。"12月5日",我會明白的,我知道你想說什麼。

  • "Five sixths", this one's even worse, "xths".

    "六分之五",這個更慘,是 "四分之三"。

  • "Sixths", just say it as close as you can, you'll be understood because people know you're

    "六分",你就儘量說得近一點,就會被人理解,因為人家知道你是個。

  • talking about fractions.

    談到分數。

  • Okay?

    好嗎?

  • On the other side we can say, like, this is a half.

    另一邊我們可以說,比如,這是一個半。

  • Right?

    對吧?

  • 1 over 2, so a half.

    1比2,所以半。

  • We can say it in "decimals" as well.

    我們也可以用 "小數 "來說。

  • "Decimals" are the point form.

    "小數 "是點陣。

  • So, this is "0.5", I hope you can see this point here.

    所以,這就是 "0.5",希望大家在這裡能夠明白這個道理。

  • We don't say: "Zero decimal five", we don't say: "Zero period five", always "point".

    我們不說:"小數點後5位",我們不說:"小數點後5位"。"零點五期",總是 "點"。

  • Okay? "Zero point five".

    好嗎? - "零點五"。"零點五"。

  • Now: "Zero point thirty-three", no, because this is not a number, this is a partial number,

    現在的。"零點33",不,因為這不是一個數字,這是一個部分數字。

  • just like a fraction, it's less than one so it's not "thirty-three",

    就像一個分數,它小於一,所以它不是 "三十三"。

  • it's "zero point three, three".

    是 "零點三,三"。

  • And as many numbers as you have: "Zero point three, three, seven, eight, nine, ten".

    還有你有多少數字就有多少數字。"零點三,三,七,八,九,十"。

  • Well, no "ten", "one, zero".

    嗯,沒有 "這個","一,零"。

  • Okay? So, and the thing, and you can go as many decimal places as you want.

    好嗎? 所以,和事情,所以,和事情,你可以去 許多小數位,只要你想。

  • So this is a whole number, this is the decimal.

    所以這是一個整數,這是小數。

  • One, two, three, four, five, six decimal places, that's what we talk about after the decimal point.

    一、二、三、四、五、六位小數,這就是我們所說的小數點後的情況。

  • Okay?

    好嗎?

  • Now, this is the 10th or one-tenth, everything that's here.

    現在,這是第十或十分之一,這裡的一切。

  • So if you have "0.3", you have "three-tenths" of whatever it is you're talking about,

    所以,如果你有 "0.3",你有 "十分之三",不管你說的是什麼。

  • "one hundredth", "one thousandth", and then we go on from there, but we don't usually talk

    "百分之一","千分之一",然後我們繼續從那裡開始,但我們通常不會談論。

  • in these terms beyond the third because it gets a little bit too complicated.

    在這些條款中,超越第三種,因為它變得有點太複雜了。

  • Now, three...

    現在,三...

  • Where does this number...? First of all: "3/100", so first of all it's here...

    這個數字在哪裡...首先:"3/100",所以首先是在這裡... ...

  • Oh, no, it's not, that's thousandths.

    哦,不,不是,那是千分之一。

  • It's over here.

    它在這裡。

  • Okay? So, "3 hundredths", "3 hundredths".

    好嗎?所以,"百分之三","百分之三"。

  • Now, if you just say: "zz", like in "pizza", "3 hundredths", close enough, then, again,

    現在,如果你只是說。"zz",就像 "披薩 "中的 "三百分之一",足夠接近,然後,再來一次。

  • people will understand you.

    人們會理解你。

  • When you're talking about sports, for example, and they say there's like point-five seconds

    當你在談論體育,例如, 他們說有像點五秒,

  • left on the clock, so he...

    剩下的時間,所以他... ...

  • The guy, basketball, he shoots it, he scores with a tenth of a second left in the game.

    那個人,籃球,他投籃,他在比賽還剩十分之一秒的時候就得分了。

  • So you understand?

    所以你明白了嗎?

  • They're talking about 0.1 second.

    他們說的是0.1秒。

  • Okay.

    好吧,我知道了

  • Next we have "exponents".

    接下來我們有 "指數"。

  • X with a small "2" or a small "3" or whatever number.

    X用小 "2 "或小 "3 "或任何數字。

  • So this whole thing is called...

    所以這整個事情叫做...

  • The "2" is actually called the exponent, the x or whatever number is called the base, and

    這個 "2 "其實叫指數,x或什麼數字叫基數,而

  • we can also refer to this as "the power".

    我們也可以將其稱為 "權力"。

  • So, the whole thing is the "exponent", "base", and "power".

    所以,整個就是 "指數"、"基數"、"動力"。

  • Now, when we talk about: "X to the power of 2", we don't say: "to the power of 2".

    現在,當我們談論,"X的2次方",我們不會說:"到2的倍數"。

  • When the number is 2, we say: "squared", so: "X squared".

    當數字是2時,我們說。"平方",所以:"X的平方"。

  • When we talk about "3", we say: "cubed".

    當我們說到 "3 "的時候,我們說。"立方"。

  • Okay?

    好嗎?

  • So we're going to look in a second, and we're going to look at measuring area of a shape

    所以我們馬上要看一下,我們要看一下形狀的面積測量。

  • or measuring the volume of a shape.

    或測量形狀的體積。

  • Different shapes, of course, but "area" is measured with "x2" or whatever the measurement

    當然,形狀不同,但 "面積 "是用 "x2 "或其他什麼測量方法來測量的。

  • is squared, and the volume is measured with "cubed".

    是平方,體積用 "立方 "來衡量。

  • Okay?

    好嗎?

  • Now, once you get past the third-four, five, six-there's two ways you can say it, you can say:

    現在,一旦你過了三四五六,有兩種說法,你可以說。

  • "X to the 4th power", if this is a "4": "X to the 4th power",

    "X到第4次冪",如果這是一個 "4"。"X到第4次方"。

  • or "X to the power of 4".

    或 "X的4次方"。

  • Now, sometimes you might see...

    現在,有時你可能會看到...

  • You might hear this expression: "The nth power".

    你可能會聽到這樣的表述:"第N個權力"。

  • "The nth power" means unlimited, it goes on forever, or infinite, we don't know where

    "第n次冪 "的意思是無限的,它一直持續下去,或者是無限的,我們不知道在哪裡。

  • it ends but this is actually an expression used in regular English as well, and we'll

    結尾,但這其實也是常規英語中使用的表達方式,我們會用

  • talk about that another time.

    下次再談吧

  • Now, if you're going the opposite direction, instead of squaring the number you want to

    現在,如果你要往相反的方向走,而不是把你想要的數字平方化,你要

  • find the "root" of the number.

    找到數字的 "根"。

  • So, 3 squared equals 9.

    所以,3的平方等於9。

  • Okay?

    好嗎?

  • The square root of 9 is 3.

    9的平方根是3。

  • How many times does 3 go into 9?

    3進入9的次數是多少?

  • 3 times, etc.

    3次,等等。

  • "Square root", finding out how many times the number goes into itself.

    "平方根",找出這個數進自己的多少倍。

  • X2, multiplying the number by itself two times.

    X2,把這個數乘以自己的2倍。

  • Okay.

    好吧,我知道了

  • So far so good, but we're not done yet.

    到目前為止還不錯,但我們還沒有完成。

  • We still have to look at shapes and what to do with them, and angles.

    我們還是要看形狀,怎麼處理,還有角度。

  • A lot more interesting stuff coming up. One sec.

    還有更多有趣的事情要發生。一秒鐘。

  • Okay, so actually we're going to look at a couple more symbols and words before we go

    好了,所以實際上我們要看 在我們去之前,一對夫婦更多的符號和單詞。

  • on to other more complicated things.

    到其他更復雜的事情。

  • I wanted to just squeeze these in because they're a little bit simple, but still need

    我想把這些擠進來,因為它們有點簡單,但還是需要。

  • to understand them.

    來了解他們。

  • "Average" and "mean", now, "average" and "mean" are synonyms, they essentially mean the same thing.

    "平均 "和 "平均",現在,"平均 "和 "平均 "是同義詞,它們本質上是同一個意思。

  • We use "mean" more with math.

    我們用 "平均 "與數學的關係比較大。

  • We use "average" more with other things, like everyday things as well.

    我們更多的是用 "平均 "來搭配其他事物,比如日常事物也是如此。

  • But they mean the same thing.

    但他們的意思是一樣的。

  • So when you're looking for the average or the mean, you're taking all the values...

    所以,當你在尋找平均值或均值時,你要把所有的值... ...

  • So in this case we have one, two, three, four values, you add them up, you take the total

    所以,在這種情況下,我們有一個,兩個,三個,四個值,你把它們加起來,你把總。

  • and then divide it by the number of values you started with.

    然後除以你開始的值的數量。

  • So the...

    所以...

  • We have four values, the total 20 divided by 4, and the average of these values is 5.

    我們有4個數值,總共20除以4,這些數值的平均值是5。

  • Okay?

    好嗎?

  • So that's "average" or "mean".

    所以這就是 "平均 "或 "平均"。

  • Now, on the other hand, you want to sometimes look for the "median".

    現在,另一方面,你有時要尋找 "中位數"。

  • Now, some...

    現在,有些...

  • In some situations you don't want the mean or the average because the extremes, the top

    在某些情況下,你不想要平均數或平均值,因為極端值、頂部

  • or the bottom are so far apart that the average will not give you a right idea of what's going

    或底部相距太遠,平均數不會給你一個正確的想法是什麼回事

  • on with whatever values you're looking at, so what you want is the "median".

    所以你想要的是 "中位數"。

  • The "median" is more like the middle number that has an equal number of values above it

    "中位數 "更像是一箇中間數,它上面的數值是相等的

  • and an equal number of values below it.

    並在其下方有相同數量的數值。

  • So that's a little bit more representative of the situation you're looking at.

    所以,你看的這種情況比較有代表性。

  • Okay, so now we're going to look at these symbols.

    好了,現在我們來看看這些符號。

  • We got this one, this one, this one, and this one - four of them.

    我們得到了這個,這個,這個,這個,還有這個--四個人。

  • Now, this one, when you have the bigger size open and then it goes to the smaller size

    現在,這一個,當你有較大的尺寸打開,然後它轉到較小的尺寸。

  • means y is larger than x.

    表示y大於x。

  • Larger, smaller, right?

    大一點,小一點,對吧?

  • So, y is larger than x, y is greater than x, y is more than x.

    所以,y比x大,y比x大,y比x多。

  • Don't forget the "than" because, again, you have a comparative here.

    不要忘了 "比",因為,你在這裡又有一個比較。

  • And if you turn it around, y is smaller than, y is less than x.

    而如果把它轉過來,y小於,y小於x。

  • Now, sometimes you might see these symbols with a line underneath, in which case:

    現在,有時你可能會看到這些符號下面有一條線,在這種情況下。

  • y is greater than or equal to x. Okay?

    y大於或等於x,好嗎?

  • Y is greater than or equal to x, y is less than or equal to...

    Y大於或等於x,y小於或等於......。

  • Sorry, y is greater...

    對不起,Y是大...

  • Less than or equal to x.

    小於或等於x。

  • And now, this one you have...

    而現在,這個你有...

  • Basically you have the equal sign, but then you have a squiggly line.

    基本上你有一個等號,但你有一個斜線。

  • This means it's approximately equal to, so it's an approximation, not exactly equal.

    這意味著它大約等於,所以這是一個近似值,而不是完全等於。

  • And then you have the equal sign with a strike through, and in this case it's just not equal.

    然後你有一個等號與罷工通過,在這種情況下,它只是不平等。

  • Okay, pretty straightforward stuff.

    好吧,很直接的東西。

  • Let's move on to some other more complicated things.

    我們再來看看其他更復雜的事情。

  • Okay, let's look at some more math stuff.

    好吧,讓我們再看看一些數學的東西。

  • We're going to look at shapes.

    我們來看看形狀。

  • Okay?

    好嗎?

  • So, first of all we're going to start with our "rectangle", means the two sides...

    所以,首先我們要從我們的 "矩形 "開始,也就是兩邊... ...

  • All four sides are not the same length.

    四面的長度都不一樣。

  • You have the "width", you have the "length".

    你有 "寬度",你有 "長度"。

  • Okay?

    好嗎?

  • Now, when you add a "height" or a "depth", both okay, depending on what you're looking at, then you...

    現在,當你添加一個 "高度 "或 "深度",兩者都沒問題,這取決於你在看什麼,然後你...

  • First of all, you've created a box.

    首先,你已經創建了一個盒子。

  • So, a rectangle is two-dimensional, a box is three-dimensional.

    所以,長方形是二維的,盒子是三維的。

  • Width, length, height or depth, both okay.

    寬度、長度、高度或深度,都可以。

  • Now, when you measure these, when you measure...

    現在,當你測量這些,當你測量... ...

  • Like, basically you want to measure the inside space, then you're measuring the area.

    就像,基本上你要測量裡面的空間,那麼你就在測量面積。

  • So you do length times width, and then the answer is whatever the number is.

    所以你做的是長度乘以寬度,然後答案是什麼數字。

  • So let's say you have two feet by four feet, so you have eight, and then the measure...

    所以我們假設你有兩英尺乘四英尺,所以你有八個,然後測量... ...

  • If you're measuring in metres, in feet, in inches, in kilometres, whatever, and then

    如果你的測量組織、部門是米,英尺,英寸,公里,不管是什麼,然後。

  • you have the square.

    你有廣場。

  • So, whatever 20 metres square, 20 square metres, etc.

    所以,什麼20米見方、20平方米等。

  • With...

    有了...

  • When you add the third dimension now you're measuring volume and you're using the 3, the

    當你增加第三個維度的時候,現在你在測量體積,你在用3的時候,你在用。

  • exponent 3 instead of the exponent 2.

    指數3而不是指數2。

  • Okay?

    好嗎?

  • Now, other shapes.

    現在,其他形狀。

  • We have a "square", all four sides are equal.

    我們有一個 "正方形",四條邊都是相等的。

  • When you put in the extra measure, the extra side, then you have a depth to it,

    當你把多餘的量,多餘的面,那麼你就有了深度。

  • then you have a "cube". Okay? So...

    那麼你就有一個 "立方體"。好嗎? - 所以...那麼...

  • And, again, another way to think about this: This is two-dimensional, that's why it's squared;

    而且,又是另一種思路。這是二維的,這就是為什麼它是平方的。

  • this is three-dimensional, cubed.

    這是立體的,立體的。

  • Okay.

    好吧,我知道了

  • A "circle" or a "sphere".

    一個 "圓 "或一個 "球"。

  • Now, I can't draw a sphere because I'm not a very good artist, like if I do like this...

    現在,我不能畫一個球體,因為我不是一個很好的藝術家,就像如果我喜歡這個... ...

  • You know, like a moon, like a ball is a sphere.

    你知道,像月亮,像球是一個球體。

  • The flat shape is the circle.

    扁形就是圓。

  • If you want to measure the outside of the circle then you're looking...

    如果你想測量圓的外側,那麼你要找... ...

  • You're trying to measure the "circumference".

    你是想測量 "周長"。

  • Sorry, I forgot to mention, if you want to measure the outside area of the rectangle,

    對不起,我忘了說,如果你想測量長方形的外面積。

  • you're measuring the "perimeter", same for square.

    你測量的是 "周長",正方形也一樣。

  • For a circle you're measuring the circumference.

    對於圓來說,你要測量的是周長。

  • If you want to measure the volume of a sphere then you're starting to get into things like

    如果你想測量一個球體的體積,那麼你就會開始接觸到一些東西,如

  • "radius", so our radius is from the centre to one side, that's half the distance from

    "半徑",所以我們的半徑是從中心到一邊的距離,也就是一半的距離。

  • side to side.

    側面的。

  • If you want to go the full distance, then you have the "diameter".

    如果你想走完全程,那麼你就有了 "直徑"。

  • "Radius", "diameter", full length, basically cutting it in half, equal points.

    "半徑","直徑",全長,基本切成兩半,等分。

  • So that's the circle.

    所以這就是圈子。

  • Then you start...

    然後你開始...

  • If you want to get into the actual measurements then you start having to look at "pi".

    如果你想進入實際的測量,那麼你開始不得不看 "pi"。

  • Okay? Just that's how it's spelled, "pi", from the...

    好嗎?只是這就是它的拼寫,"π",從... ...

  • I think Greek, if I'm not mistaken, the letter.

    我想希臘語,如果我沒記錯的話,信。

  • Now, we're getting into "triangles".

    現在,我們要進入 "三角形 "了。

  • We're going to look at triangles again in a minute, but for now the two-dimensional

    我們稍後將再次研究三角形,但現在二維的

  • triangle.

    三角形。

  • Now, three-dimensional you can have a "pyramid", you can have the base and then you have the

    現在,立體的你可以有一個 "金字塔",你可以有基礎,然後你有一個 "金字塔"。

  • sides coming up to an apex.

    兩邊來了一個頂點。

  • "Apex" means top point of something, or you can have a "prism" where you have the extra

    "Apex "的意思是指東西的頂點,也可以有一個 "稜鏡",在那裡你有額外的

  • side on this side.

    邊在這邊。

  • Okay? So, triangle, pyramid, prism.

    好嗎?所以,三角形,金字塔,稜鏡。

  • But then we have other shapes like "oval", this is like a "cone", like an ice cream cone.

    但是我們還有其他的形狀,比如說 "橢圓形",這個就像 "圓錐體",就像冰淇淋的圓錐體。

  • And there's a bunch of other shapes, there's a "rhombus", there's a "diamond", there's

    還有很多其他的形狀,有 "菱形",有 "菱形",有 "菱形",有 "菱形"。

  • a "hectagon", there's an "octagon", all kinds of shapes.

    一個 "公頃",還有一個 "八角",各種形狀。

  • If you're not sure, basically you can punch in the word you want...

    如果你不確定,基本上你可以打入你想要的字... ...

  • Just get a math book or Google "shapes", and you'll see all the different shapes that are

    只要找一本數學書或谷歌 "形狀",你就會看到所有不同的形狀,都是。

  • available to you, both two-dimensional and three-dimensional. Okay?

    提供給你,無論是二維還是三維的。好嗎?

  • There's too many of them to list here.

    太多了,這裡就不一一列舉了。

  • These are the basics, we're going to work with these.

    這些都是基礎知識,我們要用這些。

  • We're not done yet, though.

    但我們還沒有完成。

  • There's still some more math stuff to come.

    還有一些數學方面的東西。

  • We're going to look at the different types of triangles and the different angles that

    我們要看看不同類型的三角形和不同的角度,這就是

  • each of them will have. Okay?

    他們每個人都會有。好嗎?

  • Okay, almost done, don't worry.

    好了,快好了,別擔心。

  • I know you're loving this math stuff, but we're almost done.

    我知道你很喜歡這些數學的東西,但我們快完成了。

  • We're going to look at some triangles and some angles next.

    接下來我們要看一些三角形和一些角。

  • Okay?

    好嗎?

  • So there are different types of triangles.

    所以三角形有不同的類型。

  • "Isosceles", "isosceles triangle" has two equal sides and one...

    "等腰三角形"、"等腰三角形 "有兩條相等的邊和一...

  • Two equal length sides, and one that's different, and "equilateral" has all three sides equal length.

    兩條等長的邊,還有一條是不同的。"等邊 "的三條邊長度都相等。

  • By the way, just so you know, "lateral" means side, "equi" is equal or even, so "equilateral".

    對了,你要知道,"側 "是指側面,"等 "是相等或均勻,所以 "等邊"。

  • So, equilateral, all three sides are even.

    所以,等邊,三邊都是偶數。

  • And then when you have all three sides different length, we call this a "scalene", "scalene" triangle.

    然後當你的三條邊都有不同的長度時,我們稱之為 "scalene","scalene "三角形。

  • Now, the...

    現在,這個...

  • For example, the isosceles or the scalene, or really any much either of these two can

    比如說,等腰三角形或者等腰三角形,或者真正的任何一個這兩個都可以。

  • also be a "right angle triangle".

    也是一個 "直角三角形"。

  • A "right angle" is this square here, it means 90 degrees.

    一個 "直角 "就是這裡的這個方塊,它的意思是90度。

  • When you have a 90 degree angle and you want to measure its area, you have to use this

    當你有一個90度的角,你想測量它的面積,你必須使用這個方法。

  • line directly opposite to the right angle, and this line is called the "hypotenuse".

    與直角正對的線,這條線稱為 "斜邊"。

  • "Hypotenuse", okay?

    "下弦",好嗎?

  • You use that to calculate.

    你用這個來計算。

  • Now, when we're talking about triangles, or really any shape, like we can...

    現在,當我們在談論三角形,或任何形狀,就像我們可以... ...

  • A rectangle in a box, in a rhombus, etc., we have angles and when you're talking about...

    盒子裡的長方形,菱形裡的長方形等,我們有角度,當你在談論... ...

  • When we talk about angles we're talking about degrees.

    當我們談論角度時,我們談論的是度數。

  • So, a circle is 360 degrees.

    所以,一個圓是360度。

  • Now, if I have just a straight line, that's basically like the diameter of a circle.

    現在,如果我只有一條直線,那基本上就像一個圓的直徑。

  • If you think of this as a circle, this is the diameter, so it's 180 degrees for a straight line.

    如果你把這個看成一個圓,這就是直徑,所以是180度的直線。

  • So we have 360, 180, and then we have 90.

    所以我們有360,180,然後我們有90。

  • So when you have a line, when you have a square, when you have a straight line and another

    所以,當你有一條線,當你有一個正方形,當你有一條直線和另一個。

  • straight line directly on top of it making a square, a right angle,

    直線直接在上面做一個正方形,一個直角。

  • we call this a "perpendicular" line.

    我們稱之為 "垂直 "線。

  • This line is standing perpendicular to this line.

    這條線與這條線垂直而立。

  • Okay?

    好嗎?

  • We're going to get back to that in a second.

    我們馬上就會回到這個問題上。

  • Now, let's look at some other angles.

    現在,我們來看看其他一些角度。

  • If you have an angle that is less than 90 degrees...

    如果你的角度小於90度... ...

  • Okay?

    好嗎?

  • I hope you can sort of see it in this diagram.

    希望你能從這張圖中算是看出來了。

  • Less than 90 degrees it's an "acute angle", "acute".

    小於90度是 "銳角","銳角"。

  • Not "cute", "acute".

    不是 "可愛",是 "急性子"。

  • Angle, sorry, not a good one.

    角度,對不起,不是很好。

  • If you have...

    如果你有...

  • If you have an angle that is more than 90 degrees we call this an "obtuse", "obtuse angle".

    如果你的角度超過90度,我們稱之為 "鈍角"、"鈍角"。

  • And then if you have an angle that's more than 180, so for example if I'm measuring

    然後,如果你有一個角度超過180,所以,例如,如果我在測量

  • thing angle, it's more than 180 degrees, that's a "reflex angle".

    事角度,超過180度,那就是 "反射角"。

  • So you have all these different angles to work with.

    所以你有所有這些不同的角度來工作。

  • Again, very important for those of you who are doing geometry and whatnot to know the

    同樣,對於那些做幾何學和什麼的人來說,非常重要的是要知道的是

  • names of these angles.

    這些角度的名稱。

  • Now, here we have a perpendicular line, means straight at 90 degrees or at a right angle

    現在,這裡我們有一條垂直線,意思是90度直角或直角。

  • to another line.

    到另一行。

  • If it's not at a 90 degree angle, then it's on a "diagonal".

    如果不是90度角,那就是在 "對角線 "上。

  • So, diagonal is less or more than 90 degrees, it depends which way you're looking at it.

    所以,對角線小於或大於90度,要看你從哪個角度看。

  • Now, one last thing here, if you're looking at graphs...

    最後一件事,如果你在看圖... ...

  • Like, I'm not going to get into the details of the math here, but these two lines, they

    就像,我不打算進入這裡的數學細節, 但這兩行,他們是誰?

  • intersect at this point, this is, like, usually the zero point base, whatever, at this point

    在這一點上相交,這是一樣,通常是零點基點,什麼的,在這一點上

  • they intersect, cross.

    它們相交、交叉。

  • Now, generally this is the "x axis", this is the "y axis", and in this graph you have two axes.

    現在,一般來說,這是 "x軸",這是 "y軸",在這個圖中,你有兩個軸。

  • Singular: "axis", plural: "axes".

    單數:"軸",複數:"軸"。

  • Okay?

    好嗎?

  • So you know these lines.

    所以,你知道這些線路。

  • And finally we have "parallel lines".

    最後我們還有 "平行線"。

  • Parallel lines are two lines that go in the same direction, but will never meet.

    平行線是指兩條方向相同,但永遠不會相交的線。

  • Okay?

    好嗎?

  • So there's an equal distance between them, and that equal distance between them continues forever.

    所以他們之間的距離是相等的,而且他們之間的相等距離永遠持續下去。

  • They're running along the same direction, the same track apart from each other, they

    他們沿著相同的方向,相同的軌道奔跑,他們彼此相隔,他們

  • will never meet.

    將永遠不會見面。

  • Okay, so I think we've covered basically everything on this here.

    好吧,所以我想我們已經覆蓋 基本上一切在這裡。

  • Now, before I finish, I just want to say one thing:

    現在,在我結束之前,我只想說一件事。

  • I have just scratched the surface of math in this lesson.

    這節課的數學知識我只是蜻蜓點水。

  • I know math is huge, it's a huge field, I don't pretend to know even a bit about it,

    我知道數學很龐大,這是一個龐大的領域,我不裝作對它一知半解。

  • but I wanted to give this to you as a starting point.

    但我想把這個給你作為一個起點。

  • From here you can go on and do whatever math you do, whatever specialty you have.

    從這裡開始,你可以繼續做你所做的任何數學,任何專業。

  • If you need to get into more...

    如果你需要進入更多...

  • Like in more depth, more detailed math, you're going to have to look that up on your own

    像更深入,更詳細的數學,你得自己去查了。

  • because, again, I'm not going to be very helpful with the math part of it.

    因為,同樣,我也不會對數學部分很有幫助。

  • When you go to the forum at www.engvid.com to ask questions, please don't ask me any math questions.

    當你去論壇www.engvid.com,提問時,請不要問我任何數學問題。

  • You can ask me about words.

    你可以問我的話。

  • Don't ask me to do any equations or anything like that.

    不要讓我做任何方程式或類似的東西。

  • Calculus, forget it; algebra, geometry, trigonometry, whatever.

    微積分,算了吧,代數、幾何、三角函數什麼的都可以。

  • Here are your basics. Okay?

    這是你的基礎知識。好嗎?

  • If you have any questions, though, of course do come to the engVid forum and ask them.

    如果你有什麼問題,當然要到engVid論壇來問。

  • There's also going to be a quiz where you can practice with some of these words.

    還會有一個測驗,你可以用其中的一些單詞來練習。

  • If you like this video, and I hope you did, please subscribe to my YouTube channel.

    如果你喜歡這個視頻,我希望你喜歡,請訂閱我的YouTube頻道。

  • And again, I hope you enjoyed it and I'll see you again soon.

    也再次希望你喜歡,我們很快就會再見面。

  • Bye-bye.

    掰掰

Hi. Welcome to www.engvid.com.

你好,歡迎訪問www.engvid.com。

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