The magic of Vedic math - Gaurav Tekriwal

Transcriber: Andrea McDonough Reviewer: Bedirhan Cinar

翻译人员: Zhimin Lin 校对人员: Gabriella Hu

Nameste.

大家好。

I'm from India,

我来自印度，

and India is one of the oldest civilizations in the world.

一个有着世界上最古老的文化的国家。

It has contributed to the world

它为世界贡献了许多发明创造，

concepts such as yoga,

如瑜伽、

ayurveda,

阿育吠陀、

spicy chicken tikka,

辣咖喱鸡、

and Vedic math.

以及吠陀数学。

Vedic math is one of the world's easiest

吠陀数学是世界上最轻松

and simplest way to do math.

最简单的算术方法。

We are going to combine together

今天我们将一起

and do some number crunching today.

来做一些速算。

So what we are going to first do is multiply by 11.

首先我们要做的是把数字乘上11。

We're going to do it together,

我们一起来算

so if you blink, you're going to miss it.

所以你可能一眨眼就错过了，

So just watch it, OK.

所以睁大眼看清楚了。

So we're going to do 32 times 11, OK.

我们来算32乘11。

So we split 3, and we split 2,

我们把3和2分开

and we add 3 and 2 and paste it on top,

并把3和2相加后放在上面，

and we get the answer as 352.

就得到352。

That's it.

就这么简单。

Let's try another sum.

让我们再试一次。

45 times 11.

45乘11

Let's hear it.

是多少？

Exactly, that's 495.

对，495。

And 75 times 11.

那75乘11呢？

So it gives you 7,125,

你会得到7,125。

1 gets carried over and it becomes 825.

1被进一位，于是得到825。

That's how simple it is.

它就是这么简单。

OK, this is the principle behind it

好，这是它幕后的原理

where a is the coefficient.

这里a是个系数

Let's move on.

好了我们继续吧。

OK, now what we're going to do is the base method.

现在我们要用的是基数方法。

OK, this is used to multiply numbers

这是一个用来

将非常接近10的幂的数字相乘的方法，

very close to the powers of 10,

like 10, 100, 1,000, and so on.

像10、100、1000等等。

So we have a sum here, say 99 times 97.

这里我们举一个简单的计算，比如99乘97。

OK, now tell me, is 99 more than 100 or less than 100?

好，现在告诉我，99比100大还是小？

Less by how much?

小多少？

So we write minus 01.

那么我们就减01。

And 97 is less than 100 by how much?

97比100小多少？

So we write minus 03.

那我们就减03。

So what we're going to do is

我们接下来要做的是，

we're going to cross subtract

我们要交叉相减，

and get the first part of the answer, like this.

然后得到答案的第一部分，像这样。

We're going to do cross subtraction.

我们交叉相减，

97 minus 01 would give us

97减01等于

96.

96。

and we multiply 03 times 01 vertically,

然后在纵向上将03和01相乘，

and we get an answer of 03.

就得到03。

Let's check another sum.

再来算一组，

Try and do it yourselves.

大家自己试一下。

We got 98, which is,

98

is it more than a 100, less than 100?

比100大还是小？

By how much?

小多少？

And 97 is 3.

97（比100）小3，

So we got 98,

所以这里的98

we go crosswise,

交叉相减

we got 98 minus 3,

得到98减3，

or we can do 97 minus 2,

或者我们可以将97减2，

they'll all give you the same answer.

这是一样的。

So that would give us 95.

那么我们得到95，

And the second part would be

然后第二部分会是

06.

06。

So that's our answer.

这就是我们的答案。

OK, let's take a bigger number.

好，我们再来找一个更大的数。

Let's try this one.

我们来试试这个。

Here the base is 1,000.

在这里基数是1000，

So we got -004,

所以我们得到-004。

and 997 would be

997会得到

-003.

-003

We go crosswise like this,

我们像这样交叉相减，

and we get 996 minus 003 would give us

996减003等于

993,

993，

and 004 times 003 would give us

004乘003等于

012.

012，

And that's our answer.

这就是我们的答案。

Thank you.

谢谢！

14 times 12.

14乘12，

OK, here the base is 10.

好，这里的基数是10，

OK, so is 14 more than 10 or less than 10?

那么14大于还是小于10？

More, so we got plus 4,

大于，所以我们加4，

and 12, we got plus 2.

然后是12，我们加2，

Again, we apply the same rule,

我们再次应用同样的规律，

so we do 12 plus 4,

所以12加4

which gives us 16, like this.

得到16，

And we multiply 2 and 4, that gives us 8.

2乘4得到8。

So now, all of us here,

现在，在场的每一位，

we're going to do mental squaring, OK.

我们来心算乘方，

Everybody is going to participate here,

在座的每一位都来参与，

and we're going to do squares of numbers

我们将计算数字的平方，

more than 100 mentally right now.

心算比100大的数字。

So we got 101,

这里是101，

OK, now visualize on the board,

好，现在想象屏幕上

what's going to be on the right hand side.

右手边会发生什么？

Plus 01, so we got that.

加01，在这里。

OK, now we add plus sides, right?

好，现在我们加上右侧，对吧？

Yes? No?

对吗？

So we got 101 plus 01,

因此101加01，

that would give us

我们会得到

102,

102。

and, see here, like this.

然后这里，像这样，

And 01 is getting squared, right?

01被平方，对不对？

So that would give us

那会得到

01, and that's your answer.

01，这就是我们的答案。

Try the next one.

再试下一个，

Let's try 102 squared.

我们来试试102的平方，

Let's try, everybody.

大家都来试一下。

So 100,

100

so 102 would be

那么102会是

10404.

10404。

OK, now the next one, try it everybody together.

好，再试下一道，大家一起来试着做，

I'll give you 5 seconds.

我给你们5秒。

OK, let's say it together, let's say it together, OK.

好，我们一起说出来——

[10609]

10609。

10609 and that's the answer.

答案就是10609。

Woo!

哇！

104 squared, how much would that be?

104的平方会是多少？

Calculate it, 5 seconds.

5秒内算出来。

Come on, girls in the back.

加油，后面的女生。

OK, so the answer would be

所以答案会是——

10816.

10816。

OK, let's do the next one: 105 squared.

好，我们来做下一个：105的平方。

Oh, no, no, no, no,

噢不不不不，

we're going to try over, we're going to try over, OK?

我们再试一次，再试一次，好吗？

OK. I'll give you 5 seconds, just think about it.

好，我给你们5秒钟，仔细想想。

OK, now we're going to go, OK?

现在我们来说出答案，好吗？

11025.

11025。

OK, let's going to do the next one, 106 squared.

好，再尝试下一个，106的平方。

Try it, come one, everybody, it's simple and easy.

加油，大家都试一下，这很简单。

[11236]

11236。

OK, let's do it one more time.

好，再说一次——

11236.

11236。

Now 107, think, hold on, don't say anything out loud,

现在是107，想想看，等等，别出声，

just think mentally,

就在脑子里想。

107 squared.

107的平方。

OK, now let's say it out loud.

好，现在一起大声说——

11449.

11449。

And 108 squared.

108的平方。

[11664]

11664。

Fantastic, give yourself a round of applause, come on!

太棒了，给自己鼓鼓掌，来吧！

And this is the principle behind this,

背后的原理是这样的，

where a and b are the excesses

这里a和b是对于基数多余

or the deficiency from the base.

或者不足的部分。

I'm going to teach you

我会告诉你们，

in Vedic math, there are 16 sutras,

在吠陀数学中，有16道经

or word formulas, OK.

或者叫文字公式。

They are very visual

它们很直观，

and one of them is called, "vertically and crosswise,"

其中一个叫做“垂直和交叉”，

through which you can multiply any number

通过它你可以将任意数，

by any number in a single line.

与任意数在一列中相乘。

So I'm going to do a two-digit by a two-digit multiplication.

我会演示一个二位数与二位数的乘法。

Let's do this.

我们来看

So we got 31 times 12.

这里是31乘12，

OK, so we're going to apply

我们会使用

the vertically and crosswise sutra.

“垂直和交叉”经，

So we're going to do like this:

我们会这样做，

vertically, and then we're going to go crosswise,

垂直方向上，接着对角线上，

and then we're going to do vertical again.

然后再在垂直方向上。

So, 2 times 1 gives us

2乘1得出

[2],

2，

2 times 3 gives us

2乘3得到

[6],

6，

and 1 times 1 gives us

1乘1得到

[1].

1，

6 plus 1,

6加1

[7].

7，

1 times 3 gives us

1乘3得出

[3].

3，

And that's it, and that's our answer.

搞定，这就是我们的答案。

No more tedious calculations,

没有枯燥的计算，

no more going through the rough work,

没有困难的工作，

it's simple in one line.

只需要一列。

I want to show you a sum again,

我再来演示一次，

this time with carry-overs.

这一次带有进位，

The same formula, all of us here can do this, OK.

同样的公式，在场的每一位都能做到，

Same formula.

同样的公式，

So let's get started.

我们开始吧。

4 times 2 gives us

4乘2等于

[8].

8。

OK, now we go crosswise like this,

好，现在交叉，

so we're going to multiply 4 times 1,

我们要将4乘以1，

[4],

4

and 3 times 2,

3乘2，

[6]

6

4 plus 6 gives us

4加6，

[10].

10

So we put down 0, carry the 1.

因此我们写上0，对1进位，

And 3 times 1 gives us

3乘1等于，

[3],

3

plus 1,

[4].

加1，

4

Exactly, that's our answer, 408.

就是这样，答案是408。

OK, thank you for being such a participative audience,

好了，谢谢大家这么积极的参与，

and we had a great time number crunching.

我们在速算中过得很愉快。

Now I want to end with a question:

我想以一个问题来结束：

whether you'd like math to be dull or boring,

不管你觉得数学是无趣、无聊的，

or fun and interesting?

还是好玩和有趣的？

The choice is yours.

这是你们的选择。