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  • Hi this is Presh Talwalkar and today I am going to explain a math trick

    我是Presh Talwalkar,今天我來介紹一個數學小把戲

  • of how you can multiply numbers just by drawing lines.

    教你怎麼用畫線來算乘法

  • Let's say you want to multiply 12 by 13

    假設你要算 12乘以 13

  • For this one we will draw one line

    我們先畫一條線(代表 12的十位數)

  • and for the two we will leave a little bit of space

    然後稍留點空間,代表個位數的2

  • and we will draw two lines.

    再畫兩條線,

  • For the other number, we will draw lines in the other direction.

    至於另一個數13,則畫在另一個方向

  • Now we will group together different lines and we will count the dots.

    現在,把這些線加以分組,然後計算交叉點

  • Here we have six different dots.

    這裡有6 個點(代表個位數)

  • In the middle we have five different dots.

    中間有五個點

  • And on the other side we have one dot.

    另一端,我們有五個點

  • And that's the answer 156.

    所以答案是156

  • We will do another example.

    再算另一題

  • For 15 by 21,

    15乘以 21

  • we start out by drawing one line.

    先畫一條十位數的線

  • Then we'll leave a little bit space and draw five lines.

    然後一樣留點空間再畫五條線

  • For the other number we draw lines in the other direction.

    至於另一個數 21,則從另一端畫起

  • We draw two lines here and one line here.

    畫出十位數的兩條線和個位數的一條線

  • We will again group the different lines

    再把不同的線加以分組

  • Here we have five dots.

    這裡有五個交叉點

  • In the middle we have eleven dots.

    在中間,可以算出有十一個點

  • And the other end we have two dots.

    另一端則有兩個點

  • We will need to make one adjustment because we have 11.

    這裡要稍微調整一下,因為有兩位數 11

  • We will need to carry this one over which will make 3.

    需要進位,移項後百位數變成 3

  • And our answer is 315.

    得到答案 315

  • We can even do this for bigger numbers.

    接著我們可以來算更大的數目

  • For 123 we start out with one line and with some space two lines. And with some more space three lines.

    123,從百位的 1條線畫起,稍遠處則畫兩條線代表 10位數的 2,接著留點空間畫個位數的 3

  • And we draw the other lines for the other number in the other direction.

    另一個方向則分別畫出321

  • We again group the lines.

    將這些線分組

  • We have three dots here,

    這裡有三個點

  • eight dots here,

    這裡有八個

  • fourteen,

    中間十四個

  • eight,

    八個

  • and three.

    以及三個

  • Once again we're going to have to carry this one over (from the 14).

    必須再一次從中間的十四,進一位

  • So that's our answer.

    得出答案

  • It'll be 39,483.

    39,483

  • You can even use this trick when a number includes 0.

    這個小把戲一樣可以用在數字中包含 0的

  • But one thing is when you draw this line you should still draw the line, but

    當你畫線時還是要把它畫出來,但是

  • put it in a different color or different marking.

    要用不顏色或不同記號

  • And the trick will be that we don't count any of the dots for that line

    但是在計算交叉點時,與這條淺色線相交的不予計入

  • So when we make the grouping, we have three dots here.

    所以分組後,這裡有3個點

  • For the second arrangement,

    而在倒數第二個分組

  • we're only going to count the dots for the non-zero lines.

    我們只計算非「零」的線

  • So we have six dots here. We don't count any of the intersections for the zero line.

    所以這裡有六個點,任何與「零」線交叉的統統不算

  • In the middle, we again ignore the zero line, which makes seven.

    中間零線全部可以跳過,所以算出七個點

  • Here we have two dots.

    這裡有兩點

  • And two dots here.

    這裡也有兩個點

  • So you can even use this method when you have a number that includes zero.

    因此即便數字中包含零的,一樣可用這個方法來計算

  • The reason it works is you can even use it for algebraic equations.

    同理,你也可以運用它來計算代數方程式

  • Let's say you have x plus 2y times x plus 3y.

    假設你要算 x+2y 乘以 x+3y

  • We will draw one line for the x,

    我們先畫一條線代表x

  • and we will draw two lines for the 2y and we will draw the lines in blue.

    再畫兩條線代表2y,特別用藍線代表

  • We will put all the x lines in black and all the y lines in blue.

    所有的x 都以黑線表示,y則用藍線表示

  • The other number we draw the lines in the other direction

    另一個刮號內的數,畫在另一個方向

  • And again we make groupings.

    再次分組

  • So here we have six dots and because

    這裡有六個點,而因為

  • both of the lines are blue that means it's y-squared.

    兩條線都是藍色的,意謂它是y平方

  • In the middle we have five dots,

    中間部分則有五個點

  • and these are the intersections of a black and blue line,

    交叉部分則是各一條黑、藍色線

  • which means it will be an x and a y.

    代表一個x 一個 y

  • On the end we just have one dot and that's for two black lines so it's x-squared.

    在左端,有一個點以及兩條黑線,代表x的平方

  • So that's the answer.

    得出答案

  • I hope you enjoyed this trick. Please subscribe to my channel. I make videos on math and game theory.

    希望你能享受這個數學小把戲,未來我還會錄製數學和遊戲理論的短片,請訂閱我的頻道

  • You can follow me on Twitter @preshtalwalkar, and get my ebooks on Amazon.com

    可以在 Twitter @preshtalwalkar 追蹤到我,或者上亞馬遜購買電子書

Hi this is Presh Talwalkar and today I am going to explain a math trick

我是Presh Talwalkar,今天我來介紹一個數學小把戲

字幕與單字

影片操作 你可以在這邊進行「影片」的調整,以及「字幕」的顯示

A2 初級 中文 美國腔 位數 代表 計算 代數 數學 平方

通過畫線來乘以數字和代數方程。 (Multiply Numbers And Algebra Equations By Drawing Lines)

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    噹噹 發佈於 2021 年 01 月 14 日
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