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达人用砖块向你解释双重多米诺效应 – 译学馆
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达人用砖块向你解释双重多米诺效应

The Brick Double-Domino Effect Explained

[开场音乐]
[Music]
最近我偶然发现一个新的双重多米诺效应
I recently came across a new double domino effect
那就是多米诺砖块
that uses brick.
现在 我正在一个建筑工地
So, I’m on a construction site
这里的人非常慷慨地借给了我48块砖头
where they’ve very kindly lent me 48 bricks.
我们要推倒这些砖头 然后看看效果如何
We’re going to knock them over, and see if it works.
好的 让我们开始吧
Okey, here we go.
[砖块当当当地接连倒地]
[bricks clunking]
[回来的时候倒地速度加快了]
[bricks clunk faster]
啊!
Aaahhh!
怎么会这样 有一块没倒
Come on, that one brick.
[砖块再次快速倒下]
[bricks clunk fast again]
大功告成了
There we go.
所有砖块全都倒了
That toootally counts.
[最后一块砖倒地]
[final brick clunks]
好吧 刚刚那次实验效果算是不错的
Okey, i’m going to count that as effectively working well,
仅仅中断了一小会儿
to a bit stopped.
但是你可以看到 我所在的地面十分不平坦
But as you can see, I’m on a very uneven ground,
并且地面有些向上倾斜
and it’s actually sloping uphill a bit,
所以我其实还是挺开心的
so I’m pretty happy with only one,
只有1块半在回来的时候卡住了
one and a half stoppages on the way back up.
所以 砖块像多米诺骨牌一样一个个倒下
So, the wave on the way down of the
形成的波形
effectively dominoes falling over,
非常直接连贯
is all very straight-forward.
这就是一个标准的多米诺效应
That’s ya standard domino effect.
第二个返回的波浪
The second wave that comes back up again,
就比第一次过去的时候有趣多了
there’s a lot more interesting,
我们可以运用数学知识解释其中的原理
and we can look at the mathematics of why that happens.
我先将砖块都水平地放在适当的位置
So I started with the bricks lying pretty much in position,
之后将它们都以一块砖的距离间隔立起来
and then lifted them all up, onto one end,
当它倒下的时候就会像多米诺骨牌一样
but it fall over like dominoes.
但是 当它们一个个倒下的时候
But, when they fall over,
如果有一块砖不能够平直地倒下
if they can’t fall all the way flat,
下一块就会倒在
the next one ends up resting just
前面那一块的边缘
on the edge of that one,
这一块砖倒在前面那一块的边缘
this one ends up one the edge of that one,
这一块也一样
this one ends up one the edge of that one.
只有当这个倒下的过程不出差错地到最后
It is only when the wave gets right to the end,
这最后一块砖才能稳稳地倒下
and the last brick can lie flat,
最后一块砖倒下后 它后面的那块砖也就能稳稳地落地
that the brick behind it can now also lie flat,
然后这个波浪就可以反过来
and the wave goes back in the other direction.
让我们从几何学角度来仔细探讨一下
Let’s take a closer look at the geometry of this situation.
每块砖都是21厘米长
The bricks are 21 centimeters long,
并且我已将砖块间隔距离精确到21厘米
and I have positioned them exactly 21 centimeters apart.
每块砖6厘米宽
They are six centimeters wide.
如果这些砖块都平放着
Now, if the bricks were lying flat,
那么它们就会有足够的空间来触碰地面
there would be plenty of room for them all to hit the ground.
但是它们并非平放在地面上
But they’re not!
每一块砖都会稍微立起来一点
Each one sticks back slightly.
如果我们想计算
If we want to calculate
这块砖头后面的砖头悬空于地面多少厘米
how much it’s overhanging the brick behind its position,
我们可以观察这个θ角
we could look at the angle theta
因为如果我们计算出这个角度
because if we complete this,
我们就能得到一个直角三角形
we have a right angled triangle.
假设砖块就像视频里这样摆放
Assuming that the bricks lay flush up here,
我们可以算出
now the cos of that angle is 6 divided by 21.
这个角度的余弦值就是6/21
We can work that out,
但是 实际上没那个必要
but, we actually don’t have to.
我们只需关注d的长度
We only care about this distance here, d.
而不需要计算出θ的值
We don’t need to work out theta
因为我们现在得到了一个新的直角三角形
because we’ve now got another right angle triangle,
θ也在这个三角形中
with Theta in it,
意味着我们可以运用相似三角形原理
which means we can just use the fact that they’re similar triangles,
d的长度就是6²÷21 即1.7厘米
that d is six squared divided by 21, which is 1.7 centimeters.
这种计算方式的问题在于
Now there is an argument that
相比于计算d的长度
instead of calculating that d distance,
我实际上应该计算接触点到地面的长度
I should actually be looking at the contact length,
我们可以用勾股定理计算出来
which we could do,
但是我还是认为无论你使用哪一块砖
but I just like the fact that for any bricks you use,
如果你想要计算d
if you want to calculate d,
答案永远是用其宽度的平方除以其长度
It’s always their width squared, divided by their length.
综上 我用砖头解释了什么是双重多米诺效应
So that is the double domino effect, with bricks, explained.
感谢观众们观看这个视频
Thank you for watching this video on my stand-up maths channel.
像往常一样 点击订阅 赞一赞什么的
The usual, subscribe, etc.
在Patreon网站上支持我的会员请注意
For people who support me on Patreon,
你们还会在网站里看到我制作的幕后视频
as well as the bonus footage of how I set this all up,
我也将把关于砖块倒下效应的4k视频
I’m also going to upload the full 4k video,
从Gopro上传到网站上
from the GoPro, of the effect falling over.
你将会在Patreon上发现关于这些的所有视频
you’ll find all of that on Patreon.
感谢大家的观看
For everyone else, thank you so much for watching.
[结束音乐]
[Music]

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视频概述

本视频中,达人用砖块生动地展示了什么是双重多米诺效应,其中运用到了几何学的知识,生动有趣,不妨来学学吧!

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视频来源

https://www.youtube.com/watch?v=EYkBctqyKic

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