所以又到了放假的季节了
So say it’s the holiday season and you
你理应感到惊喜和开心 但是
‘re supposed to be all festive and jolly but
你是更倾向于令人沮丧的那一类人
you’re more of the grinchy type.
现在你想做的就是用锋利的东西划破什么
And all you want to do is wield sharp objects against things.
所以你将会花假期的大部分时间用来做纸雪花
So you’re doingyour holiday partly by making paper snowflakes.
不管你怎么看待假期
Regardless of your feelings about the holidays,
把东西剪成小碎片也是一种艺术
slicing things into tiny bits is an art and one
一种你会认真对待的活动 比如
that you are takingvery seriously. Like,
很多人会做“纸雪花”
some people makeso-called paper snowflakes
通过对折一张纸
by folding a piece of paper in half,
再对折一次
and then in half
几次对折后剪下来
again and again andthen cutting it up.
但剪纸雪花高手明白真正的雪花是
But paper snowflake connoisseursknow that real snowflakes have
六次折叠对称后的样子而这样做出来的只有四次
six-fold symmetry and thisthing has four-fold symmetry.
自然界是不会有这样的雪花的
That would neverhappen in nature.
所以正确做法是把纸对折两次
So you do it the real way by folding your paper in half twice,
再三等分折叠它
and then folding it in thirds.
或者我猜你会这样做
Or I suppose you could do it
对折 再三等分
by halves, and then thirds,
然后再次对折
and then halves again.
但是你不能先三等分 对折 再对折
But you can’t do thirds, thenhalves, then halves again,
因为这意味着什么呢
because what wouldthat even mean?
你要知道第一次可以以任意角度对折
But you do notice your first halves can be at any angle you want.
你不需要对齐或怎样
You don’t need to lineit up or anything.
能折六角雪花是很有趣的
It’s kind of funny becauseto get six-fold symmetry,
你需要折出十二小份
you need to fold itinto 12 sections.
如果你只折了六个部分 那你只能得到三角雪花
And if you fold into six sections, you only get three-fold symmetry.
它的确是一种雪花偶尔会形成的形状
Which is actually a way thatsnowflakes occasionally form,
所以这样做是可以的
so those are allowed.
自然界里有时甚至有十二角的雪花
And then there are even sometimes 12 fold symmetric snowflakes in nature,
你可以反复折叠制作出那种雪花
which means you can fold again to make that.
但绝不可能存在四角的雪花
But never four-fold.
折纸的困难在于
The problem with folding paper is
它的厚度开始阻碍折叠
that the thickness starts to get in the way.
开始变得不平整然而也许更自然
This makes points uneven, whichmight actually be more natural.
大多数真正的雪花是块状和裂纹的
Most real snowflakesare actually pretty lumpy and
flawed, just those
不像人们制作或分享的图片那样
aren’t the ones peopletake and share pictures of.
那也不是你想制作的雪花
And that’s not the kind of snowflake you want to make either.
我的意思是当你把这个角三折
I mean, when you fold this angle into thirds,
褶叶就在这下面
this flap is under this one.
因此这里需要短一些
So it has to be a little shorter,
至少低于边缘
at least if this edge lines up here.
但是如果你一部分向前折叠
But maybe if you foldedone in front and one
而一部分向后折叠（手风琴折叠法）那么所有的横截面
in back accordion style,then all the sections
可能都是相同的
could be the same.
事实上 除了像这样半折
In fact, then instead offolding it in half like this
你可以向前向后折叠每一个横截面
you could do eachsection back and forth.
那样好多了
And that’s much better.
如果你觉得
Or maybe you get bored
做六角雪花有点无聊 打算做个五角雪花
of six-fold symmetry and decide to make a five-fold one. Well,
我们就需要五个角 那就是十个横面
if we need five lines ofsymmetry, that’s 10 sections.
首先是对折
So first you fold it
接下来需要折成五等分
in half and then you need to fold this into fifths.
你可以使用量角器 或用眼睛打量调整
You can use a protractor or just kind of eyeball it and adjust. There,
这样就完成了五角雪花
five-fold snowflake.
事实上 如果你擅长折叠最初的五角
In fact, if youget good at folding this initial
five-fold wedge, you
你可以垂直剪切快速得到一个五角星
can do a single straight cut on it to get a star super quickly.
或者剪开得到更多星星
Or you can slice it and get lots of stars,
或者剪一些有趣的雪花形状
or cut fancy stuff in there for fancy snowflakes.
星星算是节日精神 对吧
Stars count asholiday spirit, right?
你可以用一种类似的方法得到七角雪花
And you can do seven-foldsymmetry in a similar way
但是必需要用到量角器
but you’re probably going toneed your emergency protractor.
不过没有量角器的情况下也能做出九角雪花
But you could do nine-fold without a protractor
因为你可以折叠三次 再折叠三次
because you can do thirds, and then thirds again.
如果你可以不借助量角器折出五等分
And if you can do fifthswithout a protractor,
你也折出十等分 五次折叠后就行了
you can do tenths too, because it’s a fifth times a half. Look,
我说快乐的假期 到底哪个节日更快乐呢
I said happy holidaysbut I never said which one.
情人节就是冬天的节日
Valentine’s Day istotally a winter holiday.
不过11角最好 因此现在再一次测量
11 is prime, though, so timefor the protractor again. Look,
看 最好的因数
prime factorization.
好
OK.
理论上来说 你就可以折任何边数的纸雪花
So now theoretically you can getall sorts of end-fold symmetry,
但能折出旋转对称形状吗？
but what aboutrotational symmetry?
没有对称线 意味没有对折
There’s no mirror lines, which means no folding,
所以它可行吗？
so does it even make sense as a question?
设计剪裁剪一朵雪花
Cutting a snowflakedesign efficiently
取决于每个上面都要有
is all about putting the same cut lines
相同的切割线
on top of each other
因此你只能剪一次
so you only haveto cut them once.
所以你怎样设计出这种对称旋转
So how do you take arotationally symmetric design
像这样 把所有层
like this and put all the layers
依次摞起来
on top of each other
又没有任何重叠？
without overlappinganything else?
也许并不神奇 去把材料
Maybe it’s not surprisingto see that to get stuff
对称转动对齐 旋转它
with rotational symmetryto line up, you rotate it.
如果你裁剪中心
If you make a cut to
你可以任意旋转它
the center then you can rotate all the way
且卷成对称的一个独特的东西
and roll the symmetry upinto one unique thing.
用手来达到精确的对称转动是很难的
It’s hard to draw accuraterotational symmetry by hand.
但现在你能使这些画坏的漩涡设计对称
But now I can symmetrize thisbadly-drawn swirl design.
所以先剪张漩涡纸片
So to cut out a paper swirl flake,
现在开始剪
start with a cut,
然后将纸卷成圆锥
then curl yourpaper into a cone.
你可以任意旋转一次两次甚至更多
You can swirl aroundonce or twice or more.
但是确保沿着它本身的线剪是很重要的
But the important thing is to make sure the cut lines up with itself,
因为从对称来看
because as far as symmetry
切口是不存在的
is concerned, thatcut doesn’t exist.
我喜欢把它固定 让它不滚动
I like to tape it in place so it doesn’t unroll,
再开始剪
then cut stuff
材料
out.
我发现会转的东西很好用
I find that spiralythings work well.
开始裁剪的好方法是叠纸
Folding the paper is a good way to start a cut,
但是记得叠得对称
but remember that folding creates symmetry.
所以我常用剪刀操作
So I like to use it just to get the scissors
然后做对称物
in there and then do something asymmetric. Voila,
瞧雪花
snowflake.
对于星星纸片螺旋纸片 你需要卷五次纸
For a starflake swirlflake you’ll have to curl your paper around five times,
或四次
or four times.
有趣的是我以为只要做一次
It’s funny because I thinkof this as going around
但是实际上要这样重复两次
once but really it’s going around twice,
但是平整的纸只有一张 无论怎样
and a flat sheet of paper goes around once. Anyway,
就那样做
yeah, do that.
给它一两个旋转的臂
And then give it a nicespiraly arm or two.
你可以做出很棒的星星螺旋雪花
You can make a nice fancystarflake swirlflake snowflake, awesome flake.
当然 这只是叠冻结雪花的一个小步骤
Of course, from snowflakes it’sonly one small step to folding
还有墙纸模式
and cutting freeze patterns,and then wallpaper patterns and, hey,
如果你把材料剪成条
what kind ofpatterns do you
你又可以做出什么形式？
get if you start by foldingstuff into a [INAUDIBLE] strip?
也许你想
And then maybe you’ll want to start folding
剪球形物体时一切都会会一团糟
and cutting spheres and everything will be a mess,
所以最好现在打消主意
so you’d better just stop now.