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# Zoft Pc

## Fold and Cut Theorem – Numberphile

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100 thoughts on “Fold and Cut Theorem – Numberphile”

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Origami Art for kids Hub

it's possible to do it with only two folds and one cut

Does this theorem also hold in higher dimensions? Like, is it possible to turn a cube into any abritrary shape by folding it in the 4th dimension?

Do chinese characters!

Maybe being an American there's something I'm missing. So cutting things like letters and turtles out of paper with one cut is certainly impressive. But this idea that an adult had no idea how to cut a square out of piece of paper is unfathomable. An American kindergartner could demonstrate this.

Do they not make paper snowflakes where your from?

No comments..?

cutting is easier then folding though

could u try and line up the different bits of paper correctly and cut out the whole alphabet with literally one cut

Make a turtle.

This is the best thing I've watched today!

this makes me want to think about cuts in 4 dimensions…. why

So does that mean if you were willing to do all the folding that you could do one cut and get every letter in the alphabet from that one cut?

You need to make up for the less number of cuts with more number of folds so essentially the "work done" is same.

For example, in a square, no. of folds + no. of cuts = 4 always.

now someone needs to get the letters better so that they are more curved like pixels. no curved lines but just make it like 8 bit letters

ish

Fold along the diagonal duh

can you make 1 cut circle ?

question, can you do curves if you're allowed infinite folds?

When I was around 7 or 8 my dad had some missionaries over for dinner. After dinner they found out I was into origami so they decided to show us a trick (that of course turned into a religious lesson) and his first question to me was: "Can you fold a piece of paper, so if you make only one cut and unfold it, it'll unfold into a cross?"

So I thought about it for a few seconds, and said "I think so" and proceeded to fold a piece of paper in half twice, and then on the diagonal (like in the video) and snip it in half. Unfolding it it was a cross and the missionary says "Wow, I've never had someone actually do it before."

Am I the only one who wants that as a font?…

That unsolved rubicks cube in the top right is messing with my ocd

It would be possible to do a square with only two folds, if the first is along the diagonal.

"S is the hardest letter."

S: my time to shine

S is the best looking letterreally cool 🙂

Can you do one now with the square version of the Sinhalese alphabet please? (JK, well done!)

Erik Demaine… That's the same guy (i.e., one of the co-authors) who showed that Nintendo games are NP-hard!

the only problem is that the original paper has a ton of folds

If you can cut out any two dimtional shape with one cut by folding in 3 demension can you cut out 3 denensional shape with one cut by folding in the 4th deminsion and so on?

i cqll shenanigans on your G and J the rest are impressive.

Where can we find the pdf for all the letters of the alphabet?

Francis Hopkinson (1737 – 1791) designed the first official American flag. He was an author, a composer, and one of the signers of the Declaration of Independence as a delegate from New Jersey.

As I Dane, I say that you are missing the last three letters of the alphabet: Æ, Ø and Å

statistical sudoku – gerechte designs

Now you have to make a font out of those shaped letters

So in theory you could draw anything like that with one line

ONE CUUUUUUUUT!

The next step: optimising the number of folds

can you cut the alphabet in 1 cut?

Hey! Those letters need to be rendered as a True Type font!

So we can basically create any polygon with a single straight cut. Now can we build any shape with a single curvy cut 🤔

k now do one for a fractal

k now do one for a fractal

How on earth did you memorize all the folds for the entire alphabet. Genius!!!

this is certainly cutting edge math

Someone should turn those letters into a font

Is there a one-cut theorem that deals with curved shapes, and permits cutting an arc?

Katie should scan her letters into a font! 🙂

You basically just defined topology?

Can't you create any sort of piecewise continuous shape, given the condition that you don't have to cut a straight line, and so long as all the piecewise functions are similar? Seems a pretty trivial extension of the theorem that might allow G, S, O, and maybe Q to look nicer.

it was stated that you can "one-cut" anything with straight lines. but how about a really big circle? i mean a really big collection of straight lines that it is a circle? im sorry i cant express this well in english.

I've worked out for myself how to cut out all 26 letters of the alphabet in one cut! It was really fun (and really frustrating, especially for R and S)

Compass

This is cool

AHS

why does zed bother me, its z, how do u get a d in there ?

Fantastic maths – well done! 🙂

That's really impressive!

Now do Å, Ä and Ö.

Jah just kidding, but that's mighty interesting that a field like that exists in math! ^^

Katie, you can actually improve the one cut square even further, you can do a single cut with only two folds. If you fold it in half diagonally, you get a triangle, and then you fold it in half, and cut on the line, unfold, and you have a square!

Ya it is pretty cool but to make it more intuitive use jordan curve theorem you have 2 regions an inner and outer region. So when lining up the lines your essentially separating the regions into to distinct pieces when you cut.

That look on J

One cut forever… Yes! 🙂 So cool

Does that mean if you could fold 3 dimentional objects through the 4th dimension, you could carve them into any shape with a single slice

This was so cool! Thanks.

can you cut KVSC PUNE together

You can fold the square twice, rather than thrice. Fold it diagonally, then again.

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Speaking of typography–make a font out of the cutouts !

I managed to cut out a star with a star shaped hole in the middle in one cut

Umm… Can't you just fold it along the diagonal twice, then cut once? That would be mathematically more efficient, correct?

Isn’t a curvy shape just a polygon whose number of sides approach infinity?

When One Punch Man picks up a sword… ONE CUUUUUUUUUUUUUT!

You can also do the quare with only 2 folds

So.. could you theoretically fold the paper an infinite number of times, make one cut, and get the dragon curve?

Legend

S was an epiphany. Cooool.

wtf? for a square just fold the thing diagonally twice and then make one cut… why would you claim that 3 folds and one cut is the optimum?

There are way too many smarty mcsmartertons in these numberphile comment sections.

More efficient? That is if you assume that making one cut is easier than making one fold. I don't see how making three folds and one cut is more efficient than making one fold a three cuts. It is still four actions in all.

secrets of 83

"..ish" … stop.

The accurate part about Betsy Ross is that whatever seamstress(es) made those flags probably did use this easy trick to make a reliable symmetrical star, because it was a common thing known among such folk. No secret, no mystery, no advantage over seamstress competition in the next town — just an age-old reliable way to do the thing.

It's terrible for mass production, though, and not likely used when flags were mass-produced. It would waste wayyyy too much cloth!

The alphabet has never looked so cute! I love these letters!

Now do Ä, Ö, Ü

they showed this at class and i said ‘when i get home imma subscribe’ one more subscriber!

0:34 Parker Square

For absolute nightmare level, try the danish letter Æ

You can cut a square with a single cut with only 2 folds. It will be rotated by 45 degrees, but still a square.

It is intuitively obvious that you can't optimize down to zero cuts but I'd love to see a rigorous proof.

I cant what to try it

but you will never manage to cut a circle or an ark of it

YOCO – You Only Cut Once

That's not a Q, that's a Greek Qoppa :).

you did not even help me and you did the others

That G doesn't count. You gotta take that one back to the drawing board.

10th like

7:53

ONE CUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUT!Can we get a typeface using those paper letters?

3:17 And you can tell you've done it right 'cause that's the same size as that………..ish

Your square in three folds is not efficient. It take only two folds. Fold across the diagonals.

Parker G.

Is it really more efficient when you have to fold the paper first ?

Katie is utterly bonkers – and I like that!