Surely this isn't new...

I can’t be the first person to notice that one can fold the four corners of a rectangle like so to make a rectangle half the area; but I couldn’t find any examples anywhere. Can anyone point me to “prior art” on this? (Other than the special case of a square).

I’ll honestly say I’ve never seen this result stated before. I would imagine that other people have figured it out, but I don’t think it’s all that earth-shattering.

What’s perhaps more useful to most people is that such kind of folding is more efficient when using aluminum foil to wrap up food compared to folding large portions of the foil over itself when the folding is along a horizontal or vertical axis as opposed to a diagonal one.

On a similar note, in Geometry class I derived the area of an isosceles triangle from the length of the common side and the different side using Hero(n)'s theorem, and I even later used that formula to make solving a problem on an exam easier, but apparently the writers of my Geometry book didn’t think it was all that useful of a corollary to mention.

Sorry, I’m not coming to any of your picnics; just too much pressure. :wink:

You want a folding exercise? Despite instructions from Unca Cecil himself, I still can’t fold a 5-point star from a piece of paper.

No it’s not…
… and don’t call me Shirley.

(never mind)

I watched a YouTube video about exactly this, not very long ago - I thought it was on NumberPhile -but damned if I can find it.

It shares some similarities with a rather nice visual ‘proof’ a maths teacher once taught me that the angles of a triangle must add to 180 degrees (take any triangular piece of paper, fold the fattest corner to its opposite line, fold the two sides in - the three angles line up in a row)

But, yeah, I’ve used this before when trying to eke out a piece of nearly-big-enough wrapping paper to cover a present. And very useful it is too

One thing that strikes me about this is how it amplifies even the smallest difference in the original long and short sides. Most pieces of paper towel for instance are just barely not-square, but folding like this makes it obvious.