# How can I fold paper into 3 x 4 grid? Or prove that it can't be done? [duplicate]

I am trying to fold paper so that it looks like 3 x 4 grid of 12 rectangles of equal size.

Its easy to get 4 rectangles. Just fold twice. But how to get 3?

## marked as duplicate by user63181, colormegone, Claude Leibovici, AlexR, MagdiragdagApr 5 '14 at 9:30

• The Pythagoras theorem may help $3^2+4^2=5^2$ is the relationship b/w sides of a right triangle. – DVD May 16 '13 at 6:55
• math.stackexchange.com/questions/736346/… This would help you divide it into 3 parts – Harshal Gajjar Apr 5 '14 at 7:43
• This question was asked before that question so that one is duplicate of this one :D lol – Pratik Deoghare Apr 5 '14 at 18:18
• This question is 11 months older – Henry Apr 7 '14 at 7:19

Let the paper be $[0,a]\times[0,b]$ By halving you find $(\frac a2,0)$, make a crease to find the line through $(\frac a2,0)$ and $(0,b)$. This intersects the diagonal at $(\frac a3,\frac b3)$.

If your piece of paper is a square ABCD of side length 1, then from the diagram, if AP=1/2, then QC=1/3.

(Stealing from Hagen von Eitzen's answer and Ross Millikan diagram at How can a piece of A4 paper be folded in exactly three equal parts?)

1. Fold the paper into four equal horizontal strips with two folds

2. Fold a diagonal across the top three horizontal strips

3. Fold vertical strips at the two points where the diagonal crosses the horizontal strips.

Fold the side in such a way that folded sides overlap each other then you will get three equal folds.For this you need to fold them at same rate. Thanks julian fernandez

• I apologize, by my comment (and original answer) was wrong! (same as yours!) – Wolphram jonny May 16 '13 at 6:28