# Tag Info

Accepted

### Prove that π > 3

I didn't have a knife with me, so I only used my unit circle cookie cutter to split each square like this: I then rearranged the parts into this shape: Since the angle covered by this shape is ...
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### Can you fold a square into a square of one-fifth the area?

The way to do this is:

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### Dissecting the exotic bulbfish

Cut along the red lines and move the pieces as indicated by the yellow arrows. As is usual with this kind of dissection, it helps if you look at the area to work out the length of the side of the ...
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### Pythagorean quilts

The optimal solution is which is achievable (for example) like this: For another (or perhaps, the other) way to achieve the minimal number of pieces, you can check out OP's self-answer below. Here'...
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### Careless smokers

Yes, it's possible, because one can fit 5 disjoint 1x1 squares in a 2.75x2.75 square: four in the corners, and one in the center rotated 45 degrees. The four cigaret holes can't eliminate all 5 ...
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### Mutilated chessboard

I believe this works as a short proof.
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### Cutting a 10-by-2 rectangle

Index your rectangle from (0,0) to (10,2). Then cut from These four pieces can be used to make the square. Note that this dissection works without any flipping or even any rotation of the pieces! ...
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### Obtain four equal parts with a single cut

Okay, I don't know how people here create images that fast, but I get a more sheet-like solution.
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### The Erasmus pentagon

Let $A=(-30,60),B=(0,0),C=(150,0),D=(300,300),E=(225,400)$. $F=(-12,84)$ is on $AE$ and $G=(175,50)$ is on $CD$. Then $ABCDE$ is similar to $FABCG$, by a factor of $\sqrt5$. The key point of this ...
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### Piece of Cake for King Solomon

To divide the cake into n equal pieces, Proof: Here is a drawing to illustrate how it works:
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The claim is