132
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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 ...
- 75.7k
107
votes
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66
votes
43
votes
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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 ...
- 50.8k
37
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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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34
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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 ...
- 26.3k
32
votes
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31
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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! ...
- 22.8k
28
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Tiling a rectangle with nine squares
The dimensions are
and the tiling looks like this:
Working out the dimensions of the rectangle is quite easy. We know its total area is $4209$ (i.e., $2^2 + 5^2 + 7^2 + 9^2 + 16^2 + 25^2 + 28^2 + 33^...
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Maximum Pieces of Cake in Four Cuts
If all cuts are straight cuts and the cake is a rectangular prism or cylinder, it's not possible. From Wikipedia's page on the Cake Number:
In mathematics, the cake number, denoted by Cn, is the ...
- 17.4k
26
votes
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25
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Squaring a cross
Solutions are as in the following diagram:
Addition: My original solution for E has 5 cuts and 9 separate pieces - a simpler solution is shown below, with only four cuts (to the cross) and five ...
- 13.6k
23
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Dissecting the holey octomino into a square
Well, from my viewpoint this is a four-piece dissection, since parts of each piece don't move relatively to each other. They are even connected, to some extent. However, I would completely agree that ...
- 6,802
22
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Four fanatics and one checkerboard
I'm not sure why you'd need ANY sort of dissection for this.
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votes
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Can I Haz My Eye Center'd?
One (non-straight) cut:
(Or a different image by Carl Löndahl: https://nup.pw/YK9cjY.png)
21
votes
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Cutting a cross made of 5 equal squares by 2 straight cut into 4 figure to together form a square
Here is a good way of seeing how this dissection comes about.
- 50.8k
21
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Cut this shape into 3 pieces and fit them together to form a square
Here is a solution that works in the general case of two squares of any size placed next to each other.
- 50.8k
20
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20
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Near-fill with 3x1 long triominos, how to do a different void square than the center square?
The trick to this puzzle is to:
(And here are those tilings: the center was already given, and the rest are obtainable from these by rotation.)
- 145k
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Restore the square
Apologies for the crude drawing but I think you need to do something like this
Some deduction that went into this answer
- 133k
20
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Cut this shape into 3 pieces and fit them together to form a square
A slightly different graphic:
- 56.4k
19
votes
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Cutting a square into seven rectangles
From the deleted answer from frodoswalker we know the possible ranges of the squares:
Our maximum area is $1*2+3*4+5*6+7*8+9*10+11*12+13*14=504$, which means the maximum square width is $\lfloor \...
- 18k
19
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19
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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.
- 2,023
18
votes
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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 ...
- 33.6k
18
votes
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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:
- 50.8k
18
votes
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17
votes
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The Challenge Square
You can do it like this:
The cut starts right in the center of those sides.
- 11.2k
17
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Dividing a square field into 5 equal regions
Edit/Note: I gave this answer assuming fractional fences where not allowed.
As such I did not carefully think about the second picture.
Obviously that answer is not optimal if fractional fence ...
- 8,000
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