# Questions tagged [dissection]

Problems that involve partitioning a geometric figure into smaller pieces with certain conditions on them (equal area, equal shape, possible to be rearranged into another given figure, etc.)

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### What is the fewest number of squares required to cover a 11×13 rectangle? [closed]

I can't understand this. I found a solution with 6 squares, but I don't know if it is right and how to explain it.
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### Is there a known method to dissect Jessen's icosahedron and rearrange to form a cube?

It can be shown that Jessen's icosahedron is scissors-congruent to a cube, meaning that it can be sliced into smaller polyhedral pieces that can be rearranged to form a solid cube. What is the ...
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### Prismatoid plane section with straightedge and compass

I came up with a task I'm out of ideas how to do a solution. Perhaps I'm not paying attention to an obvious thing, but still. All I came up with is to build orthogonal projections but that's not a ...
152 views

### A regular tetrahedron can be dissected into $1,2,3,4,6,8,12,$ or $24$ congruent pieces. Is this it?

By placing a tetrahedron on a face and making vertical cuts centered at the "top" vertex, it is easy to dissect the tetrahedron into $1, 2, 3,$ or $6$ congruent pieces. By cutting the ...
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### Two dissection problems for rectangles

Let us consider two integer rectangles (that is, with sides of integer length) $S$ and $T$ of the same area. Then, obviously, $S$ can be dissected into several integer rectangles $A_1$, ..., $A_n$ (we ...
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### Haberdasher problem of Henry Dudeney - is 4-piece hinged dissection of equilateral triangle into square possible?

Is it possible to divide the equilateral triangle into 4 pieces to build a square with those four pieces, provided that one or two pieces are flipped over to the other side? If possible, I wish to ...
76 views

### Dividing a disk of diameter 1 into pieces of smaller diameter

Let $F$ be an arbitrary bounded set on the plane, $n \in \mathbb{N}$. Let's define $d_n(F)$ as the minimum diameter one can ensure when cutting a set $F$ into $n$ pieces. So, here is a discussion of ...
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### Transforming a 8x8, 4x4 and 1x1 square into a 9x9 square

Good day to all of you! I have a puzzle which I just cannot solve. I attached a photo of it. The task is to transform the shape on the left into a 9x9 square (on the right) using ONLY 2 "cuts" - ...