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Any two rectilinear figures with equal area can be dissected into a finite number of pieces to form each other. This is the Wallace-Bolyai-Gerwien theorem. For minimal ...

Hoggatt and Denman (1961) showed that any obtuse triangle can be divided into eight acute isosceles triangles. There are 1, 4, 23, 180, 1806, 20198, ... (OEIS A056814) ...

The above two figures are rearrangements of each other, with the corresponding triangles and polyominoes having the same areas. Nevertheless, the bottom figure has an area ...

Gardner showed how to dissect a square into eight and nine acute scalene triangles. W. Gosper discovered a dissection of a unit square into 10 acute isosceles triangles, ...

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same. The sides ...

The simplest dissection of a square into rectangles of the same areas but different shapes, composed of the seven pieces illustrated above. The square is 210 units on a side, ...

A dissection fallacy is an apparent paradox arising when two plane figures with different areas seem to be composed by the same finite set of parts. In order to produce this ...

A nowhere-neat dissection is a dissection of an area into polygons such that no two polygons have a side in common. A nowhere-neat dissection in which squares of the same ...

A cylinder can be dissected into unequal squares, with nine squares required at a minimum. Trivial squarings can be constructed by taking rectangle dissections and matching ...

A nowhere-neat dissection in which squares of the same size are not allowed to share any part of a side.