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As you progress through levels, your job will become more difficult, as you may need to split a shape into more than just two equal pieces, and the shapes themselves become more intricate, moving ...
The problem has two parts: what aspect ratios are possible, and how many different solutions are there for a given n. [7] Frieling and Rinne had previously published a result in 1994 that states that the aspect ratio of rectangles in these dissections must be an algebraic number and that each of its conjugates must have a positive real part. [ 3 ]
In triangle geometry, the Bernoulli quadrisection problem asks how to divide a given triangle into four equal-area pieces by two perpendicular lines. Its solution by Jacob Bernoulli was published in 1687.
Square trisection, a problem of cutting and reassembling one square into three squares; Squircle, a shape intermediate between a square and a circle; Tarski's circle-squaring problem, dividing a disk into sets that can be rearranged into a square; Van Aubel's theorem and Thébault's theorem, on squares placed on the sides of a quadrilateral
The twelve pentominoes. After an introductory chapter that enumerates the polyominoes up to the hexominoes (made from six squares), the next two chapters of the book concern the pentominoes (made from five squares), the rectangular shapes that can be formed from them, and the subsets of an chessboard into which the twelve pentominoes can be packed.
For any two simple polygons of equal area, the Bolyai–Gerwien theorem asserts that the first can be cut into polygonal pieces which can be reassembled to form the second polygon. The lengths of the sides of a polygon do not in general determine its area. [9] However, if the polygon is simple and cyclic then the sides do determine the area. [10]